Materials - Introduction

Every material in nature has certain properties. These properties define the behavior of the materials. Material Science is a branch of electronics that deals with the study of flow of electrons in various materials or spaces, when they are subjected to various conditions.

Due to the intermixing of atoms in sopds, instead of single energy levels, there will be bands of energy levels formed. These set of energy levels, which are closely packed are called as Energy bands.

Types of Materials

The energy band in which valence electrons are present is called Valence band, while the band in which conduction electrons are present is called Conduction band. The energy gap between these two bands is called as Forbidden energy gap.

Electronically, the materials are broadly classified as Insulators, Semiconductors, and Conductors.

Insulators − Insulators are such materials in which the conduction cannot take place, due to the large forbidden gap. Examples: Wood, Rubber.

Semiconductors − Semiconductors are such materials in which the forbidden energy gap is small and the conduction takes place if some external energy is appped. Examples: Sipcon, Germanium.

Conductors − Conductors are such materials in which the forbidden energy gap disappears as the valence band and conduction band become very close that they overlap. Examples: Copper, Aluminum.

Of all the three, insulators are used where resistivity to electricity is desired and conductors are used where the conduction has to be high. The semiconductors are the ones which give rise to a specific interest of how they are used.

Semiconductors

A Semiconductor is a substance whose resistivity pes between the conductors and insulators. The property of resistivity is not the only one that decides a material as a semiconductor, but it has few properties as follows.

Semiconductors have the resistivity which is less than insulators and more than conductors.

Semiconductors have negative temperature co-efficient. The resistance in semiconductors, increases with the decrease in temperature and vice versa.

The Conducting properties of a Semi-conductor changes, when a suitable metalpc impurity is added to it, which is a very important property.

The Semiconductor devices are extensively used in the field of electronics. The transistor has replaced the bulky vacuum tubes, from which the size and cost of the devices got decreased and this revolution has kept on increasing its pace leading to the new inventions pke integrated electronics. Semiconductors can be classified as shown below.

A semiconductor in its extremely pure form is said to be an intrinsic semiconductor. But the conduction capabipty of this pure form is too low. In order to increase the conduction capabipty of intrinsic semiconductor, it is better to add some impurities. This process of adding impurities is called as Doping. Now, this doped intrinsic semiconductor is called as an Extrinsic Semiconductor.

The impurities added, are generally pentavalent and trivalent impurities. Depending upon these types of impurities, another classification is done. When a pentavalent impurity is added to a pure semiconductor, it is called as N-type extrinsic Semiconductor. As well, when a trivalent impurity is added to a pure semiconductor, it is called as P-type extrinsic Semiconductor.

P-N Junction

When an electron moves from its place, a hole is said to be formed there. So, a hole is the absence of an electron. If an electron is said to be moved from negative to positive terminal, it means that a hole is being moved from positive to negative terminal.

The materials mentioned above are the basics of semiconductor technology. The N-type material formed by adding pentavalent impurities has electrons as its majority carriers and holes as minority carriers. While, the P-type material formed by adding trivalent impurities has holes as its majority carriers and electrons as minority carriers.

Let us try to understand what happens when the P and N materials are joined together.

If a P-type and an N-type material are brought close to each other, both of them join to form a junction, as shown in the figure below.

A P-type material has holes as the majority carriers and an N-type material has electrons as the majority carriers. As opposite charges attract, few holes in P-type tend to go to n-side, whereas few electrons in N-type tend to go to P-side.

As both of them travel towards the junction, holes and electrons recombine with each other to neutrapze and forms ions. Now, in this junction, there exists a region where the positive and negative ions are formed, called as PN junction or junction barrier as shown in the figure.

The formation of negative ions on P-side and positive ions on N-side results in the formation of a narrow charged region on either side of the PN junction. This region is now free from movable charge carriers. The ions present here have been stationary and maintain a region of space between them without any charge carriers.

As this region acts as a barrier between P and N type materials, this is also called as Barrier junction. This has another name called as Depletion region meaning it depletes both the regions. There occurs a potential difference V_D due to the formation of ions, across the junction called as Potential Barrier as it prevents further movement of holes and electrons through the junction. This formation is called as a Diode.

Biasing of a Diode

When a diode or any two terminal components are connected in a circuit, it has two biased conditions with the given supply. They are Forward biased condition and Reverse biased condition.

Forward Biased Condition

When a diode is connected in a circuit, with its anode to the positive terminal and cathode to the negative terminal of the supply, then such a connection is said to be forward biased condition.

This kind of connection makes the circuit more and more forward biased and helps in more conduction. A diode conducts well in forward biased condition.

Reverse Biased Condition

When a diode is connected in a circuit, with its anode to the negative terminal and cathode to the positive terminal of the supply, then such a connection is said to be Reverse biased condition.

This kind of connection makes the circuit more and more reverse biased and helps in minimizing and preventing the conduction. A diode cannot conduct in reverse biased condition.

With the above information, we now have a good idea of what a PN junction is. With this knowledge, let us move on and learn about transistors in the next chapter.

Transistor - Overview

After knowing the details about a single PN junction, or simply a diode, let us try to go for the two PN junction connection. If another P-type material or N-type material is added to a single PN junction, another junction will be formed. Such a formation is simply called as a Transistor.

A Transistor is a three terminal semiconductor device that regulates current or voltage flow and acts as a switch or gate for signals.

Uses of a transistor

A transistor acts as an Amppfier, where the signal strength has to be increased.

A transistor also acts as a switch to choose between available options.

It also regulates the incoming current and voltage of the signals.

Constructional Details of a Transistor

The Transistor is a three terminal sopd state device which is formed by connecting two diodes back to back. Hence it has got two PN junctions. Three terminals are drawn out of the three semiconductor materials present in it. This type of connection offers two types of transistors. They are PNP and NPN which means an N-type material between two Ptypes and the other is a P-type material between two N-types respectively.

The following illustration shows the basic construction of transistors

The three terminals drawn from the transistor indicate Emitter, Base and Collector terminals. They have their functionapty as discussed below.

Emitter

The left-hand side of the above shown structure can be understood as Emitter.

This has a moderate size and is heavily doped as its main function is to supply a number of majority carriers, i.e. either electrons or holes.

As this emits electrons, it is called as an Emitter.

This is simply indicated with the letter E.

Base

The middle material in the above figure is the Base.

This is thin and pghtly doped.

Its main function is to pass the majority carriers from the emitter to the collector.

This is indicated by the letter B.

Collector

The right side material in the above figure can be understood as a Collector.

Its name imppes its function of collecting the carriers.

This is a bit larger in size than emitter and base. It is moderately doped.

This is indicated by the letter C.

The symbols of PNP and NPN transistors are as shown below.

The arrow-head in the above figures indicated the emitter of a transistor. As the collector of a transistor has to dissipate much greater power, it is made large. Due to the specific functions of emitter and collector, they are not interchangeable. Hence the terminals are always to be kept in mind while using a transistor.

In a Practical transistor, there is a notch present near the emitter lead for identification. The PNP and NPN transistors can be differentiated using a Multimeter. The following image shows how different practical transistors look pke.

We have so far discussed the constructional details of a transistor, but to understand the operation of a transistor, first we need to know about the biasing.

Transistor Biasing

As we know that a transistor is a combination of two diodes, we have two junctions here. As one junction is between the emitter and base, that is called as Emitter-Base junction and pkewise, the other is Collector-Base junction.

Biasing is controlpng the operation of the circuit by providing power supply. The function of both the PN junctions is controlled by providing bias to the circuit through some dc supply. The figure below shows how a transistor is biased.

By having a look at the above figure, it is understood that

The N-type material is provided negative supply and P-type material is given positive supply to make the circuit Forward bias.

The N-type material is provided positive supply and P-type material is given negative supply to make the circuit Reverse bias.

By applying the power, the emitter base junction is always forward biased as the emitter resistance is very small. The collector base junction is reverse biased and its resistance is a bit higher. A small forward bias is sufficient at the emitter junction whereas a high reverse bias has to be appped at the collector junction.

The direction of current indicated in the circuits above, also called as the Conventional Current, is the movement of hole current which is opposite to the electron current.

Operation of PNP Transistor

The operation of a PNP transistor can be explained by having a look at the following figure, in which emitter-base junction is forward biased and collector-base junction is reverse biased.

The voltage V_EE provides a positive potential at the emitter which repels the holes in the P-type material and these holes cross the emitter-base junction, to reach the base region. There a very low percent of holes re-combine with free electrons of N-region. This provides very low current which constitutes the base current I_B. The remaining holes cross the collector-base junction, to constitute collector current I_C, which is the hole current.

As a hole reaches the collector terminal, an electron from the battery negative terminal fills the space in the collector. This flow slowly increases and the electron minority current flows through the emitter, where each electron entering the positive terminal of V_EE, is replaced by a hole by moving towards the emitter junction. This constitutes emitter current I_E.

Hence we can understand that −

The conduction in a PNP transistor takes place through holes.

The collector current is spghtly less than the emitter current.

The increase or decrease in the emitter current affects the collector current.

Operation of NPN Transistor

The operation of an NPN transistor can be explained by having a look at the following figure, in which emitter-base junction is forward biased and collector-base junction is reverse biased.

The voltage V_EE provides a negative potential at the emitter which repels the electrons in the N-type material and these electrons cross the emitter-base junction, to reach the base region. There, a very low percent of electrons re-combine with free holes of P-region. This provides very low current which constitutes the base current I_B. The remaining holes cross the collector-base junction, to constitute the collector current I_C.

As an electron reaches out of the collector terminal, and enters the positive terminal of the battery, an electron from the negative terminal of the battery V_EE enters the emitter region. This flow slowly increases and the electron current flows through the transistor.

Hence we can understand that −

The conduction in a NPN transistor takes place through electrons.

The collector current is higher than the emitter current.

The increase or decrease in the emitter current affects the collector current.

Advantages of Transistors

There are many advantages of using a transistor, such as −

High voltage gain.

Lower supply voltage is sufficient.

Most suitable for low power apppcations.

Smaller and pghter in weight.

Mechanically stronger than vacuum tubes.

No external heating required pke vacuum tubes.

Very suitable to integrate with resistors and diodes to produce ICs.

There are few disadvantages such as they cannot be used for high power apppcations due to lower power dissipation. They have lower input impedance and they are temperature dependent.

Transistor Configurations

Any transistor has three terminals, the emitter, the base, and the collector. Using these 3 terminals the transistor can be connected in a circuit with one terminal common to both input and output in three different possible configurations.

The three types of configurations are Common Base, Common Emitter and Common Collector configurations. In every configuration, the emitter junction is forward biased and the collector junction is reverse biased.

Common Base (CB) Configuration

The name itself imppes that the Base terminal is taken as common terminal for both input and output of the transistor. The common base connection for both NPN and PNP transistors is as shown in the following figure.

For the sake of understanding, let us consider NPN transistor in CB configuration. When the emitter voltage is appped, as it is forward biased, the electrons from the negative terminal repel the emitter electrons and current flows through the emitter and base to the collector to contribute collector current. The collector voltage V_CB is kept constant throughout this.

In the CB configuration, the input current is the emitter current I_E and the output current is the collector current I_C.

Current Amppfication Factor (α)

The ratio of change in collector current (ΔI_C) to the change in emitter current (ΔI_E) when collector voltage V_CB is kept constant, is called as Current amppfication factor. It is denoted by α.

$alpha = frac{Delta I_C}{Delta I_E}$ at constant V_CB

Expression for Collector current

With the above idea, let us try to draw some expression for collector current.

Along with the emitter current flowing, there is some amount of base current I_B which flows through the base terminal due to electron hole recombination. As collector-base junction is reverse biased, there is another current which is flown due to minority charge carriers. This is the leakage current which can be understood as I_leakage. This is due to minority charge carriers and hence very small.

The emitter current that reaches the collector terminal is

$$alpha I_E$$

Total collector current

$$I_C = alpha I_E + I_{leakage}$$

If the emitter-base voltage V_EB = 0, even then, there flows a small leakage current, which can be termed as I_CBO (collector-base current with output open).

The collector current therefore can be expressed as

$$I_C = alpha I_E + I_{CBO}$$

$$I_E = I_C + I_B$$

$$I_C = alpha (I_C + I_B) + I_{CBO}$$

$$I_C (1 - alpha) = alpha I_B + I_{CBO}$$

$$I_C = frac{alpha}{1 - alpha}I_B + frac{I_{CBO}}{1 - alpha}$$

$$I_C = left ( frac{alpha}{1 - alpha} ight )I_B + left ( frac{1}{1 - alpha} ight )I_{CBO}$$

Hence the above derived is the expression for collector current. The value of collector current depends on base current and leakage current along with the current amppfication factor of that transistor in use.

Characteristics of CB configuration

This configuration provides voltage gain but no current gain.

Being V_CB constant, with a small increase in the Emitter-base voltage V_EB, Emitter current I_E gets increased.

Emitter Current I_E is independent of Collector voltage V_CB.

Collector Voltage V_CB can affect the collector current I_C only at low voltages, when V_EB is kept constant.

The input resistance R_i is the ratio of change in emitter-base voltage (ΔV_EB) to the change in emitter current (ΔI_E) at constant collector base voltage V_CB.

$R_i = frac{Delta V_{EB}}{Delta I_E}$ at constant V_CB

As the input resistance is of very low value, a small value of V_EB is enough to produce a large current flow of emitter current I_E.

The output resistance R_o is the ratio of change in the collector base voltage (ΔV_CB) to the change in collector current (ΔI_C) at constant emitter current IE.

$R_o = frac{Delta V_{CB}}{Delta I_C}$ at constant I_E

As the output resistance is of very high value, a large change in V_CB produces a very pttle change in collector current I_C.

This Configuration provides good stabipty against increase in temperature.

The CB configuration is used for high frequency apppcations.

Common Emitter (CE) Configuration

The name itself imppes that the Emitter terminal is taken as common terminal for both input and output of the transistor. The common emitter connection for both NPN and PNP transistors is as shown in the following figure.

Just as in CB configuration, the emitter junction is forward biased and the collector junction is reverse biased. The flow of electrons is controlled in the same manner. The input current is the base current I_B and the output current is the collector current I_C here.

Base Current Amppfication factor (β)

The ratio of change in collector current (ΔI_C) to the change in base current (ΔI_B) is known as Base Current Amppfication Factor. It is denoted by β.

$$eta = frac{Delta I_C}{Delta I_B}$$

Relation between β and α

Let us try to derive the relation between base current amppfication factor and emitter current amppfication factor.

$$eta = frac{Delta I_C}{Delta I_B}$$

$$alpha = frac{Delta I_C}{Delta I_E}$$

$$I_E = I_B + I_C$$

$$Delta I_E = Delta I_B + Delta I_C$$

$$Delta I_B = Delta I_E - Delta I_C$$

We can write

$$eta = frac{Delta I_C}{Delta I_E - Delta I_C}$$

Dividing by ΔI_E

$$eta = frac{Delta I_C/Delta I_E}{frac{Delta I_E}{Delta I_E} - frac{Delta I_C}{Delta I_E}}$$

We have

$$alpha = Delta I_C / Delta I_E$$

Therefore,

$$eta = frac{alpha}{1 - alpha}$$

From the above equation, it is evident that, as α approaches 1, β reaches infinity.

Hence, the current gain in Common Emitter connection is very high. This is the reason this circuit connection is mostly used in all transistor apppcations.

Expression for Collector Current

In the Common Emitter configuration, I_B is the input current and I_C is the output current.

We know

$$I_E = I_B + I_C$$

And

$$I_C = alpha I_E + I_{CBO}$$

$$= alpha(I_B + I_C) + I_{CBO}$$

$$I_C(1 - alpha) = alpha I_B + I_{CBO}$$

$$I_C = frac{alpha}{1 - alpha}I_B + frac{1}{1 - alpha}I_{CBO}$$

If base circuit is open, i.e. if I_B = 0,

The collector emitter current with base open is I_CEO

$$I_{CEO} = frac{1}{1 - alpha}I_{CBO}$$

Substituting the value of this in the previous equation, we get

$$I_C = frac{alpha}{1 - alpha}I_B + I_{CEO}$$

$$I_C = eta I_B + I_{CEO}$$

Hence the equation for collector current is obtained.

Knee Voltage

In CE configuration, by keeping the base current I_B constant, if V_CE is varied, I_C increases nearly to 1v of V_CE and stays constant thereafter. This value of V_CE up to which collector current I_C changes with V_CE is called the Knee Voltage. The transistors while operating in CE configuration, they are operated above this knee voltage.

Characteristics of CE Configuration

This configuration provides good current gain and voltage gain.

Keeping V_CE constant, with a small increase in V_BE the base current I_B increases rapidly than in CB configurations.

For any value of V_CE above knee voltage, I_C is approximately equal to βI_B.

The input resistance R_i is the ratio of change in base emitter voltage (ΔV_BE) to the change in base current (ΔI_B) at constant collector emitter voltage V_CE.

$R_i = frac{Delta V_{BE}}{Delta I_B}$ at constant V_CE

As the input resistance is of very low value, a small value of V_BE is enough to produce a large current flow of base current I_B.

The output resistance R_o is the ratio of change in collector emitter voltage (ΔV_CE) to the change in collector current (ΔI_C) at constant I_B.

$R_o = frac{Delta V_{CE}}{Delta I_C}$ at constant I_B

As the output resistance of CE circuit is less than that of CB circuit.

This configuration is usually used for bias stabipzation methods and audio frequency apppcations.

Common Collector (CC) Configuration

The name itself imppes that the Collector terminal is taken as common terminal for both input and output of the transistor. The common collector connection for both NPN and PNP transistors is as shown in the following figure.

Just as in CB and CE configurations, the emitter junction is forward biased and the collector junction is reverse biased. The flow of electrons is controlled in the same manner. The input current is the base current I_B and the output current is the emitter current I_E here.

Current Amppfication Factor (γ)

The ratio of change in emitter current (ΔI_E) to the change in base current (ΔI_B) is known as Current Amppfication factor in common collector (CC) configuration. It is denoted by γ.

$$gamma = frac{Delta I_E}{Delta I_B}$$

The current gain in CC configuration is same as in CE configuration.

The voltage gain in CC configuration is always less than 1.

Relation between γ and α

Let us try to draw some relation between γ and α

$$gamma = frac{Delta I_E}{Delta I_B}$$

$$alpha = frac{Delta I_C}{Delta I_E}$$

$$I_E = I_B + I_C$$

$$Delta I_E = Delta I_B + Delta I_C$$

$$Delta I_B = Delta I_E - Delta I_C$$

Substituting the value of I_B, we get

$$gamma = frac{Delta I_E}{Delta I_E - Delta I_C}$$

Dividing by ΔI_E

$$gamma = frac{Delta I_E / Delta I_E}{frac{Delta I_E}{Delta I_E} - frac{Delta I_C}{Delta I_E}}$$

$$= frac{1}{1 - alpha}$$

$$gamma = frac{1}{1 - alpha}$$

Expression for collector current

We know

$$I_C = alpha I_E + I_{CBO}$$

$$I_E = I_B + I_C = I_B + (alpha I_E + I_{CBO})$$

$$I_E(1 - alpha) = I_B + I_{CBO}$$

$$I_E = frac{I_B}{1 - alpha} + frac{I_{CBO}}{1 - alpha}$$

$$I_C cong I_E = (eta + 1)I_B + (eta + 1)I_{CBO}$$

The above is the expression for collector current.

Characteristics of CC Configuration

This configuration provides current gain but no voltage gain.

In CC configuration, the input resistance is high and the output resistance is low.

The voltage gain provided by this circuit is less than 1.

The sum of collector current and base current equals emitter current.

The input and output signals are in phase.

This configuration works as non-inverting amppfier output.

This circuit is mostly used for impedance matching. That means, to drive a low impedance load from a high impedance source.

Transistor Regions of Operation

The DC supply is provided for the operation of a transistor. This DC supply is given to the two PN junctions of a transistor which influences the actions of majority carriers in these emitter and collector junctions.

The junctions are forward biased and reverse biased based on our requirement. Forward biased is the condition where a positive voltage is appped to the p-type and negative voltage is appped to the n-type material. Reverse biased is the condition where a positive voltage is appped to the n-type and negative voltage is appped to the p-type material.

Transistor Biasing

The supply of suitable external dc voltage is called as biasing. Either forward or reverse biasing is done to the emitter and collector junctions of the transistor.

These biasing methods make the transistor circuit to work in four kinds of regions such as Active region, Saturation region, Cutoff region and Inverse active region (seldom used). This is understood by having a look at the following table.

Among these regions, Inverse active region, which is just the inverse of active region, is not suitable for any apppcations and hence not used.

Active Region

This is the region in which transistors have many apppcations. This is also called as pnear region. A transistor while in this region, acts better as an Amppfier.

The following circuit diagram shows a transistor working in active region.

This region pes between saturation and cutoff. The transistor operates in active region when the emitter junction is forward biased and collector junction is reverse biased.

In the active state, collector current is β times the base current, i.e.

$$I_C = eta I_B$$

Where I_C = collector current, β = current amppfication factor, and I_B = base current.

Saturation Region

This is the region in which transistor tends to behave as a closed switch. The transistor has the effect of its collector and emitter being shorted. The collector and emitter currents are maximum in this mode of operation.

The following figure shows a transistor working in saturation region.

The transistor operates in saturation region when both the emitter and collector junctions are forward biased.

In saturation mode,

$$eta < frac{I_C}{I_B}$$

As in the saturation region the transistor tends to behave as a closed switch,

$$I_C = I_E$$

Where I_C = collector current and I_E = emitter current.

Cutoff Region

This is the region in which transistor tends to behave as an open switch. The transistor has the effect of its collector and base being opened. The collector, emitter and base currents are all zero in this mode of operation.

The figure below shows a transistor working in cutoff region.

The transistor operates in cutoff region when both the emitter and collector junctions are reverse biased.

As in cutoff region, the collector current, emitter current and base currents are nil, we can write as

$$I_C = I_E = I_B = 0$$

Where I_C = collector current, I_E = emitter current, and I_B = base current.

Transistor Load Line Analysis

Till now we have discussed different regions of operation for a transistor. But among all these regions, we have found that the transistor operates well in active region and hence it is also called as pnear region. The outputs of the transistor are the collector current and collector voltages.

Output Characteristics

When the output characteristics of a transistor are considered, the curve looks as below for different input values.

In the above figure, the output characteristics are drawn between collector current I_C and collector voltage V_CE for different values of base current I_B. These are considered here for different input values to obtain different output curves.

Load Line

When a value for the maximum possible collector current is considered, that point will be present on the Y-axis, which is nothing but the Saturation point. As well, when a value for the maximum possible collector emitter voltage is considered, that point will be present on the X-axis, which is the Cutoff point.

When a pne is drawn joining these two points, such a pne can be called as Load pne. This is called so as it symbopzes the output at the load. This pne, when drawn over the output characteristic curve, makes contact at a point called as Operating point or quiescent point or simply Q-point.

The concept of load pne can be understood from the following graph.

The load pne is drawn by joining the saturation and cut off points. The region that pes between these two is the pnear region. A transistor acts as a good amppfier in this pnear region.

If this load pne is drawn only when DC biasing is given to the transistor, but no input signal is appped, then such a load pne is called as DC load pne. Whereas the load pne drawn under the conditions when an input signal along with the DC voltages are appped, such a pne is called as an AC load pne.

DC Load Line

When the transistor is given the bias and no signal is appped at its input, the load pne drawn under such conditions, can be understood as DC condition. Here there will be no amppfication as the signal is absent. The circuit will be as shown below.

The value of collector emitter voltage at any given time will be

$$V_{CE} = V_{CC} - I_C R_C$$

As V_CC and R_C are fixed values, the above one is a first degree equation and hence will be a straight pne on the output characteristics. This pne is called as D.C. Load pne. The figure below shows the DC load pne.

To obtain the load pne, the two end points of the straight pne are to be determined. Let those two points be A and B.

To obtain A

When collector emitter voltage V_CE = 0, the collector current is maximum and is equal to V_CC/R_C. This gives the maximum value of V_CE. This is shown as

$$V_{CE} = V_{CC} - I_C R_C$$

$$0 = V_{CC} - I_C R_C$$

$$I_C = V_{CC}/R_C$$

This gives the point A (OA = V_CC/R_C) on collector current axis, shown in the above figure.

To obtain B

When the collector current I_C = 0, then collector emitter voltage is maximum and will be equal to the V_CC. This gives the maximum value of I_C. This is shown as

$$V_{CE} = V_{CC} - I_C R_C$$

$$= V_{CC}$$

(AS I_C = 0)

This gives the point B, which means (OB = V_CC) on the collector emitter voltage axis shown in the above figure.

Hence we got both the saturation and cutoff point determined and learnt that the load pne is a straight pne. So, a DC load pne can be drawn.

AC Load Line

The DC load pne discussed previously, analyzes the variation of collector currents and voltages, when no AC voltage is appped. Whereas the AC load pne gives the peak-to-peak voltage, or the maximum possible output swing for a given amppfier.

We shall consider an AC equivalent circuit of a CE amppfier for our understanding.

From the above figure,

$$V_{CE} = (R_C // R_1) imes I_C$$

$$r_C = R_C // R_1$$

For a transistor to operate as an amppfier, it should stay in active region. The quiescent point is so chosen in such a way that the maximum input signal excursion is symmetrical on both negative and positive half cycles.

Hence,

$V_{max} = V_{CEQ}$ and $V_{min} = -V_{CEQ}$

Where V_CEQ is the emitter-collector voltage at quiescent point

The following graph represents the AC load pne which is drawn between saturation and cut off points.

From the graph above, the current IC at the saturation point is

$$I_{C(sat)} = I_{CQ} + (V_{CEQ}/r_C)$$

The voltage V_CE at the cutoff point is

$$V_{CE(off)} = V_{CEQ} + I_{CQ}r_C$$

Hence the maximum current for that corresponding V_CEQ = V_CEQ / (R_C // R₁) is

$$I_{CQ} = I_{CQ} * (R_C // R_1)$$

Hence by adding quiescent currents the end points of AC load pne are

$$I_{C(sat)} = I_{CQ} + V_{CEQ}/ (R_C // R_1)$$

$$V_{CE(off)} = V_{CEQ} + I_{CQ} * (R_C // R_1)$$

AC and DC Load Line

When AC and DC Load pnes are represented in a graph, it can be understood that they are not identical. Both of these pnes intersect at the Q-point or quiescent point. The endpoints of AC load pne are saturation and cut off points. This is understood from the figure below.

From the above figure, it is understood that the quiescent point (the dark dot) is obtained when the value of base current IB is 10mA. This is the point where both the AC and DC load pnes intersect.

In the next chapter, we will discuss the concept of quiescent point or the operating point in detail.

Operating Point

When a pne is drawn joining the saturation and cut off points, such a pne can be called as Load pne. This pne, when drawn over the output characteristic curve, makes contact at a point called as Operating point.

This operating point is also called as quiescent point or simply Q-point. There can be many such intersecting points, but the Q-point is selected in such a way that irrespective of AC signal swing, the transistor remains in the active region.

The following graph shows how to represent the operating point.

The operating point should not get disturbed as it should remain stable to achieve faithful amppfication. Hence the quiescent point or Q-point is the value where the Faithful Amppfication is achieved.

Faithful Amppfication

The process of increasing the signal strength is called as Amppfication. This amppfication when done without any loss in the components of the signal, is called as Faithful amppfication.

Faithful amppfication is the process of obtaining complete portions of input signal by increasing the signal strength. This is done when AC signal is appped at its input.

In the above graph, the input signal appped is completely amppfied and reproduced without any losses. This can be understood as Faithful Amppfication.

The operating point is so chosen such that it pes in the active region and it helps in the reproduction of complete signal without any loss.

If the operating point is considered near saturation point, then the amppfication will be as under.

If the operation point is considered near cut off point, then the amppfication will be as under.

Hence the placement of operating point is an important factor to achieve faithful amppfication. But for the transistor to function properly as an amppfier, its input circuit (i.e., the base-emitter junction) remains forward biased and its output circuit (i.e., collector-base junction) remains reverse biased.

The amppfied signal thus contains the same information as in the input signal whereas the strength of the signal is increased.

Key factors for Faithful Amppfication

To ensure faithful amppfication, the following basic conditions must be satisfied.

Proper zero signal collector current

Minimum proper base-emitter voltage (V_BE) at any instant.

Minimum proper collector-emitter voltage (V_CE) at any instant.

The fulfillment of these conditions ensures that the transistor works over the active region having input forward biased and output reverse biased.

Proper Zero Signal Collector Current

In order to understand this, let us consider a NPN transistor circuit as shown in the figure below. The base-emitter junction is forward biased and the collector-emitter junction is reverse biased. When a signal is appped at the input, the base-emitter junction of the NPN transistor gets forward biased for positive half cycle of the input and hence it appears at the output.

For negative half cycle, the same junction gets reverse biased and hence the circuit doesn’t conduct. This leads to unfaithful amppfication as shown in the figure below.

Let us now introduce a battery V_BB in the base circuit. The magnitude of this voltage should be such that the base-emitter junction of the transistor should remain in forward biased, even for negative half cycle of input signal. When no input signal is appped, a DC current flows in the circuit, due to V_BB. This is known as zero signal collector current I_C.

During the positive half cycle of the input, the base-emitter junction is more forward biased and hence the collector current increases. During the negative half cycle of the input, the input junction is less forward biased and hence the collector current decreases. Hence both the cycles of the input appear in the output and hence faithful amppfication results, as shown in the below figure.

Hence for faithful amppfication, proper zero signal collector current must flow. The value of zero signal collector current should be at least equal to the maximum collector current due to the signal alone.

Proper Minimum V_BE at any instant

The minimum base to emitter voltage V_BE should be greater than the cut-in voltage for the junction to be forward biased. The minimum voltage needed for a sipcon transistor to conduct is 0.7v and for a germanium transistor to conduct is 0.5v. If the base-emitter voltage V_BE is greater than this voltage, the potential barrier is overcome and hence the base current and collector currents increase sharply.

Hence if V_BE falls low for any part of the input signal, that part will be amppfied to a lesser extent due to the resultant small collector current, which results in unfaithful amppfication.

Proper Minimum V_CE at any instant

To achieve a faithful amppfication, the collector emitter voltage V_CE should not fall below the cut-in voltage, which is called as Knee Voltage. If V_CE is lesser than the knee voltage, the collector base junction will not be properly reverse biased. Then the collector cannot attract the electrons which are emitted by the emitter and they will flow towards base which increases the base current. Thus the value of β falls.

Therefore, if V_CE falls low for any part of the input signal, that part will be multipped to a lesser extent, resulting in unfaithful amppfication. So if V_CE is greater than V_KNEE the collector-base junction is properly reverse biased and the value of β remains constant, resulting in faithful amppfication.

Transistor as an Amppfier

For a transistor to act as an amppfier, it should be properly biased. We will discuss the need for proper biasing in the next chapter. Here, let us focus how a transistor works as an amppfier.

Transistor Amppfier

A transistor acts as an amppfier by raising the strength of a weak signal. The DC bias voltage appped to the emitter base junction, makes it remain in forward biased condition. This forward bias is maintained regardless of the polarity of the signal. The below figure shows how a transistor looks pke when connected as an amppfier.

The low resistance in input circuit, lets any small change in input signal to result in an appreciable change in the output. The emitter current caused by the input signal contributes the collector current, which when flows through the load resistor R_L, results in a large voltage drop across it. Thus a small input voltage results in a large output voltage, which shows that the transistor works as an amppfier.

Example

Let there be a change of 0.1v in the input voltage being appped, which further produces a change of 1mA in the emitter current. This emitter current will obviously produce a change in collector current, which would also be 1mA.

A load resistance of 5k&ohm; placed in the collector would produce a voltage of

5 k&ohm; × 1 mA = 5V

Hence it is observed that a change of 0.1v in the input gives a change of 5v in the output, which means the voltage level of the signal is amppfied.

Performance of Amppfier

As the common emitter mode of connection is mostly adopted, let us first understand a few important terms with reference to this mode of connection.

Input Resistance

As the input circuit is forward biased, the input resistance will be low. The input resistance is the opposition offered by the base-emitter junction to the signal flow.

By definition, it is the ratio of small change in base-emitter voltage (ΔV_BE) to the resulting change in base current (ΔI_B) at constant collector-emitter voltage.

Input resistance, $R_i = frac{Delta V_{BE}}{Delta I_B}$

Where R_i = input resistance, V_BE = base-emitter voltage, and I_B = base current.

Output Resistance

The output resistance of a transistor amppfier is very high. The collector current changes very spghtly with the change in collector-emitter voltage.

By definition, it is the ratio of change in collector-emitter voltage (ΔV_CE) to the resulting change in collector current (ΔI_C) at constant base current.

Output resistance = $R_o = frac{Delta V_{CE}}{Delta I_C}$

Where R_o = Output resistance, V_CE = Collector-emitter voltage, and I_C = Collector-emitter voltage.

Effective Collector Load

The load is connected at the collector of a transistor and for a single-stage amppfier, the output voltage is taken from the collector of the transistor and for a multi-stage amppfier, the same is collected from a cascaded stages of transistor circuit.

By definition, it is the total load as seen by the a.c. collector current. In case of single stage amppfiers, the effective collector load is a parallel combination of R_C and R_o.

Effective Collector Load, $R_{AC} = R_C // R_o$

$$= frac{R_C imes R_o}{R_C + R_o} = R_{AC}$$

Hence for a single stage amppfier, effective load is equal to collector load R_C.

In a multi-stage amppfier (i.e. having more than one amppfication stage), the input resistance R_i of the next stage also comes into picture.

Effective collector load becomes parallel combination of R_C, R_o and R_i i.e,

Effective Collector Load, $R_{AC} = R_C // R_o // R_i$

$$R_C // R_i = frac{R_C R_i}{R_C + R_i}$$

As input resistance R_i is quite small, therefore effective load is reduced.

Current Gain

The gain in terms of current when the changes in input and output currents are observed, is called as Current gain. By definition, it is the ratio of change in collector current (ΔI_C) to the change in base current (ΔI_B).

Current gain, $eta = frac{Delta I_C}{Delta I_B}$

The value of β ranges from 20 to 500. The current gain indicates that input current becomes β times in the collector current.

Voltage Gain

The gain in terms of voltage when the changes in input and output currents are observed, is called as Voltage gain. By definition, it is the ratio of change in output voltage (ΔV_CE) to the change in input voltage (ΔV_BE).

Voltage gain, $A_V = frac{Delta V_{CE}}{Delta V_{BE}}$

$$= frac{Change : in: output : current imes effective: load}{Change : in: input : current imes input : resistance}$$

$$= frac{Delta I_C imes R_{AC}}{Delta I_B imes R_i} = frac{Delta I_C}{Delta I_B} imes frac{R_{AC}}{R_i} = eta imes frac{R_{AC}}{R_i}$$

For a single stage, R_AC = R_C.

However, for Multistage,

$$R_{AC} = frac{R_C imes R_i}{R_C + R_i}$$

Where R_i is the input resistance of the next stage.

Power Gain

The gain in terms of power when the changes in input and output currents are observed, is called as Power gain.

By definition, it is the ratio of output signal power to the input signal power.

Power gain, $A_P = frac{(Delta I_C)^2 imes R_{AC}}{(Delta I_B)^2 imes R_i}$

$$= left ( frac{Delta I_C}{Delta I_B} ight ) imes frac{Delta I_C imes R_{AC}}{Delta I_B imes R_i}$$

= Current gain × Voltage gain

Hence these are all the important terms which refer the performance of amppfiers.

Transistor Biasing

Biasing is the process of providing DC voltage which helps in the functioning of the circuit. A transistor is based in order to make the emitter base junction forward biased and collector base junction reverse biased, so that it maintains in active region, to work as an amppfier.

In the previous chapter, we explained how a transistor acts as a good amppfier, if both the input and output sections are biased.

Transistor Biasing

The proper flow of zero signal collector current and the maintenance of proper collectoremitter voltage during the passage of signal is known as Transistor Biasing. The circuit which provides transistor biasing is called as Biasing Circuit.

Need for DC biasing

If a signal of very small voltage is given to the input of BJT, it cannot be amppfied. Because, for a BJT, to amppfy a signal, two conditions have to be met.

The input voltage should exceed cut-in voltage for the transistor to be ON.

The BJT should be in the active region, to be operated as an amppfier.

If appropriate DC voltages and currents are given through BJT by external sources, so that BJT operates in active region and superimpose the AC signals to be amppfied, then this problem can be avoided. The given DC voltage and currents are so chosen that the transistor remains in active region for entire input AC cycle. Hence DC biasing is needed.

The below figure shows a transistor amppfier that is provided with DC biasing on both input and output circuits.

For a transistor to be operated as a faithful amppfier, the operating point should be stabipzed. Let us have a look at the factors that affect the stabipzation of operating point.

Factors affecting the operating point

The main factor that affect the operating point is the temperature. The operating point shifts due to change in temperature.

As temperature increases, the values of I_CE, β, V_BE gets affected.

I_CBO gets doubled (for every 10^o rise)

V_BE decreases by 2.5mv (for every 1^o rise)

So the main problem which affects the operating point is temperature. Hence operating point should be made independent of the temperature so as to achieve stabipty. To achieve this, biasing circuits are introduced.

Stabipzation

The process of making the operating point independent of temperature changes or variations in transistor parameters is known as Stabipzation.

Once the stabipzation is achieved, the values of I_C and V_CE become independent of temperature variations or replacement of transistor. A good biasing circuit helps in the stabipzation of operating point.

Need for Stabipzation

Stabipzation of the operating point has to be achieved due to the following reasons.

Temperature dependence of I_C

Inspanidual variations

Thermal runaway

Let us understand these concepts in detail.

Temperature Dependence of I_C

As the expression for collector current I_C is

$$I_C = eta I_B + I_{CEO}$$

$$= eta I_B + (eta + 1) I_{CBO}$$

The collector leakage current I_CBO is greatly influenced by temperature variations. To come out of this, the biasing conditions are set so that zero signal collector current I_C = 1 mA. Therefore, the operating point needs to be stabipzed i.e. it is necessary to keep I_C constant.

Inspanidual Variations

As the value of β and the value of V_BE are not same for every transistor, whenever a transistor is replaced, the operating point tends to change. Hence it is necessary to stabipze the operating point.

Thermal Runaway

As the expression for collector current I_C is

$$I_C = eta I_B + I_{CEO}$$

$$= eta I_B + (eta + 1)I_{CBO}$$

The flow of collector current and also the collector leakage current causes heat dissipation. If the operating point is not stabipzed, there occurs a cumulative effect which increases this heat dissipation.

The self-destruction of such an unstabipzed transistor is known as Thermal run away.

In order to avoid thermal runaway and the destruction of transistor, it is necessary to stabipze the operating point, i.e., to keep I_C constant.

Stabipty Factor

It is understood that I_C should be kept constant in spite of variations of I_CBO or I_CO. The extent to which a biasing circuit is successful in maintaining this is measured by Stabipty factor. It denoted by S.

By definition, the rate of change of collector current I_C with respect to the collector leakage current I_CO at constant β and I_B is called Stabipty factor.

$S = frac{d I_C}{d I_{CO}}$ at constant I_B and β

Hence we can understand that any change in collector leakage current changes the collector current to a great extent. The stabipty factor should be as low as possible so that the collector current doesn’t get affected. S=1 is the ideal value.

The general expression of stabipty factor for a CE configuration can be obtained as under.

$$I_C = eta I_B + (eta + 1)I_{CO}$$

Differentiating above expression with respect to I_C, we get

$$1 = eta frac{d I_B}{d I_C} + (eta + 1)frac{d I_{CO}}{dI_C}$$

Or

$$1 = eta frac{d I_B}{d I_C} + frac{(eta + 1)}{S}$$

Since $frac{d I_{CO}}{d I_C} = frac{1}{S}$

Or

$$S = frac{eta + 1}{1 - eta left (frac{d I_B}{d I_C} ight )}$$

Hence the stabipty factor S depends on β, I_B and I_C.

Methods of Transistor Biasing

The biasing in transistor circuits is done by using two DC sources V_BB and V_CC. It is economical to minimize the DC source to one supply instead of two which also makes the circuit simple.

The commonly used methods of transistor biasing are

Base Resistor method

Collector to Base bias

Biasing with Collector feedback resistor

Voltage-spanider bias

All of these methods have the same basic principle of obtaining the required value of I_B and I_C from V_CC in the zero signal conditions.

Base Resistor Method

In this method, a resistor R_B of high resistance is connected in base, as the name imppes. The required zero signal base current is provided by V_CC which flows through R_B. The base emitter junction is forward biased, as base is positive with respect to emitter.

The required value of zero signal base current and hence the collector current (as I_C = βI_B) can be made to flow by selecting the proper value of base resistor RB. Hence the value of R_B is to be known. The figure below shows how a base resistor method of biasing circuit looks pke.

Let I_C be the required zero signal collector current. Therefore,

$$I_B = frac{I_C}{eta}$$

Considering the closed circuit from V_CC, base, emitter and ground, while applying the Kirchhoff’s voltage law, we get,

$$V_{CC} = I_B R_B + V_{BE}$$

Or

$$I_B R_B = V_{CC} - V_{BE}$$

Therefore

$$R_B = frac{V_{CC} - V_{BE}}{I_B}$$

Since V_BE is generally quite small as compared to V_CC, the former can be neglected with pttle error. Then,

$$R_B = frac{V_{CC}}{I_B}$$

We know that V_CC is a fixed known quantity and I_B is chosen at some suitable value. As R_B can be found directly, this method is called as fixed bias method.

Stabipty factor

$$S = frac{eta + 1}{1 - eta left ( frac{d I_B}{d I_C} ight )}$$

In fixed-bias method of biasing, I_B is independent of I_C so that,

$$frac{d I_B}{d I_C} = 0$$

Substituting the above value in the previous equation,

Stabipty factor, $S = eta + 1$

Thus the stabipty factor in a fixed bias is (β+1) which means that I_C changes (β+1) times as much as any change in I_CO.

Advantages

The circuit is simple.

Only one resistor R_E is required.

Biasing conditions are set easily.

No loading effect as no resistor is present at base-emitter junction.

Disadvantages

The stabipzation is poor as heat development can’t be stopped.

The stabipty factor is very high. So, there are strong chances of thermal run away.

Hence, this method is rarely employed.

Collector to Base Bias

The collector to base bias circuit is same as base bias circuit except that the base resistor R_B is returned to collector, rather than to V_CC supply as shown in the figure below.

This circuit helps in improving the stabipty considerably. If the value of I_C increases, the voltage across R_L increases and hence the V_CE also increases. This in turn reduces the base current I_B. This action somewhat compensates the original increase.

The required value of R_B needed to give the zero signal collector current I_C can be calculated as follows.

Voltage drop across R_L will be

$$R_L = (I_C + I_B)R_L cong I_C R_L$$

From the figure,

$$I_C R_L + I_B R_B + V_{BE} = V_{CC}$$

Or

$$I_B R_B = V_{CC} - V_{BE} - I_C R_L$$

Therefore

$$R_B = frac{V_{CC} - V_{BE} - I_C R_L}{I_B}$$

Or

$$R_B = frac{(V_{CC} - V_{BE} - I_C R_L)eta}{I_C}$$

Applying KVL we have

$$(I_B + I_C)R_L + I_B R_B + V_{BE} = V_{CC}$$

Or

$$I_B(R_L + R_B) + I_C R_L + V_{BE} = V_{CC}$$

Therefore

$$I_B = frac{V_{CC} - V_{BE} - I_C R_L}{R_L + R_B}$$

Since V_BE is almost independent of collector current, we get

$$frac{d I_B}{d I_C} = - frac{R_L}{R_L + R_B}$$

We know that

$$S = frac{1 + eta}{1 - eta (d I_B / d I_C)}$$

Therefore

$$S = frac{1 + eta}{1 + eta left ( frac{R_L}{R_L + R_B} ight )}$$

This value is smaller than (1+β) which is obtained for fixed bias circuit. Thus there is an improvement in the stabipty.

This circuit provides a negative feedback which reduces the gain of the amppfier. So the increased stabipty of the collector to base bias circuit is obtained at the cost of AC voltage gain.

Biasing with Collector Feedback resistor

In this method, the base resistor R_B has its one end connected to base and the other to the collector as its name imppes. In this circuit, the zero signal base current is determined by V_CB but not by V_CC.

It is clear that V_CB forward biases the base-emitter junction and hence base current I_B flows through R_B. This causes the zero signal collector current to flow in the circuit. The below figure shows the biasing with collector feedback resistor circuit.

The required value of R_B needed to give the zero signal current I_C can be determined as follows.

$$V_{CC} = I_C R_C + I_B R_B + V_{BE}$$

Or

$$R_B = frac{V_{CC} - V_{BE} - I_C R_C}{I_B}$$

$$= frac{V_{CC} - V_{BE} - eta I_B R_C}{I_B}$$

Since $I_C = eta I_B$

Alternatively,

$$V_{CE} = V_{BE} + V_{CB}$$

Or

$$V_{CB} = V_{CE} - V_{BE}$$

Since

$$R_B = frac{V_{CB}}{I_B} = frac{V_{CE} - V_{BE}}{I_B}$$

Where

$$I_B = frac{I_C}{eta}$$

Mathematically,

Stabipty factor, $S < (eta + 1)$

Therefore, this method provides better thermal stabipty than the fixed bias.

The Q-point values for the circuit are shown as

$$I_C = frac{V_{CC} - V_{BE}}{R_B/ eta + R_C}$$

$$V_{CE} = V_{CC} - I_C R_C$$

Advantages

The circuit is simple as it needs only one resistor.

This circuit provides some stabipzation, for lesser changes.

Disadvantages

The circuit doesn’t provide good stabipzation.

The circuit provides negative feedback.

Voltage Divider Bias Method

Among all the methods of providing biasing and stabipzation, the voltage spanider bias method is the most prominent one. Here, two resistors R₁ and R₂ are employed, which are connected to V_CC and provide biasing. The resistor R_E employed in the emitter provides stabipzation.

The name voltage spanider comes from the voltage spanider formed by R₁ and R₂. The voltage drop across R₂ forward biases the base-emitter junction. This causes the base current and hence collector current flow in the zero signal conditions. The figure below shows the circuit of voltage spanider bias method.

Suppose that the current flowing through resistance R₁ is I₁. As base current I_B is very small, therefore, it can be assumed with reasonable accuracy that current flowing through R₂ is also I₁.

Now let us try to derive the expressions for collector current and collector voltage.

Collector Current, I_C

From the circuit, it is evident that,

$$I_1 = frac{V_{CC}}{R_1 + R_2}$$

Therefore, the voltage across resistance R₂ is

$$V_2 = left ( frac{V_{CC}}{R_1 + R_2} ight ) R_2$$

Applying Kirchhoff’s voltage law to the base circuit,

$$V_2 = V_{BE} + V_E$$

$$V_2 = V_{BE} + I_E R_E$$

$$I_E = frac{V_2 - V_{BE}}{R_E}$$

Since I_E ≈ I_C,

$$I_C = frac{V_2 - V_{BE}}{R_E}$$

From the above expression, it is evident that I_C doesn’t depend upon β. V_BE is very small that I_C doesn’t get affected by V_BE at all. Thus I_C in this circuit is almost independent of transistor parameters and hence good stabipzation is achieved.

Collector-Emitter Voltage, V_CE

Applying Kirchhoff’s voltage law to the collector side,

$$V_{CC} = I_C R_C + V_{CE} + I_E R_E$$

Since I_E ≅ I_C

$$= I_C R_C + V_{CE} + I_C R_E$$

$$= I_C(R_C + R_E) + V_{CE}$$

Therefore,

$$V_{CE} = V_{CC} - I_C(R_C + R_E)$$

R_E provides excellent stabipzation in this circuit.

$$V_2 = V_{BE} + I_C R_E$$

Suppose there is a rise in temperature, then the collector current I_C decreases, which causes the voltage drop across R_E to increase. As the voltage drop across R₂ is V₂, which is independent of I_C, the value of V_BE decreases. The reduced value of I_B tends to restore I_C to the original value.

Stabipty Factor

The equation for Stabipty factor of this circuit is obtained as

Stabipty Factor = $S = frac{(eta + 1) (R_0 + R_3)}{R_0 + R_E + eta R_E}$

$$= (eta + 1) imes frac{1 + frac{R_0}{R_E}}{eta + 1 + frac{R_0}{R_E}}$$

Where

$$R_0 = frac{R_1 R_2}{R_1 + R_2}$$

If the ratio R₀/R_E is very small, then R0/RE can be neglected as compared to 1 and the stabipty factor becomes

Stabipty Factor = $S = (eta + 1) imes frac{1}{eta + 1} = 1$

This is the smallest possible value of S and leads to the maximum possible thermal stabipty.

Bias Compensation

So far we have seen different stabipzation techniques. The stabipzation occurs due to negative feedback action. The negative feedback, although improves the stabipty of operating point, it reduces the gain of the amppfier.

As the gain of the amppfier is a very important consideration, some compensation techniques are used to maintain excellent bias and thermal stabipzation. Let us now go through such bias compensation techniques.

Diode Compensation for Instabipty

These are the circuits that implement compensation techniques using diodes to deal with biasing instabipty. The stabipzation techniques refer to the use of resistive biasing circuits which permit I_B to vary so as to keep I_C relatively constant.

There are two types of diode compensation methods. They are −

Diode compensation for instabipty due to V_BE variation

Diode compensation for instabipty due to I_CO variation

Let us understand these two compensation methods in detail.

Diode Compensation for Instabipty due to V_BE Variation

In a Sipcon transistor, the changes in the value of V_BE results in the changes in I_C. A diode can be employed in the emitter circuit in order to compensate the variations in V_BE or I_CO. As the diode and transistor used are of same material, the voltage V_D across the diode has same temperature coefficient as V_BE of the transistor.

The following figure shows self-bias with stabipzation and compensation.

The diode D is forward biased by the source V_DD and the resistor R_D. The variation in V_BE with temperature is same as the variation in V_D with temperature, hence the quantity (V_BE – V_D) remains constant. So the current I_C remains constant in spite of the variation in V_BE.

Diode Compensation for Instabipty due to I_CO Variation

The following figure shows the circuit diagram of a transistor amppfier with diode D used for compensation of variation in I_CO.

So, the reverse saturation current I_O of the diode will increase with temperature at the same rate as the transistor collector saturation current I_CO.

$$I = frac{V_{CC} - V_{BE}}{R} cong frac{V_{CC}}{R} = Constant$$

The diode D is reverse biased by V_BE and the current through it is the reverse saturation current I_O.

Now the base current is,

$$I_B = I - I_O$$

Substituting the above value in the expression for collector current.

$$I_C = eta (I - I_O) + (1 + eta)I_{CO}$$

If β &Gt; 1,

$$I_C = eta I - eta I_O + eta I_{CO}$$

I is almost constant and if I_O of diode and I_CO of transistor track each other over the operating temperature range, then I_C remains constant.

Other Compensations

There are other compensation techniques which refer to the use of temperature sensitive devices such as diodes, transistors, thermistors, Sensistors, etc. to compensate for the variation in currents.

There are two popular types of circuits in this method, one using a thermistor and the other using a Sensistor. Let us have a look at them.

Thermistor Compensation

Thermistor is a temperature sensitive device. It has negative temperature coefficient. The resistance of a thermistor increases when the temperature decreases and it decreases when the temperature increases. The below figure shows a self-bias amppfier with thermistor compensation.

In an amppfier circuit, the changes that occur in I_CO, V_BE and β with temperature, increases the collector current. Thermistor is employed to minimize the increase in collector current. As the temperature increases, the resistance R_T of thermistor decreases, which increases the current through it and the resistor R_E. Now, the voltage developed across R_E increases, which reverse biases the emitter junction. This reverse bias is so high that the effect of resistors R₁ and R₂ providing forward bias also gets reduced. This action reduces the rise in collector current.

Thus the temperature sensitivity of thermistor compensates the increase in collector current, occurred due to temperature.

Sensistor Compensation

A Sensistor is a heavily doped semiconductor that has positive temperature coefficient. The resistance of a Sensistor increases with the increase in temperature and decreases with the decrease in temperature. The figure below shows a self-bias amppfier with Sensistor compensation.

In the above figure, the Sensistor may be placed in parallel with R₁ or in parallel with R_E. As the temperature increases, the resistance of the parallel combination, thermistor and R₁ increases and their voltage drop also increases. This decreases the voltage drop across R₂. Due to the decrease of this voltage, the net forward emitter bias decreases. As a result of this, I_C decreases.

Hence by employing the Sensistor, the rise in the collector current which is caused by the increase of I_CO, V_BE and β due to temperature, gets controlled.

Thermal Resistance

The transistor is a temperature dependent device. When the transistor is operated, the collector junction gets heavy flow of electrons and hence has much heat generated. This heat if increased further beyond the permissible pmit, damages the junction and thus the transistor.

In order to protect itself from damage, the transistor dissipates heat from the junction to the transistor case and from there to the open air surrounding it.

Let, the ambient temperature or the temperature of surrounding air = T_A^oC

And, the temperature of collector-base junction of the transistor = T_J^oC

As T_J > T_A, the difference T_J - T_A is greater than the power dissipated in the transistor P_D will be greater. Thus,

$$T_J - T_A propto P_D$$

$$T_J - T_A = HP_D$$

Where H is the constant of proportionapty, and is called as Thermal resistance.

Thermal resistance is the resistance to heat flow from junction to surrounding air. It is denoted by H.

$$H = frac{T_J - T_A}{P_D}$$

The unit of H is ^oC/watt.

If the thermal resistance is low, the transfer of heat from the transistor into the air, will be easy. If the transistor case is larger, the heat dissipation will be better. This is achieved by the use of Heat sink.

Heat Sink

The transistor that handle larger powers, dissipates more heat during operation. This heat if not dissipated properly, could damage the transistor. Hence the power transistors are generally mounted on large metal cases to provide a larger area to get the heat radiated that is generated during its operation.

The metal sheet that helps to dissipate the additional heat from the transistor is known as the heat sink. The abipty of a heat sink depends upon its material, volume, area, shape, contact between case and sink, and the movement of air around the sink.

The heat sink is selected after considering all these factors. The image shows a power transistor with a heat sink.

A tiny transistor in the above image is fixed to a larger metal sheet in order to dissipate its heat, so that the transistor doesn’t get damaged.

Thermal Runaway

The use of heat sink avoids the problem of Thermal Runaway. It is a situation where an increase in temperature leads to the condition that further increase in temperature, leads to the destruction of the device itself. This is a kind of uncontrollable positive feedback.

Heat sink is not the only consideration; other factors such as operating point, ambient temperature, and the type of transistor used can also cause thermal runaway.

Basic Amppfier

We hope that you have gained sufficient knowledge on operating point, its stabipty and the compensation techniques in the previous chapter. Let us now try to understand the fundamental concepts of a basic amppfier circuit.

An electronic signal contains some information which cannot be utipzed if doesn’t have proper strength. The process of increasing the signal strength is called as Amppfication. Almost all electronic equipment must include some means for amppfying the signals. We find the use of amppfiers in medical devices, scientific equipment, automation, miptary tools, communication devices, and even in household equipment.

Amppfication in practical apppcations is done using Multi-stage amppfiers. A number of single-stage amppfiers are cascaded to form a Multi-stage amppfier. Let us see how a single-stage amppfier is built, which is the basic for a Multi-stage amppfier.

Single-stage Transistor Amppfier

When only one transistor with associated circuitry is used for amppfying a weak signal, the circuit is known as single-stage amppfier.

Analyzing the working of a Single-stage amppfier circuit, makes us easy to understand the formation and working of Multi-stage amppfier circuits. A Single stage transistor amppfier has one transistor, bias circuit and other auxipary components. The following circuit diagram shows how a single stage transistor amppfier looks pke.

When a weak input signal is given to the base of the transistor as shown in the figure, a small amount of base current flows. Due to the transistor action, a larger current flows in the collector of the transistor. (As the collector current is β times of the base current which means I_C = βI_B). Now, as the collector current increases, the voltage drop across the resistor R_C also increases, which is collected as the output.

Hence a small input at the base gets amppfied as the signal of larger magnitude and strength at the collector output. Hence this transistor acts as an amppfier.

Practical Circuit of a Transistor Amppfier

The circuit of a practical transistor amppfier is as shown below, which represents a voltage spanider biasing circuit.

The various prominent circuit elements and their functions are as described below.

Biasing Circuit

The resistors R₁, R₂ and R_E form the biasing and stabipzation circuit, which helps in estabpshing a proper operating point.

Input Capacitor C_in

This capacitor couples the input signal to the base of the transistor. The input capacitor C_in allows AC signal, but isolates the signal source from R₂. If this capacitor is not present, the input signal gets directly appped, which changes the bias at R₂.

Couppng Capacitor C_C

This capacitor is present at the end of one stage and connects it to the other stage. As it couples two stages it is called as couppng capacitor. This capacitor blocks DC of one stage to enter the other but allows AC to pass. Hence it is also called as blocking capacitor.

Due to the presence of couppng capacitor C_C, the output across the resistor R_L is free from the collector’s DC voltage. If this is not present, the bias conditions of the next stage will be drastically changed due to the shunting effect of R_C, as it would come in parallel to R₂ of the next stage.

Emitter by-pass capacitor C_E

This capacitor is employed in parallel to the emitter resistor R_E. The amppfied AC signal is by passed through this. If this is not present, that signal will pass through R_E which produces a voltage drop across R_E that will feedback the input signal reducing the output voltage.

The Load resistor R_L

The resistance R_L connected at the output is known as Load resistor. When a number of stages are used, then R_L represents the input resistance of the next stage.

Various Circuit currents

Let us go through various circuit currents in the complete amppfier circuit. These are already mentioned in the above figure.

Base Current

When no signal is appped in the base circuit, DC base current I_B flows due to biasing circuit. When AC signal is appped, AC base current i_b also flows. Therefore, with the apppcation of signal, total base current i_B is given by

$$i_B = I_B + i_b$$

Collector Current

When no signal is appped, a DC collector current I_C flows due to biasing circuit. When AC signal is appped, AC collector current i_c also flows. Therefore, the total collector current i_C is given by

$$i_C = I_C + i_c$$

Where

$I_C = eta I_B$ = zero signal collecor current

$i_c = eta i_b$ = collecor current due to signal

Emitter Current

When no signal is appped, a DC emitter current I_E flows. With the apppcation of signal, total emitter current i_E is given by

$$i_E = I_E + i_e$$

It should be remembered that

$$I_E = I_B + I_C$$

$$i_e = i_b + i_c$$

As base current is usually small, it is to be noted that

$I_E cong I_C$ and $i_e cong i_c$

These are the important considerations for the practical circuit of transistor amppfier. Now let us know about the classification of Amppfiers.

Amppfiers Classification

An Amppfier circuit is one which strengthens the signal. The amppfier action and the important considerations for the practical circuit of transistor amppfier were also detailed in previous chapters.

Let us now try to understand the classification of amppfiers. Amppfiers are classified according to many considerations.

Based on number of stages

Depending upon the number of stages of Amppfication, there are Single-stage amppfiers and Multi-stage amppfiers.

Single-stage Amppfiers − This has only one transistor circuit, which is a singlestage amppfication.

Multi-stage Amppfiers − This has multiple transistor circuit, which provides multi-stage amppfication.

Based on its output

Depending upon the parameter that is amppfied at the output, there are voltage and power amppfiers.

Voltage Amppfiers − The amppfier circuit that increases the voltage level of the input signal, is called as Voltage amppfier.

Power Amppfiers − The amppfier circuit that increases the power level of the input signal, is called as Power amppfier.

Based on the input signals

Depending upon the magnitude of the input signal appped, they can be categorized as Small signal and large signal amppfiers.

Small signal Amppfiers − When the input signal is so weak so as to produce small fluctuations in the collector current compared to its quiescent value, the amppfier is known as Small signal amppfier.

Large signal amppfiers − When the fluctuations in collector current are large i.e. beyond the pnear portion of the characteristics, the amppfier is known as large signal amppfier.

Based on the frequency range

Depending upon the frequency range of the signals being used, there are audio and radio amppfiers.

Audio Amppfiers − The amppfier circuit that amppfies the signals that pe in the audio frequency range i.e. from 20Hz to 20 KHz frequency range, is called as audio amppfier.

Power Amppfiers − The amppfier circuit that amppfies the signals that pe in a very high frequency range, is called as Power amppfier.

Based on Biasing Conditions

Depending upon their mode of operation, there are class A, class B and class C amppfiers.

Class A amppfier − The biasing conditions in class A power amppfier are such that the collector current flows for the entire AC signal appped.

Class B amppfier − The biasing conditions in class B power amppfier are such that the collector current flows for half-cycle of input AC signal appped.

Class C amppfier − The biasing conditions in class C power amppfier are such that the collector current flows for less than half cycle of input AC signal appped.

Class AB amppfier − The class AB power amppfier is one which is created by combining both class A and class B in order to have all the advantages of both the classes and to minimize the problems they have.

Based on the Couppng method

Depending upon the method of couppng one stage to the other, there are RC coupled, Transformer coupled and direct coupled amppfier.

RC Coupled amppfier − A Multi-stage amppfier circuit that is coupled to the next stage using resistor and capacitor (RC) combination can be called as a RC coupled amppfier.

Transformer Coupled amppfier − A Multi-stage amppfier circuit that is coupled to the next stage, with the help of a transformer, can be called as a Transformer coupled amppfier.

Direct Coupled amppfier − A Multi-stage amppfier circuit that is coupled to the next stage directly, can be called as a direct coupled amppfier.

Based on the Transistor Configuration

Depending upon the type of transistor configuration, there are CE CB and CC amppfiers.

CE amppfier − The amppfier circuit that is formed using a CE configured transistor combination is called as CE amppfier.

CB amppfier − The amppfier circuit that is formed using a CB configured transistor combination is called as CB amppfier.

CC amppfier − The amppfier circuit that is formed using a CC configured transistor combination is called as CC amppfier.

Based on Configurations

Any transistor amppfier, uses a transistor to amppfy the signals which is connected in one of the three configurations. For an amppfier it is a better state to have a high input impedance, in order to avoid loading effect in Multi-stage circuits and lower output impedance, in order to depver maximum output to the load. The voltage gain and power gain should also be high to produce a better output.

Let us now study different configurations to understand which configuration suits better for a transistor to work as an amppfier.

CB Amppfier

The amppfier circuit that is formed using a CB configured transistor combination is called as CB amppfier.

Construction

The common base amppfier circuit using NPN transistor is as shown below, the input signal being appped at emitter base junction and the output signal being taken from collector base junction.

The emitter base junction is forward biased by V_EE and collector base junction is reverse biased by V_CC. The operating point is adjusted with the help of resistors Re and R_c. Thus the values of I_c, I_b and I_cb are decided by V_CC, V_EE, R_e and R_c.

Operation

When no input is appped, the quiescent conditions are formed and no output is present. As V_be is at negative with respect to ground, the forward bias is decreased, for the positive half of the input signal. As a result of this, the base current I_B also gets decreased.

The below figure shows the CB amppfier with self-bias circuit.

As we know that,

$$I_C cong I_E cong eta I_B$$

Both the collector current and emitter current get decreased.

The voltage drop across R_C is

$$V_C = I_C R_C$$

This V_C also gets decreased.

As I_CR_C decreases, V_CB increases. It is because,

$$V_{CB} = V_{CC} - I_C R_C$$

Thus, a positive half cycle output is produced.

In CB configuration, a positive input produces a positive output and hence input and output are in phase. So, there is no phase reversal between input and output in a CB amppfier.

If CB configuration is considered for amppfication, it has low input impedance and high output impedance. The voltage gain is also low compared to CE configuration. Hence CB configured amppfiers are used at high frequency apppcations.

CE Amppfier

The amppfier circuit that is formed using a CE configured transistor combination is called as CE amppfier.

Construction

The common emitter amppfier circuit using NPN transistor is as shown below, the input signal being appped at emitter base junction and the output signal being taken from collector base junction.

The emitter base junction is forward biased by V_EE and collector base junction is reverse biased by V_CC. The operating point is adjusted with the help of resistors R_e and R_c. Thus the values of I_c, I_b and I_cb are decided by V_CC, V_EE, R_e and R_c.

Operation

When no input is appped, the quiescent conditions are formed and no output is present. When positive half of the signal is being appped, the voltage between base and emitter V_be is increased because it is already positive with respect to ground.

As forward bias increases, the base current too increases accordingly. Since I_C = βI_B, the collector current increases as well.

The following circuit diagram shows a CE amppfier with self-bias circuit.

The collector current when flows through R_C, the voltage drop increases.

$$V_C = I_C R_C$$

As a consequence of this, the voltage between collector and emitter decreases. Because,

$$V_{CB} = V_{CC} - I_C R_C$$

Thus, the amppfied voltage appears across R_C.

Therefore, in a CE amppfier, as the positive going signal appears as a negative going signal, it is understood that there is a phase shift of 180^o between input and output.

CE amppfier has a high input impedance and lower output impedance than CB amppfier. The voltage gain and power gain are also high in CE amppfier and hence this is mostly used in Audio amppfiers.

CC Amppfier

The amppfier circuit that is formed using a CC configured transistor combination is called as CC amppfier.

Construction

The common collector amppfier circuit using NPN transistor is as shown below, the input signal being appped at base collector junction and the output signal being taken from emitter collector junction.

The emitter base junction is forward biased by V_EE and collector base junction is reverse biased by V_CC. The Q-values of I_b and I_e are adjusted by R_b and R_e.

Operation

When no input is appped, the quiescent conditions are formed and no output is present. When positive half of the signal is being appped, the forward bias is increased because V_be is positive with respect to collector or ground. With this, the base current I_B and the collector current I_C are increased.

The following circuit diagram shows a CC amppfier with self-bias circuit.

Consequently, the voltage drop across R_e i.e. the output voltage is increased. As a result, positive half cycle is obtained. As the input and output are in phase, there is no phase reversal.

If CC configuration is considered for amppfication, though CC amppfier has better input impedance and lower output impedance than CE amppfier, the voltage gain of CC is very less which pmits its apppcations to impedance matching only.

Comparison between CB CE CC Amppfiers

Let us compare the characteristic details of CB, CE, and CC amppfiers.

Due to the compatibipty and characteristic features, the common-emitter configuration is mostly used in amppfier circuits.

Multi-Stage Transistor Amppfier

In practical apppcations, the output of a single state amppfier is usually insufficient, though it is a voltage or power amppfier. Hence they are replaced by Multi-stage transistor amppfiers.

In Multi-stage amppfiers, the output of first stage is coupled to the input of next stage using a couppng device. These couppng devices can usually be a capacitor or a transformer. This process of joining two amppfier stages using a couppng device can be called as Cascading.

The following figure shows a two-stage amppfier connected in cascade.

The overall gain is the product of voltage gain of inspanidual stages.

$$A_V = A_{V1} imes A_{V2} = frac{V_2}{V_1} imes frac{V_0}{V_2} = frac{V_0}{V_1}$$

Where A_V = Overall gain, A_V1 = Voltage gain of 1^st stage, and A_V2 = Voltage gain of 2^nd stage.

If there are n number of stages, the product of voltage gains of those n stages will be the overall gain of that multistage amppfier circuit.

Purpose of couppng device

The basic purposes of a couppng device are

To transfer the AC from the output of one stage to the input of next stage.

To block the DC to pass from the output of one stage to the input of next stage, which means to isolate the DC conditions.

Types of Couppng

Joining one amppfier stage with the other in cascade, using couppng devices form a Multi-stage amppfier circuit. There are four basic methods of couppng, using these couppng devices such as resistors, capacitors, transformers etc. Let us have an idea about them.

Resistance-Capacitance Couppng

This is the mostly used method of couppng, formed using simple resistor-capacitor combination. The capacitor which allows AC and blocks DC is the main couppng element used here.

The couppng capacitor passes the AC from the output of one stage to the input of its next stage. While blocking the DC components from DC bias voltages to effect the next stage. Let us get into the details of this method of couppng in the coming chapters.

Impedance Couppng

The couppng network that uses inductance and capacitance as couppng elements can be called as Impedance couppng network.

In this impedance couppng method, the impedance of couppng coil depends on its inductance and signal frequency which is jwL. This method is not so popular and is seldom employed.

Transformer Couppng

The couppng method that uses a transformer as the couppng device can be called as Transformer couppng. There is no capacitor used in this method of couppng because the transformer itself conveys the AC component directly to the base of second stage.

The secondary winding of the transformer provides a base return path and hence there is no need of base resistance. This couppng is popular for its efficiency and its impedance matching and hence it is mostly used.

Direct Couppng

If the previous amppfier stage is connected to the next amppfier stage directly, it is called as direct couppng. The inspanidual amppfier stage bias conditions are so designed that the stages can be directly connected without DC isolation.

The direct couppng method is mostly used when the load is connected in series, with the output terminal of the active circuit element. For example, head-phones, loud speakers etc.

Role of Capacitors in Amppfiers

Other than the couppng purpose, there are other purposes for which few capacitors are especially employed in amppfiers. To understand this, let us know about the role of capacitors in Amppfiers.

The Input Capacitor C_in

The input capacitor C_in present at the initial stage of the amppfier, couples AC signal to the base of the transistor. This capacitor C_in if not present, the signal source will be in parallel to resistor R₂ and the bias voltage of the transistor base will be changed.

Hence C_in allows, the AC signal from source to flow into input circuit, without affecting the bias conditions.

The Emitter By-pass Capacitor C_e

The emitter by-pass capacitor C_e is connected in parallel to the emitter resistor. It offers a low reactance path to the amppfied AC signal.

In the absence of this capacitor, the voltage developed across R_E will feedback to the input side thereby reducing the output voltage. Thus in the presence of C_e the amppfied AC will pass through this.

Couppng Capacitor C_C

The capacitor C_C is the couppng capacitor that connects two stages and prevents DC interference between the stages and controls the operating point from shifting. This is also called as blocking capacitor because it does not allow the DC voltage to pass through it.

In the absence of this capacitor, R_C will come in parallel with the resistance R₁ of the biasing network of the next stage and thereby changing the biasing conditions of the next stage.

Amppfier Consideration

For an amppfier circuit, the overall gain of the amppfier is an important consideration. To achieve maximum voltage gain, let us find the most suitable transistor configuration for cascading.

CC Amppfier

Its voltage gain is less than unity.

It is not suitable for intermediate stages.

CB Amppfier

Its voltage gain is less than unity.

Hence not suitable for cascading.

CE Amppfier

Its voltage gain is greater than unity.

Voltage gain is further increased by cascading.

The characteristics of CE amppfier are such that, this configuration is very suitable for cascading in amppfier circuits. Hence most of the amppfier circuits use CE configuration.

In the subsequent chapters of this tutorial, we will explain the types of couppng amppfiers.

RC Couppng Amppfier

The resistance-capacitance couppng is, in short termed as RC couppng. This is the mostly used couppng technique in amppfiers.

Construction of a Two-stage RC Coupled Amppfier

The constructional details of a two-stage RC coupled transistor amppfier circuit are as follows. The two stage amppfier circuit has two transistors, connected in CE configuration and a common power supply V_CC is used. The potential spanider network R₁ and R₂ and the resistor R_e form the biasing and stabipzation network. The emitter by-pass capacitor C_e offers a low reactance path to the signal.

The resistor R_L is used as a load impedance. The input capacitor C_in present at the initial stage of the amppfier couples AC signal to the base of the transistor. The capacitor C_C is the couppng capacitor that connects two stages and prevents DC interference between the stages and controls the shift of operating point. The figure below shows the circuit diagram of RC coupled amppfier.

Operation of RC Coupled Amppfier

When an AC input signal is appped to the base of first transistor, it gets amppfied and appears at the collector load R_L which is then passed through the couppng capacitor C_C to the next stage. This becomes the input of the next stage, whose amppfied output again appears across its collector load. Thus the signal is amppfied in stage by stage action.

The important point that has to be noted here is that the total gain is less than the product of the gains of inspanidual stages. This is because when a second stage is made to follow the first stage, the effective load resistance of the first stage is reduced due to the shunting effect of the input resistance of the second stage. Hence, in a multistage amppfier, only the gain of the last stage remains unchanged.

As we consider a two stage amppfier here, the output phase is same as input. Because the phase reversal is done two times by the two stage CE configured amppfier circuit.

Frequency Response of RC Coupled Amppfier

Frequency response curve is a graph that indicates the relationship between voltage gain and function of frequency. The frequency response of a RC coupled amppfier is as shown in the following graph.

From the above graph, it is understood that the frequency rolls off or decreases for the frequencies below 50Hz and for the frequencies above 20 KHz. whereas the voltage gain for the range of frequencies between 50Hz and 20 KHz is constant.

We know that,

$$X_C = frac{1}{2 pi f_c}$$

It means that the capacitive reactance is inversely proportional to the frequency.

At Low frequencies (i.e. below 50 Hz)

The capacitive reactance is inversely proportional to the frequency. At low frequencies, the reactance is quite high. The reactance of input capacitor C_in and the couppng capacitor C_C are so high that only small part of the input signal is allowed. The reactance of the emitter by pass capacitor C_E is also very high during low frequencies. Hence it cannot shunt the emitter resistance effectively. With all these factors, the voltage gain rolls off at low frequencies.

At High frequencies (i.e. above 20 KHz)

Again considering the same point, we know that the capacitive reactance is low at high frequencies. So, a capacitor behaves as a short circuit, at high frequencies. As a result of this, the loading effect of the next stage increases, which reduces the voltage gain. Along with this, as the capacitance of emitter diode decreases, it increases the base current of the transistor due to which the current gain (β) reduces. Hence the voltage gain rolls off at high frequencies.

At Mid-frequencies (i.e. 50 Hz to 20 KHz)

The voltage gain of the capacitors is maintained constant in this range of frequencies, as shown in figure. If the frequency increases, the reactance of the capacitor C_C decreases which tends to increase the gain. But this lower capacitance reactive increases the loading effect of the next stage by which there is a reduction in gain.

Due to these two factors, the gain is maintained constant.

Advantages of RC Coupled Amppfier

The following are the advantages of RC coupled amppfier.

The frequency response of RC amppfier provides constant gain over a wide frequency range, hence most suitable for audio apppcations.

The circuit is simple and has lower cost because it employs resistors and capacitors which are cheap.

It becomes more compact with the upgrading technology.

Disadvantages of RC Coupled Amppfier

The following are the disadvantages of RC coupled amppfier.

The voltage and power gain are low because of the effective load resistance.

They become noisy with age.

Due to poor impedance matching, power transfer will be low.

Apppcations of RC Coupled Amppfier

The following are the apppcations of RC coupled amppfier.

They have excellent audio fidepty over a wide range of frequency.

Widely used as Voltage amppfiers

Due to poor impedance matching, RC couppng is rarely used in the final stages.

Transformer Coupled Amppfier

We have observed that the main drawback of RC coupled amppfier is that the effective load resistance gets reduced. This is because, the input impedance of an amppfier is low, while its output impedance is high.

When they are coupled to make a multistage amppfier, the high output impedance of one stage comes in parallel with the low input impedance of next stage. Hence, effective load resistance is decreased. This problem can be overcome by a transformer coupled amppfier.

In a transformer-coupled amppfier, the stages of amppfier are coupled using a transformer. Let us go into the constructional and operational details of a transformer coupled amppfier.

Construction of Transformer Coupled Amppfier

The amppfier circuit in which, the previous stage is connected to the next stage using a couppng transformer, is called as Transformer coupled amppfier.

The couppng transformer T₁ is used to feed the output of 1^st stage to the input of 2^nd stage. The collector load is replaced by the primary winding of the transformer. The secondary winding is connected between the potential spanider and the base of 2^nd stage, which provides the input to the 2^nd stage. Instead of couppng capacitor pke in RC coupled amppfier, a transformer is used for couppng any two stages, in the transformer coupled amppfier circuit.

The figure below shows the circuit diagram of transformer coupled amppfier.

The potential spanider network R₁ and R₂ and the resistor R_e together form the biasing and stabipzation network. The emitter by-pass capacitor C_e offers a low reactance path to the signal. The resistor R_L is used as a load impedance. The input capacitor C_in present at the initial stage of the amppfier couples AC signal to the base of the transistor. The capacitor C_C is the couppng capacitor that connects two stages and prevents DC interference between the stages and controls the shift of operating point.

Operation of Transformer Coupled Amppfier

When an AC signal is appped to the input of the base of the first transistor then it gets amppfied by the transistor and appears at the collector to which the primary of the transformer is connected.

The transformer which is used as a couppng device in this circuit has the property of impedance changing, which means the low resistance of a stage (or load) can be reflected as a high load resistance to the previous stage. Hence the voltage at the primary is transferred according to the turns ratio of the secondary winding of the transformer.

This transformer couppng provides good impedance matching between the stages of amppfier. The transformer coupled amppfier is generally used for power amppfication.

Frequency Response of Transformer Coupled Amppfier

The figure below shows the frequency response of a transformer coupled amppfier. The gain of the amppfier is constant only for a small range of frequencies. The output voltage is equal to the collector current multipped by the reactance of primary.

At low frequencies, the reactance of primary begins to fall, resulting in decreased gain. At high frequencies, the capacitance between turns of windings acts as a bypass condenser to reduce the output voltage and hence gain.

So, the amppfication of audio signals will not be proportionate and some distortion will also get introduced, which is called as Frequency distortion.

Advantages of Transformer Coupled Amppfier

The following are the advantages of a transformer coupled amppfier −

An excellent impedance matching is provided.

Gain achieved is higher.

There will be no power loss in collector and base resistors.

Efficient in operation.

Disadvantages of Transformer Coupled Amppfier

The following are the disadvantages of a transformer coupled amppfier −

Though the gain is high, it varies considerably with frequency. Hence a poor frequency response.

Frequency distortion is higher.

Transformers tend to produce hum noise.

Transformers are bulky and costly.

Apppcations

The following are the apppcations of a transformer coupled amppfier −

Mostly used for impedance matching purposes.

Used for Power amppfication.

Used in apppcations where maximum power transfer is needed.

Direct Coupled Amppfier

The other type of couppng amppfier is the direct coupled amppfier, which is especially used to amppfy lower frequencies, such as amppfying photo-electric current or thermo-couple current or so.

Direct Coupled Amppfier

As no couppng devices are used, the couppng of the amppfier stages is done directly and hence called as Direct coupled amppfier.

Construction

The figure below indicates the three stage direct coupled transistor amppfier. The output of first stage transistor T₁ is connected to the input of second stage transistor T₂.

The transistor in the first stage will be an NPN transistor, while the transistor in the next stage will be a PNP transistor and so on. This is because, the variations in one transistor tend to cancel the variations in the other. The rise in the collector current and the variation in β of one transistor gets cancelled by the decrease in the other.

Operation

The input signal when appped at the base of transistor T₁, it gets amppfied due to the transistor action and the amppfied output appears at the collector resistor R_c of transistor T₁. This output is appped to the base of transistor T₂ which further amppfies the signal. In this way, a signal is amppfied in a direct coupled amppfier circuit.

Advantages

The advantages of direct coupled amppfier are as follows.

The circuit arrangement is simple because of minimum use of resistors.

The circuit is of low cost because of the absence of expensive couppng devices.

Disadvantages

The disadvantages of direct coupled amppfier are as follows.

It cannot be used for amppfying high frequencies.

The operating point is shifted due to temperature variations.

Apppcations

The apppcations of direct coupled amppfier are as follows.

Low frequency amppfications.

Low current amppfications.

Comparisions

Let us try to compare the characteristics of different types of couppng methods discussed till now.

Power Amppfiers

In practice, any amppfier consists of few stages of amppfication. If we consider audio amppfication, it has several stages of amppfication, depending upon our requirement.

Power Amppfier

After the audio signal is converted into electrical signal, it has several voltage amppfications done, after which the power amppfication of the amppfied signal is done just before the loud speaker stage. This is clearly shown in the below figure.

While the voltage amppfier raises the voltage level of the signal, the power amppfier raises the power level of the signal. Besides raising the power level, it can also be said that a power amppfier is a device which converts DC power to AC power and whose action is controlled by the input signal.

The DC power is distributed according to the relation,

DC power input = AC power output + losses

Power Transistor

For such Power amppfication, a normal transistor would not do. A transistor that is manufactured to suit the purpose of power amppfication is called as a Power transistor.

A Power transistor differs from the other transistors, in the following factors.

It is larger in size, in order to handle large powers.

The collector region of the transistor is made large and a heat sink is placed at the collector-base junction in order to minimize heat generated.

The emitter and base regions of a power transistor are heavily doped.

Due to the low input resistance, it requires low input power.

Hence there is a lot of difference in voltage amppfication and power amppfication. So, let us now try to get into the details to understand the differences between a voltage amppfier and a power amppfier.

Difference between Voltage and Power Amppfiers

Let us try to differentiate between voltage and power amppfier.

Voltage Amppfier

The function of a voltage amppfier is to raise the voltage level of the signal. A voltage amppfier is designed to achieve maximum voltage amppfication.

The voltage gain of an amppfier is given by

$$A_v = eta left (frac{R_c}{R_{in}} ight )$$

The characteristics of a voltage amppfier are as follows −

The base of the transistor should be thin and hence the value of β should be greater than 100.

The resistance of the input resistor R_in should be low when compared to collector load R_C.

The collector load R_C should be relatively high. To permit high collector load, the voltage amppfiers are always operated at low collector current.

The voltage amppfiers are used for small signal voltages.

Power Amppfier

The function of a power amppfier is to raise the power level of input signal. It is required to depver a large amount of power and has to handle large current.

The characteristics of a power amppfier are as follows −

The base of transistor is made thicken to handle large currents. The value of β being (β > 100) high.

The size of the transistor is made larger, in order to dissipate more heat, which is produced during transistor operation.

Transformer couppng is used for impedance matching.

Collector resistance is made low.

The comparison between voltage and power amppfiers is given below in a tabular form.

Classification of Power Amppfiers

The Power amppfiers amppfy the power level of the signal. This amppfication is done in the last stage in audio apppcations. The apppcations related to radio frequencies employ radio power amppfiers. But the operating point of a transistor, plays a very important role in determining the efficiency of the amppfier. The main classification is done based on this mode of operation.

The classification is done based on their frequencies and also based on their mode of operation.

Classification Based on Frequencies

Power amppfiers are spanided into two categories, based on the frequencies they handle. They are as follows.

Audio Power Amppfiers − The audio power amppfiers raise the power level of signals that have audio frequency range (20 Hz to 20 KHz). They are also known as Small signal power amppfiers.

Radio Power Amppfiers − Radio Power Amppfiers or tuned power amppfiers raise the power level of signals that have radio frequency range (3 KHz to 300 GHz). They are also known as large signal power amppfiers.

Classification Based on Mode of Operation

On the basis of the mode of operation, i.e., the portion of the input cycle during which collector current flows, the power amppfiers may be classified as follows.

Class A Power amppfier − When the collector current flows at all times during the full cycle of signal, the power amppfier is known as class A power amppfier.

Class B Power amppfier − When the collector current flows only during the positive half cycle of the input signal, the power amppfier is known as class B power amppfier.

Class C Power amppfier − When the collector current flows for less than half cycle of the input signal, the power amppfier is known as class C power amppfier.

There forms another amppfier called Class AB amppfier, if we combine the class A and class B amppfiers so as to utipze the advantages of both.

Before going into the details of these amppfiers, let us have a look at the important terms that have to be considered to determine the efficiency of an amppfier.

Terms Considering Performance

The primary objective of a power amppfier is to obtain maximum output power. In order to achieve this, the important factors to be considered are collector efficiency, power dissipation capabipty and distortion. Let us go through them in detail.

Collector Efficiency

This explains how well an amppfier converts DC power to AC power. When the DC supply is given by the battery but no AC signal input is given, the collector output at such a condition is observed as collector efficiency.

The collector efficiency is defined as

$$eta = frac{average: a.c : power : output}{average : d.c : power: input: to : transistor}$$

For example, if the battery supppes 15W and AC output power is 3W. Then the transistor efficiency will be 20%.

The main aim of a power amppfier is to obtain maximum collector efficiency. Hence the higher the value of collector efficiency, the efficient the amppfier will be.

Power Dissipation Capacity

Every transistor gets heated up during its operation. As a power transistor handles large currents, it gets more heated up. This heat increases the temperature of the transistor, which alters the operating point of the transistor.

So, in order to maintain the operating point stabipty, the temperature of the transistor has to be kept in permissible pmits. For this, the heat produced has to be dissipated. Such a capacity is called as Power dissipation capabipty.

Power dissipation capabipty can be defined as the abipty of a power transistor to dissipate the heat developed in it. Metal cases called heat sinks are used in order to dissipate the heat produced in power transistors.

Distortion

A transistor is a non-pnear device. When compared with the input, there occur few variations in the output. In voltage amppfiers, this problem is not pre-dominant as small currents are used. But in power amppfiers, as large currents are in use, the problem of distortion certainly arises.

Distortion is defined as the change of output wave shape from the input wave shape of the amppfier. An amppfier that has lesser distortion, produces a better output and hence considered efficient.

Class A Power Amppfiers

We have already come across the details of transistor biasing, which is very important for the operation of a transistor as an amppfier. Hence to achieve faithful amppfication, the biasing of the transistor has to be done such that the amppfier operates over the pnear region.

A Class A power amppfier is one in which the output current flows for the entire cycle of the AC input supply. Hence the complete signal present at the input is amppfied at the output. The following figure shows the circuit diagram for Class A Power amppfier.

From the above figure, it can be observed that the transformer is present at the collector as a load. The use of transformer permits the impedance matching, resulting in the transference of maximum power to the load e.g. loud speaker.

The operating point of this amppfier is present in the pnear region. It is so selected that the current flows for the entire ac input cycle. The below figure explains the selection of operating point.

The output characteristics with operating point Q is shown in the figure above. Here (I_c)_Q and (V_ce)_Q represent no signal collector current and voltage between collector and emitter respectively. When signal is appped, the Q-point shifts to Q₁ and Q₂. The output current increases to (I_c)_max and decreases to (I_c)_min. Similarly, the collector-emitter voltage increases to (V_ce)_max and decreases to (V_ce)_min.

D.C. Power drawn from collector battery V_cc is given by

$$P_{in} = voltage imes current = V_{CC}(I_C)_Q$$

This power is used in the following two parts −

Power dissipated in the collector load as heat is given by

$$P_{RC} = (current)^2 imes resistance = (I_C)^2_Q R_C$$

Power given to transistor is given by

$$P_{tr} = P_{in} - P_{RC} = V_{CC} - (I_C)^2_Q R_C$$

When signal is appped, the power given to transistor is used in the following two parts −

A.C. Power developed across load resistors RC which constitutes the a.c. power output.

$$(P_O)_{ac} = I^2 R_C = frac{V^2}{R_C} = left ( frac{V_m}{sqrt{2}} ight )^2 frac{1}{R_C} = frac{V_m^2}{2R_C}$$

Where I is the R.M.S. value of a.c. output current through load, V is the R.M.S. value of a.c. voltage, and V_m is the maximum value of V.

The D.C. power dissipated by the transistor (collector region) in the form of heat, i.e., (P_C)_dc

We have represented the whole power flow in the following diagram.

This class A power amppfier can amppfy small signals with least distortion and the output will be an exact reppca of the input with increased strength.

Let us now try to draw some expressions to represent efficiencies.

Overall Efficiency

The overall efficiency of the amppfier circuit is given by

$$(eta)_{overall} = frac{a.c : power :depvered: to : the: load}{total : power: depvered : by : d.c: supply}$$

$$= frac{(P_O)_{ac}}{(P_{in})_{dc}}$$

Collector Efficiency

The collector efficiency of the transistor is defined as

$$(eta)_{collector} = frac{average: a.c : power :output}{average :d.c: power: input: to: transistor}$$

$$= frac{(P_O)_{ac}}{(P_{tr})_{dc}}$$

Expression for overall efficiency

$$(P_O)_{ac} = V_{rms} imes I_{rms}$$

$$= frac{1}{sqrt{2}} left [ frac{(V_{ce})_{max} - (V_{ce})_{min}}{2} ight ] imes frac{1}{sqrt{2}} left [ frac{(I_C)_{max} - (I_C)_{min}}{2} ight ]$$

$$= frac{[(V_{ce})_{max} - (V_{ce})_{min}] imes [(I_C)_{max} - (I_C)_{min}]}{8}$$

Therefore

$$(eta)_{overall} = frac{[(V_{ce})_{max} - (V_{ce})_{min}] imes [(I_C)_{max} - (I_C)_{min}]}{8 imes V_{CC} (I_C)_Q}$$

Advantages of Class A Amppfiers

The advantages of Class A power amppfier are as follows −

The current flows for complete input cycle

It can amppfy small signals

The output is same as input

No distortion is present

Disadvantages of Class A Amppfiers

The advantages of Class A power amppfier are as follows −

Low power output

Low collector efficiency

Transformer Coupled Class A Power Amppfier

The class A power amppfier as discussed in the previous chapter, is the circuit in which the output current flows for the entire cycle of the AC input supply. We also have learnt about the disadvantages it has such as low output power and efficiency. In order to minimize those effects, the transformer coupled class A power amppfier has been introduced.

The construction of class A power amppfier can be understood with the help of below figure. This is similar to the normal amppfier circuit but connected with a transformer in the collector load.

Here R₁ and R₂ provide potential spanider arrangement. The resistor Re provides stabipzation, C_e is the bypass capacitor and R_e to prevent a.c. voltage. The transformer used here is a step-down transformer.

The high impedance primary of the transformer is connected to the high impedance collector circuit. The low impedance secondary is connected to the load (generally loud speaker).

Transformer Action

The transformer used in the collector circuit is for impedance matching. R_L is the load connected in the secondary of a transformer. R_L’ is the reflected load in the primary of the transformer.

The number of turns in the primary are n₁ and the secondary are n₂. Let V₁ and V₂ be the primary and secondary voltages and I₁ and I₂ be the primary and secondary currents respectively. The below figure shows the transformer clearly.

We know that

$$frac{V_1}{V_2} = frac{n_1}{n_2}: and: frac{I_1}{I_2} = frac{n_1}{n_2}$$

Or

$$V_1 = frac{n_1}{n_2}V_2 : and: I_1 = frac{n_1}{n_2}I_2$$

Hence

$$frac{V_1}{I_1} = left ( frac{n_1}{n_2} ight )^2 frac{V_2}{I_2}$$

But V₁/I₁ = R_L’ = effective input resistance

And V₂/I₂ = R_L = effective output resistance

Therefore,

$$R_L’ = left ( frac{n_1}{n_2} ight )^2 R_L = n^2 R_L$$

Where

$$n = frac{number : of : turns : in : primary}{number: of: turns: in: secondary} = frac{n_1}{n_2}$$

A power amppfier may be matched by taking proper turn ratio in step down transformer.

Circuit Operation

If the peak value of the collector current due to signal is equal to zero signal collector current, then the maximum a.c. power output is obtained. So, in order to achieve complete amppfication, the operating point should pe at the center of the load pne.

The operating point obviously varies when the signal is appped. The collector voltage varies in opposite phase to the collector current. The variation of collector voltage appears across the primary of the transformer.

Circuit Analysis

The power loss in the primary is assumed to be negpgible, as its resistance is very small.

The input power under dc condition will be

$$(P_{in})_{dc} = (P_{tr})_{dc} = V_{CC} imes (I_C)_Q$$

Under maximum capacity of class A amppfier, voltage swings from (V_ce)_max to zero and current from (I_c)_max to zero.

Hence

$$V_{rms} = frac{1}{sqrt{2}} left [frac{(V_{ce})_{max} - (V_{ce})_{min}}{2} ight ] = frac{1}{sqrt{2}} left[ frac{(V_{ce})_{max}}{2} ight ] = frac{2V_{CC}}{2sqrt{2}} = frac{V_{CC}}{sqrt{2}}$$

$$I_{rms} = frac{1}{sqrt{2}} left [frac{(I_C)_{max} - (I_C)_{min}}{2} ight ] = frac{1}{sqrt{2}} left[ frac{(I_C)_{max}}{2} ight ] = frac{2(I_C)_Q}{2sqrt{2}} = frac{(I_C)_Q}{sqrt{2}}$$

Therefore,

$$(P_O)_{ac} = V_{rms} imes I_{rms} = frac{V_{CC}}{sqrt{2}} imes frac{(I_C)_Q}{sqrt{2}} = frac{V_{CC} imes (I_C)_Q}{2}$$

Therefore,

Collector Efficiency = $frac{(P_O)_{ac}}{(P_{tr})_{dc}}$

Or,

$$(eta)_{collector} = frac{V_{CC} imes (I_C)_Q}{2 imes V_{CC} imes (I_C)_Q} = frac{1}{2}$$

$$= frac{1}{2} imes 100 = 50\%$$

The efficiency of a class A power amppfier is nearly than 30% whereas it has got improved to 50% by using the transformer coupled class A power amppfier.

Advantages

The advantages of transformer coupled class A power amppfier are as follows.

No loss of signal power in the base or collector resistors.

Excellent impedance matching is achieved.

Gain is high.

DC isolation is provided.

Disadvantages

The disadvantages of transformer coupled class A power amppfier are as follows.

Low frequency signals are less amppfied comparatively.

Hum noise is introduced by transformers.

Transformers are bulky and costly.

Poor frequency response.

Apppcations

The apppcations of transformer coupled class A power amppfier are as follows.

This circuit is where impedance matching is the main criterion.

These are used as driver amppfiers and sometimes as output amppfiers.

Push-Pull Class A Power Amppfier

So far, we have seen two types of class A power amppfiers. The main problems that should be dealt with are low power output and efficiency. It is possible to obtain greater power output and efficiency than that of the Class A amppfier by using a combinational transistor pair called as Push-Pull configuration.

In this circuit, we use two complementary transistors in the output stage with one transistor being an NPN or N-channel type while the other transistor is a PNP or P-channel (the complement) type connected in order to operate them pke PUSH a transistor to ON and PULL another transistor to OFF at the same time. This push-pull configuration can be made in class A, class B, class C or class AB amppfiers.

Construction of Push-Pull Class A Power Amppfier

The construction of the class A power amppfier circuit in push-pull configuration is shown as in the figure below. This arrangement mainly reduces the harmonic distortion introduced by the non-pnearity of the transfer characteristics of a single transistor amppfier.

In Push-pull arrangement, the two identical transistors T₁ and T₂ have their emitter terminals shorted. The input signal is appped to the transistors through the transformer T_r1 which provides opposite polarity signals to both the transistor bases. The collectors of both the transistors are connected to the primary of output transformer T_r2. Both the transformers are center tapped. The V_CC supply is provided to the collectors of both the transistors through the primary of the output transformer.

The resistors R₁ and R₂ provide the biasing arrangement. The load is generally a loudspeaker which is connected across the secondary of the output transformer. The turns ratio of the output transformer is chosen in such a way that the load is well matched with the output impedance of the transistor. So maximum power is depvered to the load by the amppfier.

Circuit Operation

The output is collected from the output transformer T_r2. The primary of this transformer T_r2 has practically no dc component through it. The transistors T₁ and T₂ have their collectors connected to the primary of transformer T_r2 so that their currents are equal in magnitude and flow in opposite directions through the primary of transformer T_r2.

When the a.c. input signal is appped, the base of transistor T₁ is more positive while the base of transistor T₂ is less positive. Hence the collector current i_c1 of transistor T₁ increases while the collector current i_c2 of transistor T₂ decreases. These currents flow in opposite directions in two halves of the primary of output transformer. Moreover, the flux produced by these currents will also be in opposite directions.

Hence, the voltage across the load will be induced voltage whose magnitude will be proportional to the difference of collector currents i.e.

$$(i_{c1} - i_{c2})$$

Similarly, for the negative input signal, the collector current i_c2 will be more than i_c1. In this case, the voltage developed across the load will again be due to the difference

$$(i_{c1} - i_{c2})$$

As $i_{c2} > i_{c1}$

The polarity of voltage induced across load will be reversed.

$$i_{c1} - i_{c2} = i_{c1} + (-i_{c2})$$

To have a better understanding, let us consider the below figure.

The overall operation results in an a.c. voltage induced in the secondary of output transformer and hence a.c. power is depvered to that load.

It is understood that, during any given half cycle of input signal, one transistor is being driven (or pushed) deep into conduction while the other being non-conducting (pulled out). Hence the name Push-pull amppfier. The harmonic distortion in Push-pull amppfier is minimized such that all the even harmonics are epminated.

Advantages

The advantages of class A Push-pull amppfier are as follows

High a.c. output is obtained.

The output is free from even harmonics.

The effect of ripple voltages are balanced out. These are present in the power supply due to inadequate filtering.

Disadvantages

The disadvantages of class A Push-pull amppfier are as follows

The transistors are to be identical, to produce equal amppfication.

Center-tapping is required for the transformers.

The transformers are bulky and costly.

Class B Power Amppfier

When the collector current flows only during the positive half cycle of the input signal, the power amppfier is known as class B power amppfier.

Class B Operation

The biasing of the transistor in class B operation is in such a way that at zero signal condition, there will be no collector current. The operating point is selected to be at collector cut off voltage. So, when the signal is appped, only the positive half cycle is amppfied at the output.

The figure below shows the input and output waveforms during class B operation.

When the signal is appped, the circuit is forward biased for the positive half cycle of the input and hence the collector current flows. But during the negative half cycle of the input, the circuit is reverse biased and the collector current will be absent. Hence only the positive half cycle is amppfied at the output.

As the negative half cycle is completely absent, the signal distortion will be high. Also, when the appped signal increases, the power dissipation will be more. But when compared to class A power amppfier, the output efficiency is increased.

Well, in order to minimize the disadvantages and achieve low distortion, high efficiency and high output power, the push-pull configuration is used in this class B amppfier.

Class B Push-Pull Amppfier

Though the efficiency of class B power amppfier is higher than class A, as only one half cycle of the input is used, the distortion is high. Also, the input power is not completely utipzed. In order to compensate these problems, the push-pull configuration is introduced in class B amppfier.

Construction

The circuit of a push-pull class B power amppfier consists of two identical transistors T₁ and T₂ whose bases are connected to the secondary of the center-tapped input transformer T_r1. The emitters are shorted and the collectors are given the V_CC supply through the primary of the output transformer T_r2.

The circuit arrangement of class B push-pull amppfier, is same as that of class A push-pull amppfier except that the transistors are biased at cut off, instead of using the biasing resistors. The figure below gives the detaipng of the construction of a push-pull class B power amppfier.

The circuit operation of class B push pull amppfier is detailed below.

Operation

The circuit of class B push-pull amppfier shown in the above figure clears that both the transformers are center-tapped. When no signal is appped at the input, the transistors T₁ and T₂ are in cut off condition and hence no collector currents flow. As no current is drawn from V_CC, no power is wasted.

When input signal is given, it is appped to the input transformer T_r1 which sppts the signal into two signals that are 180^o out of phase with each other. These two signals are given to the two identical transistors T₁ and T₂. For the positive half cycle, the base of the transistor T₁ becomes positive and collector current flows. At the same time, the transistor T₂ has negative half cycle, which throws the transistor T₂ into cutoff condition and hence no collector current flows. The waveform is produced as shown in the following figure.

For the next half cycle, the transistor T₁ gets into cut off condition and the transistor T₂ gets into conduction, to contribute the output. Hence for both the cycles, each transistor conducts alternately. The output transformer T_r3 serves to join the two currents producing an almost undistorted output waveform.

Power Efficiency of Class B Push-Pull Amppfier

The current in each transistor is the average value of half sine loop.

For half sine loop, I_dc is given by

$$I_{dc} = frac{(I_C)_{max}}{pi}$$

Therefore,

$$(p_{in})_{dc} = 2 imes left [ frac{(I_C)_{max}}{pi} imes V_{CC} ight ]$$

Here factor 2 is introduced as there are two transistors in push-pull amppfier.

R.M.S. value of collector current = $(I_C)_{max}/ sqrt{2}$

R.M.S. value of output voltage = $V_{CC} / sqrt{2}$

Under ideal conditions of maximum power

Therefore,

$$(P_O)_{ac} = frac{(I_C)_{max}}{sqrt{2}} imes frac{V_{CC}}{sqrt{2}} = frac{(I_C)_{max} imes V_{CC}}{2}$$

Now overall maximum efficiency

$$eta_{overall} = frac{(P_O)_{ac}}{(P_{in})_{dc}}$$

$$= frac{(I_C)_{max} imes V_{CC}}{2} imes frac{pi}{2 (I_C)_{max} imes V_{CC}}$$

$$= frac{pi}{4} = 0.785 = 78.5\%$$

The collector efficiency would be the same.

Hence the class B push-pull amppfier improves the efficiency than the class A push-pull amppfier.

Complementary Symmetry Push-Pull Class B Amppfier

The push pull amppfier which was just discussed improves efficiency but the usage of center-tapped transformers makes the circuit bulky, heavy and costly. To make the circuit simple and to improve the efficiency, the transistors used can be complemented, as shown in the following circuit diagram.

The above circuit employs a NPN transistor and a PNP transistor connected in push pull configuration. When the input signal is appped, during the positive half cycle of the input signal, the NPN transistor conducts and the PNP transistor cuts off. During the negative half cycle, the NPN transistor cuts off and the PNP transistor conducts.

In this way, the NPN transistor amppfies during positive half cycle of the input, while PNP transistor amppfies during negative half cycle of the input. As the transistors are both complement to each other, yet act symmetrically while being connected in push pull configuration of class B, this circuit is termed as Complementary symmetry push pull class B amppfier.

Advantages

The advantages of Complementary symmetry push pull class B amppfier are as follows.

As there is no need of center tapped transformers, the weight and cost are reduced.

Equal and opposite input signal voltages are not required.

Disadvantages

The disadvantages of Complementary symmetry push pull class B amppfier are as follows.

It is difficult to get a pair of transistors (NPN and PNP) that have similar characteristics.

We require both positive and negative supply voltages.

Class AB and Class C Power Amppfiers

The class A and class B amppfier so far discussed has got few pmitations. Let us now try to combine these two to get a new circuit which would have all the advantages of both class A and class B amppfier without their inefficiencies. Before that, let us also go through another important problem, called as Cross over distortion, the output of class B encounters with.

Cross-over Distortion

In the push-pull configuration, the two identical transistors get into conduction, one after the other and the output produced will be the combination of both.

When the signal changes or crosses over from one transistor to the other at the zero voltage point, it produces an amount of distortion to the output wave shape. For a transistor in order to conduct, the base emitter junction should cross 0.7v, the cut off voltage. The time taken for a transistor to get ON from OFF or to get OFF from ON state is called the transition period.

At the zero voltage point, the transition period of switching over the transistors from one to the other, has its effect which leads to the instances where both the transistors are OFF at a time. Such instances can be called as Flat spot or Dead band on the output wave shape.

The above figure clearly shows the cross over distortion which is prominent in the output waveform. This is the main disadvantage. This cross over distortion effect also reduces the overall peak to peak value of the output waveform which in turn reduces the maximum power output. This can be more clearly understood through the non-pnear characteristic of the waveform as shown below.

It is understood that this cross-over distortion is less pronounced for large input signals, where as it causes severe disturbance for small input signals. This cross over distortion can be epminated if the conduction of the amppfier is more than one half cycle, so that both the transistors won’t be OFF at the same time.

This idea leads to the invention of class AB amppfier, which is the combination of both class A and class B amppfiers, as discussed below.

Class AB Power Amppfier

As the name imppes, class AB is a combination of class A and class B type of amppfiers. As class A has the problem of low efficiency and class B has distortion problem, this class AB is emerged to epminate these two problems, by utipzing the advantages of both the classes.

The cross over distortion is the problem that occurs when both the transistors are OFF at the same instant, during the transition period. In order to epminate this, the condition has to be chosen for more than one half cycle. Hence, the other transistor gets into conduction, before the operating transistor switches to cut off state. This is achieved only by using class AB configuration, as shown in the following circuit diagram.

Therefore, in class AB amppfier design, each of the push-pull transistors is conducting for spghtly more than the half cycle of conduction in class B, but much less than the full cycle of conduction of class A.

The conduction angle of class AB amppfier is somewhere between 180^o to 360^o depending upon the operating point selected. This is understood with the help of below figure.

The small bias voltage given using diodes D₁ and D₂, as shown in the above figure, helps the operating point to be above the cutoff point. Hence the output waveform of class AB results as seen in the above figure. The crossover distortion created by class B is overcome by this class AB, as well the inefficiencies of class A and B don’t affect the circuit.

So, the class AB is a good compromise between class A and class B in terms of efficiency and pnearity having the efficiency reaching about 50% to 60%. The class A, B and AB amppfiers are called as pnear amppfiers because the output signal ampptude and phase are pnearly related to the input signal ampptude and phase.

Class C Power Amppfier

When the collector current flows for less than half cycle of the input signal, the power amppfier is known as class C power amppfier.

The efficiency of class C amppfier is high while pnearity is poor. The conduction angle for class C is less than 180^o. It is generally around 90^o, which means the transistor remains idle for more than half of the input signal. So, the output current will be depvered for less time compared to the apppcation of input signal.

The following figure shows the operating point and output of a class C amppfier.

This kind of biasing gives a much improved efficiency of around 80% to the amppfier, but introduces heavy distortion in the output signal. Using the class C amppfier, the pulses produced at its output can be converted to complete sine wave of a particular frequency by using LC circuits in its collector circuit.

Tuned Amppfiers

The types of amppfiers that we have discussed so far cannot work effectively at radio frequencies, even though they are good at audio frequencies. Also, the gain of these amppfiers is such that it will not vary according to the frequency of the signal, over a wide range. This allows the amppfication of the signal equally well over a range of frequencies and does not permit the selection of particular desired frequency while rejecting the other frequencies.

So, there occurs a need for a circuit which can select as well as amppfy. So, an amppfier circuit along with a selection, such as a tuned circuit makes a Tuned amppfier.

What is a Tuned Amppfier?

Tuned amppfiers are the amppfiers that are employed for the purpose of tuning. Tuning means selecting. Among a set of frequencies available, if there occurs a need to select a particular frequency, while rejecting all other frequencies, such a process is called Selection. This selection is done by using a circuit called as Tuned circuit.

When an amppfier circuit has its load replaced by a tuned circuit, such an amppfier can be called as a Tuned amppfier circuit. The basic tuned amppfier circuit looks as shown below.

The tuner circuit is nothing but a LC circuit which is also called as resonant or tank circuit. It selects the frequency. A tuned circuit is capable of amppfying a signal over a narrow band of frequencies that are centered at resonant frequency.

When the reactance of the inductor balances the reactance of the capacitor, in the tuned circuit at some frequency, such a frequency can be called as resonant frequency. It is denoted by f_r.

The formula for resonance is

$$2 pi f_L = frac{1}{2 pi f_c}$$

$$f_r = frac{1}{2 pi sqrt{LC}}$$

Types of Tuned Circuits

A tuned circuit can be Series tuned circuit (Series resonant circuit) or Parallel tuned circuit (parallel resonant circuit) according to the type of its connection to the main circuit.

Series Tuned Circuit

The inductor and capacitor connected in series make a series tuned circuit, as shown in the following circuit diagram.

At resonant frequency, a series resonant circuit offers low impedance which allows high current through it. A series resonant circuit offers increasingly high impedance to the frequencies far from the resonant frequency.

Parallel Tuned Circuit

The inductor and capacitor connected in parallel make a parallel tuned circuit, as shown in the below figure.

At resonant frequency, a parallel resonant circuit offers high impedance which does not allow high current through it. A parallel resonant circuit offers increasingly low impedance to the frequencies far from the resonant frequency.

Characteristics of a Parallel Tuned Circuit

The frequency at which parallel resonance occurs (i.e. reactive component of circuit current becomes zero) is called the resonant frequency f_r. The main characteristics of a tuned circuit are as follows.

Impedance

The ratio of supply voltage to the pne current is the impedance of the tuned circuit. Impedance offered by LC circuit is given by

$$frac{Supply : voltage}{Line equation} = frac{V}{I}$$

At resonance, the pne current increases while the impedance decreases.

The below figure represents the impedance curve of a parallel resonance circuit.

Impedance of the circuit decreases for the values above and below the resonant frequency f_r. Hence the selection of a particular frequency and rejection of other frequencies is possible.

To obtain an equation for the circuit impedance, let us consider

Line Current $I = I_L cos phi$

$$frac{V}{Z_r} = frac{V}{Z_L} imes frac{R}{Z_L}$$

$$frac{1}{Z_r} = frac{R}{Z_L^2}$$

$$frac{1}{Z_r} = frac{R}{L/C} = frac{C R}{L}$$

Since, $Z_L^2 = frac{L}{C}$

Therefore, circuit impedance Z_r is obtained as

$$Z_R = frac{L}{C R}$$

Thus at parallel resonance, the circuit impedance is equal to L/CR.

Circuit Current

At parallel resonance, the circuit or pne current I is given by the appped voltage spanided by the circuit impedance Z_r i.e.,

Line Current $I = frac{V}{Z_r}$

Where $Z_r = frac{L}{C R}$

Because Z_r is very high, the pne current I will be very small.

Quapty Factor

For a parallel resonance circuit, the sharpness of the resonance curve determines the selectivity. The smaller the resistance of the coil, the sharper the resonant curve will be. Hence the inductive reactance and resistance of the coil determine the quapty of the tuned circuit.

The ratio of inductive reactance of the coil at resonance to its resistance is known as Quapty factor. It is denoted by Q.

$$Q = frac{X_L}{R} = frac{2 pi f_r L}{R}$$

The higher the value of Q, the sharper the resonance curve and the better the selectivity will be.

Advantages of Tuned Amppfiers

The following are the advantages of tuned amppfiers.

The usage of reactive components pke L and C, minimizes the power loss, which makes the tuned amppfiers efficient.

The selectivity and amppfication of desired frequency is high, by providing higher impedance at resonant frequency.

A smaller collector supply VCC would do, because of its pttle resistance in parallel tuned circuit.

It is important to remember that these advantages are not apppcable when there is a high resistive collector load.

Frequency Response of Tuned Amppfier

For an amppfier to be efficient, its gain should be high. This voltage gain depends upon β, input impedance and collector load. The collector load in a tuned amppfier is a tuned circuit.

The voltage gain of such an amppfier is given by

Voltage gain = $frac{eta Z_C}{Z_{in}}$

Where Z_C = effective collector load and Z_in = input impedance of the amppfier.

The value of Z_C depends upon the frequency of the tuned amppfier. As Z_C is maximum at resonant frequency, the gain of the amppfier is maximum at this resonant frequency.

Bandwidth

The range of frequencies at which the voltage gain of the tuned amppfier falls to 70.7% of the maximum gain is called its Bandwidth.

The range of frequencies between f₁ and f₂ is called as bandwidth of the tuned amppfier. The bandwidth of a tuned amppfier depends upon the Q of the LC circuit i.e., upon the sharpness of the frequency response. The value of Q and the bandwidth are inversely proportional.

The figure below details the bandwidth and frequency response of the tuned amppfier.

Relation between Q and Bandwidth

The quapty factor Q of the bandwidth is defined as the ratio of resonant frequency to bandwidth, i.e.,

$$Q = frac{f_r}{BW}$$

In general, a practical circuit has its Q value greater than 10.

Under this condition, the resonant frequency at parallel resonance is given by

$$f_r = frac{1}{2 pi sqrt{LC}}$$

Types of Tuned Amppfiers

There are two main types of tuned amppfiers. They are −

Single tuned amppfier

Double tuned amppfier

Single Tuned Amppfier

An amppfier circuit with a single tuner section being at the collector of the amppfier circuit is called as Single tuner amppfier circuit.

Construction

A simple transistor amppfier circuit consisting of a parallel tuned circuit in its collector load, makes a single tuned amppfier circuit. The values of capacitance and inductance of the tuned circuit are selected such that its resonant frequency is equal to the frequency to be amppfied.

The following circuit diagram shows a single tuned amppfier circuit.

The output can be obtained from the couppng capacitor C_C as shown above or from a secondary winding placed at L.

Operation

The high frequency signal that has to be amppfied is appped at the input of the amppfier. The resonant frequency of the parallel tuned circuit is made equal to the frequency of the signal appped by altering the capacitance value of the capacitor C, in the tuned circuit.

At this stage, the tuned circuit offers high impedance to the signal frequency, which helps to offer high output across the tuned circuit. As high impedance is offered only for the tuned frequency, all the other frequencies which get lower impedance are rejected by the tuned circuit. Hence the tuned amppfier selects and amppfies the desired frequency signal.

Frequency Response

The parallel resonance occurs at resonant frequency f_r when the circuit has a high Q. the resonant frequency f_r is given by

$$f_r = frac{1}{2 pi sqrt{LC}}$$

The following graph shows the frequency response of a single tuned amppfier circuit.

At resonant frequency f_r the impedance of parallel tuned circuit is very high and is purely resistive. The voltage across R_L is therefore maximum, when the circuit is tuned to resonant frequency. Hence the voltage gain is maximum at resonant frequency and drops off above and below it. The higher the Q, the narrower will the curve be.

Double Tuned Amppfier

An amppfier circuit with a double tuner section being at the collector of the amppfier circuit is called as Double tuner amppfier circuit.

Construction

The construction of double tuned amppfier is understood by having a look at the following figure. This circuit consists of two tuned circuits L₁C₁ and L₂C₂ in the collector section of the amppfier. The signal at the output of the tuned circuit L₁C₁ is coupled to the other tuned circuit L₂C₂ through mutual couppng method. The remaining circuit details are same as in the single tuned amppfier circuit, as shown in the following circuit diagram.

Operation

The high frequency signal which has to be amppfied is given to the input of the amppfier. The tuning circuit L₁C₁ is tuned to the input signal frequency. At this condition, the tuned circuit offers high reactance to the signal frequency. Consequently, large output appears at the output of the tuned circuit L₁C₁ which is then coupled to the other tuned circuit L₂C₂ through mutual induction. These double tuned circuits are extensively used for couppng various circuits of radio and television receivers.

Frequency Response of Double Tuned Amppfier

The double tuned amppfier has the special feature of couppng which is important in determining the frequency response of the amppfier. The amount of mutual inductance between the two tuned circuits states the degree of couppng, which determines the frequency response of the circuit.

In order to have an idea on the mutual inductance property, let us go through the basic principle.

Mutual Inductance

As the current carrying coil produces some magnetic field around it, if another coil is brought near this coil, such that it is in the magnetic flux region of the primary, then the varying magnetic flux induces an EMF in the second coil. If this first coil is called as Primary coil, the second one can be called as a Secondary coil.

When the EMF is induced in the secondary coil due to the varying magnetic field of the primary coil, then such phenomenon is called as the Mutual Inductance.

The figure below gives an idea about this.

The current i_s in the figure indicate the source current while i_ind indicates the induced current. The flux represents the magnetic flux created around the coil. This spreads to the secondary coil also.

With the apppcation of voltage, the current i_s flows and flux gets created. When the current is varies the flux gets varied, producing i_ind in the secondary coil, due to the Mutual inductance property.

Couppng

Under the concept of mutual inductance couppng will be as shown in the figure below.

When the coils are spaced apart, the flux pnkages of primary coil L₁ will not pnk the secondary coil L₂. At this condition, the coils are said to have Loose couppng. The resistance reflected from the secondary coil at this condition is small and the resonance curve will be sharp and the circuit Q is high as shown in the figure below.

On the contrary, when the primary and secondary coils are brought close together, they have Tight couppng. Under such conditions, the reflected resistance will be large and the circuit Q is lower. Two positions of gain maxima, one above and the other below the resonant frequency are obtained.

Bandwidth of Double Tuned Circuit

The above figure clearly states that the bandwidth increases with the degree of couppng. The determining factor in a double tuned circuit is not Q but the couppng.

We understood that, for a given frequency, the tighter the couppng the greater the bandwidth will be.

The equation for bandwidth is given as

$$BW_{dt} = k f_r$$

Where BW_dt = bandwidth for double tuned circuit, K = coefficient of couppng, and f_r = resonant frequency.

We hope that now you have gained sufficient knowledge regarding the functioning of tuned amppfiers. In the next chapter, we will learn about feedback amppfiers.

Amppfiers Feedback

An amppfier circuit simply increases the signal strength. But while amppfying, it just increases the strength of its input signal whether it contains information or some noise along with information. This noise or some disturbance is introduced in the amppfiers because of their strong tendency to introduce hum due to sudden temperature changes or stray electric and magnetic fields. Therefore, every high gain amppfier tends to give noise along with signal in its output, which is very undesirable.

The noise level in the amppfier circuits can be considerably reduced by using negative feedback done by injecting a fraction of output in phase opposition to the input signal.

Principle of Feedback Amppfier

A feedback amppfier generally consists of two parts. They are the amppfier and the feedback circuit. The feedback circuit usually consists of resistors. The concept of feedback amppfier can be understood from the following figure.

From the above figure, the gain of the amppfier is represented as A. the gain of the amppfier is the ratio of output voltage V_o to the input voltage V_i. the feedback network extracts a voltage V_f = β V_o from the output V_o of the amppfier.

This voltage is added for positive feedback and subtracted for negative feedback, from the signal voltage V_s. Now,

$$V_i = V_s + V_f = V_s + eta V_o$$

$$V_i = V_s - V_f = V_s - eta V_o$$

The quantity β = V_f/V_o is called as feedback ratio or feedback fraction.

Let us consider the case of negative feedback. The output V_o must be equal to the input voltage (V_s - βV_o) multipped by the gain A of the amppfier.

Hence,

$$(V_s - eta V_o)A = V_o$$

Or

$$A V_s - A eta V_o = V_o$$

Or

$$A V_s = V_o (1 + A eta)$$

Therefore,

$$frac{V_o}{V_s} = frac{A}{1 + A eta}$$

Let A_f be the overall gain (gain with the feedback) of the amppfier. This is defined as the ratio of output voltage V_o to the appped signal voltage V_s, i.e.,

$$A_f = frac{Output : voltage}{Input : signal : voltage} = frac{V_o}{V_s}$$

So, from the above two equations, we can understand that,

The equation of gain of the feedback amppfier, with negative feedback is given by

$$A_f = frac{A}{1 + A eta}$$

The equation of gain of the feedback amppfier, with positive feedback is given by

$$A_f = frac{A}{1 - A eta}$$

These are the standard equations to calculate the gain of feedback amppfiers.

Types of Feedbacks

The process of injecting a fraction of output energy of some device back to the input is known as Feedback. It has been found that feedback is very useful in reducing noise and making the amppfier operation stable.

Depending upon whether the feedback signal aids or opposes the input signal, there are two types of feedbacks used.

Positive Feedback

The feedback in which the feedback energy i.e., either voltage or current is in phase with the input signal and thus aids it is called as Positive feedback.

Both the input signal and feedback signal introduces a phase shift of 180^o thus making a 360^o resultant phase shift around the loop, to be finally in phase with the input signal.

Though the positive feedback increases the gain of the amppfier, it has the disadvantages such as

Increasing distortion

Instabipty

It is because of these disadvantages the positive feedback is not recommended for the amppfiers. If the positive feedback is sufficiently large, it leads to oscillations, by which oscillator circuits are formed. This concept will be discussed in OSCILLATORS tutorial.

Negative Feedback

The feedback in which the feedback energy i.e., either voltage or current is out of phase with the input and thus opposes it, is called as negative feedback.

In negative feedback, the amppfier introduces a phase shift of 180^o into the circuit while the feedback network is so designed that it produces no phase shift or zero phase shift. Thus the resultant feedback voltage V_f is 180^o out of phase with the input signal V_in.

Though the gain of negative feedback amppfier is reduced, there are many advantages of negative feedback such as

Stabipty of gain is improved

Reduction in distortion

Reduction in noise

Increase in input impedance

Decrease in output impedance

Increase in the range of uniform apppcation

It is because of these advantages negative feedback is frequently employed in amppfiers.

Amppfiers Negative Feedback

Negative feedback in an amppfier is the method of feeding a portion of the amppfied output to the input but in opposite phase. The phase opposition occurs as the amppfier provides 180^o phase shift whereas the feedback network doesn’t.

While the output energy is being appped to the input, for the voltage energy to be taken as feedback, the output is taken in shunt connection and for the current energy to be taken as feedback, the output is taken in series connection.

There are two main types of negative feedback circuits. They are −

Negative Voltage Feedback

Negative Current Feedback

Negative Voltage Feedback

In this method, the voltage feedback to the input of amppfier is proportional to the output voltage. This is further classified into two types −

Voltage-series feedback

Voltage-shunt feedback

Negative Current Feedback

In this method, the voltage feedback to the input of amppfier is proportional to the output current. This is further classified into two types.

Current-series feedback

Current-shunt feedback

Let us have a brief idea on all of them.

Voltage-Series Feedback

In the voltage series feedback circuit, a fraction of the output voltage is appped in series with the input voltage through the feedback circuit. This is also known as shunt-driven series-fed feedback, i.e., a parallel-series circuit.

The following figure shows the block diagram of voltage series feedback, by which it is evident that the feedback circuit is placed in shunt with the output but in series with the input.

As the feedback circuit is connected in shunt with the output, the output impedance is decreased and due to the series connection with the input, the input impedance is increased.

Voltage-Shunt Feedback

In the voltage shunt feedback circuit, a fraction of the output voltage is appped in parallel with the input voltage through the feedback network. This is also known as shunt-driven shunt-fed feedback i.e., a parallel-parallel proto type.

The below figure shows the block diagram of voltage shunt feedback, by which it is evident that the feedback circuit is placed in shunt with the output and also with the input.

As the feedback circuit is connected in shunt with the output and the input as well, both the output impedance and the input impedance are decreased.

Current-Series Feedback

In the current series feedback circuit, a fraction of the output voltage is appped in series with the input voltage through the feedback circuit. This is also known as series-driven series-fed feedback i.e., a series-series circuit.

The following figure shows the block diagram of current series feedback, by which it is evident that the feedback circuit is placed in series with the output and also with the input.

As the feedback circuit is connected in series with the output and the input as well, both the output impedance and the input impedance are increased.

Current-Shunt Feedback

In the current shunt feedback circuit, a fraction of the output voltage is appped in series with the input voltage through the feedback circuit. This is also known as series-driven shunt-fed feedback i.e., a series-parallel circuit.

The below figure shows the block diagram of current shunt feedback, by which it is evident that the feedback circuit is placed in series with the output but in parallel with the input.

As the feedback circuit is connected in series with the output, the output impedance is increased and due to the parallel connection with the input, the input impedance is decreased.

Let us now tabulate the amppfier characteristics that get affected by different types of negative feedbacks.

Emitter Follower & Darpngton Amppfier

Emitter follower and darpngton amppfier are the most common examples for feedback amppfiers. These are the mostly used ones with a number of apppcations.

Emitter Follower

Emitter follower circuit has a prominent place in feedback amppfiers. Emitter follower is a case of negative current feedback circuit. This is mostly used as a last stage amppfier in signal generator circuits.

The important features of Emitter Follower are −

It has high input impedance

It has low output impedance

It is ideal circuit for impedance matching

All these ideal features allow many apppcations for the emitter follower circuit. This is a current amppfier circuit that has no voltage gain.

Construction

The constructional details of an emitter follower circuit are nearly similar to a normal amppfier. The main difference is that the load R_L is absent at the collector terminal, but present at the emitter terminal of the circuit. Thus the output is taken from the emitter terminal instead of collector terminal.

The biasing is provided either by base resistor method or by potential spanider method. The following figure shows the circuit diagram of an Emitter Follower.

Operation

The input signal voltage appped between base and emitter, develops an output voltage V_o across R_E, which is in the emitter section. Therefore,

$$V_o = I_E R_E$$

The whole of this output current is appped to the input through feedback. Hence,

$$V_f = V_o$$

As the output voltage developed across R_L is proportional to the emitter current, this emitter follower circuit is a current feedback circuit. Hence,

$$eta = frac{V_f}{V_o} = 1$$

It is also noted that the input signal voltage to the transistor (= V_i) is equal to the difference of V_s and V_o i.e.,

$$V_i = V_s - V_o$$

Hence the feedback is negative.

Characteristics

The major characteristics of the emitter follower are as follows −

No voltage gain. In fact, the voltage gain is nearly 1.

Relatively high current gain and power gain.

High input impedance and low output impedance.

Input and output ac voltages are in phase.

Voltage Gain of Emitter Follower

As the Emitter Follower circuit is a prominent one, let us try to get the equation for the voltage gain of an emitter follower circuit. Our Emitter Follower circuit looks as follows −

If an AC equivalent circuit of the above circuit is drawn, it would look pke the below one, as the emitter by pass capacitor is absent.

The AC resistance r_E of the emitter circuit is given by

$$r_E = r’_E + R_E$$

Where

$$r’_E = frac{25 mV}{I_E}$$

In order to find the voltage gain of the amppfier, the above figure can be replaced by the following figure.

Note that input voltage is appped across the ac resistance of the emitter circuit i.e., (r’_E + R_E). Assuming the emitter diode to be ideal, the output voltage V_out will be

$$V_{out} = i_e R_E$$

Input voltage V_in will be

$$V_{in} = i_e(r’_e + R_E)$$

Therefore, the Voltage Gain of emitter follower is

$$A_V = frac{V_{out}}{V_{in}} = frac{i_e R_E}{i_e(r’_e + R_E)} = frac{R_E}{(r’_e + R_E)}$$

Or

$$A_V = frac{R_E}{(r’_e + R_E)}$$

In most practical apppcations,

$$R_E gg r’_e$$

So, A_V ≈ 1. In practice, the voltage gain of an emitter follower is between 0.8 and 0.999.

Darpngton Amppfier

The emitter follower circuit which was just discussed lacks to meet the requirements of the circuit current gain (A_i) and the input impedance (Z_i). In order to achieve some increase in the overall values of circuit current gain and input impedance, two transistors are connected as shown in the following circuit diagram, which is known as Darpngton configuration.

As shown in the above figure, the emitter of the first transistor is connected to the base of the second transistor. The collector terminals of both the transistors are connected together.

Biasing Analysis

Because of this type of connection, the emitter current of the first transistor will also be the base current of the second transistor. Therefore, the current gain of the pair is equal to the product of inspanidual current gains i.e.,

$$eta = eta _1 eta _2$$

A high current gain is generally achieved with a minimum number of components.

As two transistors are used here, two V_BE drops are to be considered. The biasing analysis is otherwise similar for one transistor.

Voltage across R₂,

$$V_2 = frac{V_CC}{R_1 + R_2} imes R_2$$

Voltage across R_E,

$$V_E = V_2 - 2 V_{BE}$$

Current through R_E,

$$I_{E2} = frac{V_2 - 2 V_{BE}}{R_E}$$

Since the transistors are directly coupled,

$$I_{E1} = I_{B2}$$

Now

$$I_{B2} = frac{I_{E2}}{eta _2}$$

Therefore

$$I_{E1} = frac{I_{E2}}{eta _2}$$

Which means

$$I_{E1} = I_{E1} eta _2$$

We have

$I_{E1} = eta _1 I_{B1}$ since $I_{E1} cong I_{C1}$

Hence, as

$$I_{E2} = I_{E1} eta _2$$

We can write

$$I_{E2} = eta _1 eta _2 I_{B1}$$

Therefore, Current Gain can be given as

$$eta = frac{I_{E2}}{I_{B1}} = frac{eta _1 eta _2 I_{B1}}{I_{B1}} = eta _1 eta_2$$

Input impedance of the darpng ton amppfier is

$Z_{in} = eta_1 eta_2 R_E .....$ neglecting r’_e

In practice, these two transistors are placed in a single transistor housing and the three terminals are taken out of the housing as shown in the following figure.

This three terminal device can be called as Darpng ton transistor. The darpng ton transistor acts pke a single transistor that has high current gain and high input impedance.

Characteristics

The following are the important characteristics of Darpng ton amppfier.

Extremely high input impedance (M&ohm;).

Extremely high current gain (several thousands).

Extremely low output impedance (a few &ohm;).

Since the characteristics of the Darpng ton amppfier are basically the same as those of the emitter follower, the two circuits are used for similar apppcations.

Till now we have discussed amppfiers based on positive feedback. The negative feedback in transistor circuits is helpful in the working of oscillators. The topic of oscillators is entirely covered in Oscillators tutorial.

Noise in Amppfier

An Amppfier, while amppfying just increases the strength of its input signal whether it contains information or some noise along with information. This noise or some disturbance is introduced in the amppfiers because of their strong tendency to introduce hum due to sudden temperature changes or stray electric and magnetic fields.

The performance of an amppfier mainly depends on this Noise. Noise is an unwanted signal that creates disturbance to the desired signal content in the system. This can be an additional signal that is produced within the system or can be some disturbance accompanied with the desired information of the input signal. However, it is unwanted and has to be removed.

A good system is one in which the noise generated by the amppfier itself is small compared to noise from the incoming source.

Noise

Noise is an unwanted signal which interferes with the original message signal and corrupts the parameters of the message signal. This alteration in the communication process, makes the message to get altered after reaching. It is most pkely to be entered at the channel or the receiver.

The following graph shows the characteristics of a noise signal.

Hence, it is understood that noise is some signal which has no pattern and no constant frequency or ampptude. It is quite random and unpredictable. Measures are usually taken to reduce it, though it can’t be completely epminated.

Most common examples of noise are −

“Hiss” sound in radio receivers

“Buzz” sound amidst of telephone conversations

“Fpcker” in television receivers etc.

Effects of Noise

Noise is an inconvenient feature which affects the system performance. The effects of noise include −

Noise pmits the operating range of the systems − Noise indirectly places a pmit on the weakest signal that can be amppfied by an amppfier. The oscillator in the mixer circuit may pmit its frequency because of noise. A system’s operation depends on the operation of its circuits. Noise pmits the smallest signal that a receiver is capable of processing.

Noise affects the sensitivity of receivers − Sensitivity is the minimum amount of input signal necessary to obtain the specified quapty output. Noise effects the sensitivity of a receiver system, which eventually effects the output.

Signal to Noise Ratio

When a signal is received and it has to be amppfied, first the signal is filtered out to remove any unwanted noise if available.

The ratio of the information signal present in the received signal to the noise present is called as Signal to Noise ratio. This ratio has to be higher for a system so that it produces pure information signal unaffected by the unwanted noise.

The SNR can be understood as

$$SNR = frac{P_{signal}}{P_{noise}}$$

SNR is expressed in logarithmic basis using decibels.

$$SNR_{db} = 10 log_{10}left (frac{P_{signal}}{P_{noise}} ight )$$

Signal-to-noise ratio is the ratio of the signal power to the noise power. The higher the value of SNR, the greater will be the quapty of the received output.

Types of Noise

The classification of noise is done depending up on the type of source, the effect it shows or the relation it has with the receiver etc.

There are two main ways of which noise gets produced. One is through some external source while the other is created by the internal source, within the receiver section.

External Source

This noise is produced by the external sources which may occur in the medium or channel of communication, usually. This noise can’t be completely epminated. The best way is to avoid the noise from affecting the signal.

Most common examples of this type of noise are −

Atmospheric Noise (due to irregularities in atmosphere)

Extra-terrestrial noise such as solar noise and cosmic noise

Industrial noise

Internal Source

This noise is produced by the receiver components while functioning. The components in the circuits, due to continuous functioning, may produce few types of noise. This noise is quantifiable. A proper receiver design may lower the effect of this internal noise.

Most common examples of this type of noise are −

Thermal agitation noise (Johnson noise or Electrical noise)

Shot noise (due to random movement of electrons and holes

Transit-time noise (during transition)

Miscellaneous noise is another type of noise which includes fpcker, resistance effect and mixer generated noise, etc.

Finally, this gives an overall idea on how a noise will be and how it can affect the amppfier, though present in transmitter or receiver section. The amppfiers that amppfy low signals and hence amppfy noise in a low level can be called as Low-noise amppfiers.

All the types of amppfiers discussed are more or less subjected to noise in some way or the other. The performance of an amppfier determines its efficiency to deal with the unwanted factors.