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

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