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.