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## Q. 5.9

Objective: Design a pnp bipolar transistor circuit to meet a set of specifications.

Specifications: The circuit configuration to be designed is shown in Figure 5.36(a). The quiescent emitter-collector voltage is to be $V_{EC Q} = 2.5 V$.

Choices: Discrete resistors with tolerances of ±10 percent are to be used, an emitter resistor with a nominal value of $R_{E} = 2 k\Omega$ is to be used, and a transistor with β = 60 and $V_{E B}(on) = 0.7 V$ is available.

## Verified Solution

(ideal Q-point value): Writing the Kirchhoff’s voltage law equation around the C–E loop, we obtain
$V^{+} = I_{E Q} R_{E} + V_{EC Q}$
or
$5 = I_{E Q}(2) + 2.5$
which yields $I_{E Q} = 1.25 mA$. The collector current is
$I_{C Q} = \left(\frac{β}{1 + β} \right) \cdot I_{E Q} = \left(\frac{60}{61} \right) (1.25) = 1.23 mA$
The base current is
$I_{B Q} = \frac{I_{E Q}}{1 + β} = \frac{1.25}{61} = 0.0205 mA$
Writing the Kirchhoff’s voltage law equation around the E–B loop, we find
$V^{+} = I_{E Q} R_{E} + V_{E B}(on) + I_{B Q} R_{B} + V_{B B}$

or
$5 = (1.25)(2) + 0.7 + (0.0205)R_{B} + (−2)$
which yields $R_{B} = 185 k \Omega$.
$V_{EC} = V^{+} − I_{E} R_{E} = V^{+} − I_{C} \left(\frac{1 + β}{β} \right) R_{E}$
or
$V_{EC} = 5 − I_{C} \left(\frac{61}{60} \right) (2) = 5 − I_{C}(2.03)$
The load line, using the nominal value of $R_{E}$ , and the calculated Q-point are shown in Figure 5.37(a).
Trade-offs: As shown in Appendix C, a standard resistor value of 185 kΩ is not available. We will pick a value of 180 kΩ. We will consider $R_{B}$ and $R_{E}$ resistor tolerances of ±10 percent.
The quiescent collector current is given by
$I_{C Q} = β \left[ \frac{V^{+} − V_{E B}(on) − V_{B B}}{R_{B} + (1 + β)R_{E}} \right] = (60) \left[\frac{6.3}{R_{B} + (61)R_{E}} \right ]$

and the load line is given by
$V_{EC} = V^{+} − I_{C} \left(\frac{1 + β}{β} \right) R_{E} = 5 − \left(\frac{61}{60} \right) I_{C} R_{E}$
The extreme values of $R_{E}$ are:
2 kΩ − 10% = 1.8 kΩ           2 kΩ + 10% = 2.2 kΩ.

The extreme values of $R_{B}$ are:
180 kΩ − 10% = 162 kΩ              180 kΩ + 10% = 198 kΩ.
The Q-point values for the extreme values of $R_{B}$ and $R_{E}$ are given in the following table.

 $R_{E}$ $R_{E}$ 1.8 kΩ 2.2 kΩ 162 kΩ $I_{CQ} = 1.39 mA$ $I_{CQ} = 1.28 mA$ $V_{ECQ} = 2.46 V$ $V_{ECQ} = 2.14 V$ 198 kΩ $I_{CQ} = 1.23 mA$ $I_{CQ} = 1.14 mA$ $V_{ECQ} = 2.75 V$ $V_{ECQ} = 2.45 V$

Figure 5.37(b) shows the Q-points for the various possible extreme values of emitter and base resistances. The shaded area shows the region in which the Q-point will occur over the range of resistor values.
Comment: This example shows that an ideal Q-point can be determined based on a set of specifications, but, because of resistor tolerance, the actual Q-point will vary over a range of values. Other examples will consider the tolerances involved in transistor parameters.