Question 5.17: Objective: Design a bias-stable pnp transistor circuit to me...
Objective: Design a bias-stable pnp transistor circuit to meet a set of specifications.
Specifications: The circuit configuration to be designed is shown in Figure 5.57(a). The transistor Q-point values are to be: V_{EC Q} = 7 V, I_{C Q} ≅ 0.5 mA, and V_{RE} ≅ 1 V.
Choices: Assume transistor parameters of β = 80 and V_{E B}(on) = 0.7 V. Standard resistor values are to be used in the final design.
The Thevenin equivalent circuit is shown in Figure 5.57(b). The Thevenin
equivalent resistance is R_{T H} = R_{1} || R_{2} and the Thevenin equivalent voltage, measured with respect to ground, is given by
V_{T H} = \left( \frac{R_{2}}{R_{1} + R_{R}} \right) (V^{+} − V^{−}) + V^{−}
= \frac{1}{R_{1}} \left( \frac{R_{1} R_{2}}{R_{1} + R_{2}} \right) (V^{+} − V^{−}) + V^{−}
For V_{RE} ≅ 1 V and I_{C Q} ≅ 0.5 mA, then we can set
R_{E} = \frac{1}{0.5} = 2 k \Omega
For a bias stable circuit, we want
R_{T H} = \frac{R_{1} R_{2}}{R_{1} + R_{2}} = (0.1)(1 + β) R_{E}
= (0.1)(81)(2) = 16.2 kΩ
Then the Thevenin equivalent voltage can be written as
V_{T H} = \frac{1}{R_{1}} (16.2)[9 − (− 9)] + (− 9) = \frac{1}{R_{1}} (291.6) − 9
The KVL equation around the E–B loop is given by
V^{+} = I_{E Q} R_{E} + V_{E B}(on) + I_{B Q} R_{T H} + V_{T H}
The transistor is to be biased in the forward-active mode so that I_{E Q} = (1 + β)I_{B Q} .
We then have
V^{+} = (1 + β)I_{B Q} R_{E} + V_{E B}(on) + I_{B Q} R_{T H} + V_{T H}
For I_{C Q} = 0.5 mA, then I_{B Q} = 0.00625 mA so we can write
9 = (81)(0.00625)(2) + 0.7 + (0.00625)(16.2) + \frac{1}{R_{1}} (291.6) − 9
We find R_{1} = 18.0 k \Omega. Then, from R_{T H} = R_{1} || R_{2} = 16.2 k \Omega, we find R_{2} = 162 k \Omega.
For I_{C Q} = 0.5 mA, then I_{E Q} = 0.506 mA. The KVL equation around the E–C
loop yields
V^{+} = I_{E Q} R_{E} + V_{EC Q} + I_{C Q} R_{C} + V^{−}
or
9 = (0.506)(2) + 7 + (0.50)R_{C} + (−9)
which yields
R_{C} ≅ 20 k \Omega
Trade-offs: All resistor values are standard values except for R_{2} = 162 k \Omega. A standard discrete value of 160 kΩ is available. However, because of the bias-stable design, the Q-point will not change significantly. The change in Q-point values with a change in transistor current gain β is considered in end-of-chapter problems such as Problems 5.31 and 5.34.
Comment: In many cases, specifications such as a collector current level or an emitter–collector voltage value are not absolute, but are given as approximate values.
For this reason, the emitter resistor, for example, is determined to be 2 kΩ, which is a standard discrete resistor value. The final bias resistor values are also chosen to be standard values. However, these small changes compared to the calculated resistor values will not change the Q-point values significantly.