## Chapter 5

## 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.

## Step-by-Step

## 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.

(ideal load line): The load line equation is

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.