Analysis and Design of a 3-Stage BJT Circuit

PhysicsBipolar Junction Transistor (BJT) Amplifier CircuitsHardSTEM

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For the 3-stage circuit shown, given that $h_{FE}=200$ and $|V_{BE}|=0.6\text{ V}$:

a. Design a current mirror that will provide a $0.5\text{ mA}$ bias current to the long-tailed pair. (10 points)

b. Find the other bias currents and the value of $R_{E4}$ such that clipping at the output is minimum and symmetric, i.e., $V_O = 0V$. If you cannot determine the bias current of the second stage, take $I_{C3}=1\text{ mA}$. (30 points)

This question includes visual content: A circuit diagram showing a 3-stage amplifier. The first stage is a PNP differential pair (T1, T2) fed by a 0.5 mA current source connected to +Vcc. T1 and T2 have 20k ohm resistors to -Vee = -12V at their collectors. The differential input is labeled Vi. The second stage uses an NPN transistor T3 in a common-emitter configuration with a 12k ohm collector resistor to +Vcc = +12V and a 4k ohm emitter resistor to -Vee = -12V. The base of T3 is connected to the collector of T2. The third stage is a PNP transistor T4 where its base is connected to the collector of T3. T4 has a resistor RE4 connected from its emitter to +Vcc and its collector is connected to -Vee. The output Vo is taken from the emitter of T4.

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1
Step 1

Let's solve this multi-stage transistor circuit problem. We have a differential pair, a gain stage, and an output stage. We need to design a current mirror and analyze the bias points.

Given Values

- $V_{CC} = +12$ V, $V_{EE} = -12$ V

- $I_{tail} = 0.5$ mA

- $\beta = 200$, $|V_{BE}| = 0.6$ V

- Target: Symmetric clipping, $V_o = 0$ V

2
Step 2

Part A asks us to design a current mirror to provide the 0.5 milliamp bias current. Since the differential pair uses PNP transistors with emitters at the top, we need a PNP current mirror referenced to the positive rail.

Part A: Current Mirror Design

+Vcc-VeeIo = 0.5mAR_bias
3
Step 3

The current is determined by the bias resistor $R_{bias}$. The reference current flows from $V_{CC}$, through the diode-connected transistor, through $R_{bias}$, to $-V_{EE}$.

$$R_{bias} = \frac{V_{CC} - V_{BE} - (-V_{EE})}{I_{REF}}$$
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Step 4

Substituting the values: 12 volts minus 0.6 volts minus negative 12, all divided by 0.5 milliamps.

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Step 5

This simplifies to 23.4 volts over 0.5 milliamps, which gives us 46.8 kilo-ohms. We can use a standard 47k resistor.

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Step 6

Now for Part B. Let's find the bias currents starting with Stage 1. The tail current is 0.5 mA, which splits equally between $T_1$ and $T_2$.

Stage 1: Differential Pair

$$I_{C1} \approx I_{C2} = \frac{I_{tail}}{2} = \frac{0.5 \text{ mA}}{2} = 0.25 \text{ mA}$$
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Step 7

We need the collector voltage of $T_2$ because it biases the next stage. The current flows down through the 20k resistor to $-12$V.

$$V_{C2} = -V_{EE} + I_{C2}R_{C2}$$
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Step 8

Plugging in the numbers gives us negative 7 volts.

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Step 9

Stage 2 is an emitter-degenerated Common Emitter amplifier. The base of $T_3$ is connected to $V_{C2}$, so the base voltage is -7 V.

Stage 2: Driver Stage (T3)

$$V_{B3} = V_{C2} = -7 \text{ V}$$

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About This Question

Subject
Physics
Topic
Bipolar Junction Transistor (BJT) Amplifier Circuits
Difficulty
Hard
Exam
STEM
Question Type
Open Ended

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