Math Problem Statement

Analyze the circuit diagrams in Figures 1 and 2. Determine the voltage gain with a load resistor and capacitor, explain the effect of the load resistance on gain, and evaluate the role of capacitor C2.

Solution

Let us analyze and solve the questions from the provided circuit diagrams and descriptions.

Question 8: Voltage Gain with Load Resistor and Capacitor

The voltage gain (AvA_v) for the circuit in Figure 2 with a load resistor (RL=100ΩR_L = 100 \, \Omega) and capacitor (C3=1μFC_3 = 1 \, \mu\text{F}) can be calculated using the formula:

Av=βRLreA_v = - \frac{\beta \cdot R_L}{r_e}

Where:

  • β=150\beta = 150 (given transistor gain)
  • RL=100ΩR_L = 100 \, \Omega
  • re=VTIEr_e = \frac{V_T}{I_E} is the intrinsic emitter resistance, with VT26mVV_T \approx 26 \, \text{mV} at room temperature and IEI_E is the emitter current.

To calculate rer_e, we need IEI_E, which depends on the circuit's biasing. If the collector current (ICI_C) is approximately equal to IEI_E, we estimate:

re=26mVIEr_e = \frac{26 \, \text{mV}}{I_E}

Substitute values once IEI_E is known, calculate rer_e, and then substitute in the gain equation to find AvA_v.


Question 9: Effect of Load Resistance on Gain

Adding a load resistor (RLR_L) decreases the overall voltage gain because the effective load resistance ReffR_{eff} seen by the transistor becomes:

Reff=(RCRLRC+RL)R_{eff} = \left( \frac{R_C \cdot R_L}{R_C + R_L} \right)

Here:

  • RC=3.6kΩR_C = 3.6 \, \text{k}\Omega (collector resistor)
  • RL=100ΩR_L = 100 \, \Omega

Since RLR_L is much smaller than RCR_C, ReffR_{eff} significantly reduces, which reduces AvA_v.


Question 10: Effect of Removing Capacitor C2C_2

C2C_2 bypasses the emitter resistor to stabilize the gain at high

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Math Problem Analysis

Mathematical Concepts

Analog Circuits
Transistor Voltage Gain
Load Resistance
Emitter Resistance

Formulas

Voltage Gain: Av = -β * RL / re
Emitter Resistance: re = VT / IE
Effective Resistance: Reff = (RC * RL) / (RC + RL)

Theorems

Transistor Small-Signal Analysis

Suitable Grade Level

Undergraduate Engineering