Question

For the circuit shown in the Figure below, \(g_m\) of the transistor is 

• A. 0.0635A/V
• B. 0.0827A/V
• C. 0.026A/V
• D. 0.071A/V

Hint:

Remember that transconductance \(g_m\) can be derived using the collector current and thermal voltage. Be careful while converting units during calculation.

Answer 1

The Correct Option is A

Step 1: We are given the circuit parameters, and we need to find the transconductance \(g_m\) which is given by: \[ g_m = \frac{I_C}{V_T} \] where \(V_T\) is the thermal voltage equal to 26mV. 
Step 2: First, find the Base current \(I_B\): \[ V_{BB} - V_{BE(on)} = I_B \times R_B \] \[ I_B = \frac{5 - 0.7}{200 \times 10^3} = \frac{4.3}{200 \times 10^3} = 21.5 \times 10^{-6} A = 21.5 \mu A \] 
Step 3: Find the Collector current \(I_C\): \[ I_C = \beta \times I_B = 100 \times 21.5 \times 10^{-6} = 2.15 \times 10^{-3} A = 2.15 mA \] 
Step 4: Calculate transconductance: \[ g_m = \frac{I_C}{V_T} = \frac{2.15 \times 10^{-3}}{26 \times 10^{-3}} = \frac{2.15}{26} = 0.0827 A/V \] Thus the value is 0.0827 A/V.