JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B. Tech III ELECTRONIC CIRCUIT ANALYSIS Previous Question Paper (September - 2021 - R18)

The transconductance g_m is defined as the change in collector current I_C with respect to the change in base-emitter voltage V_BE, keeping collector-emitter voltage V_CE constant. For a BJT operating in the active region, the collector current is given by the equation:

where I_S is the reverse saturation current and V_T is the thermal voltage. Differentiating I_C with respect to V_BE:

Substituting the expression for I_C back into the equation, we get:

The thermal voltage V_T is temperature-dependent and is defined as V_T = kT / q, where k is the Boltzmann constant, T is the absolute temperature in Kelvin, and q is the electron charge. Thus, the final relation is:

In a common emitter (CE) amplifier with an unbypassed emitter resistance R_E, the emitter resistor introduces negative current series feedback. Using the small-signal hybrid-π model, the input signal is applied to the base, and the output is taken at the collector.

Input Resistance (R_i): Looking into the base, the resistance is the sum of the base resistance and the reflected emitter resistance. Since the emitter current i_e is approximately (β+1)i_b, the resistance seen at the base is r_π + (β+1)R_E. Thus:

Voltage Gain (A_v): The voltage gain is the ratio of output voltage V_o to input voltage V_i. The output voltage is V_o = -g_m * v_be * R_C. The input voltage is V_i = i_b * r_π + i_e * R_E. Since i_e = (β+1)i_b and v_be = i_b * r_π, we have:

Using the relation g_m * r_π = β, the expression simplifies to: