Applications of Semiconductor Devices — Formula Sheet

V_dc = V_m / π

I_dc = V_dc / R_L = V_m / (π × R_L)

V_dc = 2V_m / π

I_dc = 2V_m / (π × R_L)

I_s = (V_i - V_z) / R_s

I_s = I_z + I_L

I_z = I_s - I_L

P_d = V_z × I_z

A_V = V_0 / V_i

A_V = -β × R_L / r_i

A_V = -g_m × R_L

A_I = i_0 / i_i = β

A_P = A_I × A_V = β × A_V

I_C = V_CC / R_L (at saturation)

I_B = (V_BB - V_BE) / R_B

Aβ = 1 (condition for sustained oscillations)

CUT-OFF region

Base current I_B = 0 (or negative). Transistor does not conduct. Collector current I_C ≈ 0. Output voltage V_CE = V_CC (switch is OFF).

SATURATION region

Base current I_B > saturation value. Transistor conducts fully. V_CE ≈ 0. Collector current I_C = V_CC/R_L (switch is ON). Output voltage V_0 ≈ 0.

Half-wave rectifier uses ONE diode and utilizes only one half of the AC input. V_dc = V_m/π

Full-wave rectifier uses TWO diodes and a centre-tapped transformer. V_dc = 2V_m/π

Transistor amplification is based on the principle

small ΔI_B → large ΔI_C, with ΔI_C = β × ΔI_B

Voltage Gain

A_V = -β × R_L / r_i (negative sign = 180° phase inversion between input and output)