Diodes, Rectifiers and Regulators

Diodes conduct in one direction. They turn AC into DC (rectifiers), shape waveforms (clippers and clampers), and hold voltages steady (Zener regulators).

Diode basics

• Diode equation: I = I_s(e^(V/(ηV_T)) − 1), V_T ≈ 26 mV at room temperature.
• Cut-in voltage about 0.7 V (Si), 0.3 V (Ge).
• Models: ideal switch; constant drop (0.7 V); drop + resistance.
• Reverse saturation current roughly doubles for every 10 °C rise.
• Dynamic resistance r_d = ηV_T/I_D (about 26 mV/I_D).

Rectifiers

For a sinusoidal input with peak V_m (ideal diodes):

• Rectification efficiency: 40.6% (half-wave), 81.2% (full-wave).
• Ripple frequency: f (half-wave), 2f (full-wave).

Capacitor filter: ripple (peak-to-peak) ≈ I_dc/(f C) for half-wave and I_dc/(2 f C) for full-wave.

Clippers and clampers

• Clipper: removes the part of the signal above or below a level (diode + bias).
• Clamper: shifts the whole waveform up or down by adding a DC level (diode + capacitor); the peak-to-peak value is unchanged.
• Voltage multipliers (doublers, triplers) stack clamped capacitors.

Zener regulator

A Zener diode in reverse breakdown holds a nearly constant voltage V_Z.

• Series resistor: I_s = (V_in − V_Z)/R_s = I_Z + I_L.
• The Zener must keep I_Z ≥ I_Z,min under the worst case (lowest V_in, highest I_L), and not exceed its power rating P_Z = V_Z I_Z,max (highest V_in, lowest I_L).

Worked example

A 230 V, 50 Hz supply goes through a 10:1 transformer into a bridge rectifier.

• V_m = 230√2/10 = 32.5 V; V_dc = 2 × 32.5/π = 20.7 V; ripple frequency 100 Hz.

Practice