Diode Equivalent Circuits

Every diode in a real circuit needs a model you can solve on paper. The diode equivalent circuit replaces the non-linear device with resistors and voltage sources so you can apply Kirchhoff's laws directly. Rectifiers in mobile chargers and signal clamps in audio equipment both depend on choosing the right model.

Core Concept

The ideal diode model treats the device as a perfect switch. Forward biased means zero voltage drop and zero resistance. Reverse biased means open circuit. This model works when supply voltages are much larger than 0.7 V, like a 50 V power supply circuit.

The offset voltage model adds the forward voltage drop, 0.7 V for silicon diodes like the 1N4007 and 0.3 V for germanium types like the OA79. The diode conducts only when the applied voltage exceeds this threshold. This model handles most exam problems and practical rectifier designs.

The complete model also includes bulk resistance r_d, which is the ohmic resistance of the semiconductor body and metal contacts. For a 1N4007, r_d is roughly 10 to 20 Ω. This matters at high currents where the extra voltage drop across r_d becomes significant.

Key Equations

Ideal model forward current: V_D = 0, I_D = (V_S - 0) / R_L

Offset model forward current: I_D = (V_S - V_gamma) / R_L where V_gamma = 0.7 V for silicon.

Complete model: V_D = V_gamma + I_D * r_d so I_D = (V_S - V_gamma) / (R_L + r_d)

PIV (peak inverse voltage) rating must satisfy: PIV >= V_S(peak) for safe reverse bias operation.

Given:
V_S = 12 V DC supply
R_L = 1 kΩ load
Diode: 1N4007 (silicon), r_d = 10 Ω
V_gamma = 0.7 V

Why this formula:
Complete model accounts for both threshold voltage and bulk resistance.

Formula:
I_D = (V_S - V_gamma) / (R_L + r_d)

Substitution:
I_D = (12 - 0.7) / (1000 + 10)
I_D = 11.3 / 1010

Calculation:
I_D = 0.01119 A = 11.19 mA

Voltage across diode:
V_D = V_gamma + I_D * r_d
V_D = 0.7 + 0.01119 * 10
V_D = 0.7 + 0.112 = 0.812 V

Final Answer:
I_D = 11.19 mA, V_D = 0.812 V

Exam Tip: GATE frequently asks which model to use in a given context. If R_L is large (several kΩ) and V_S is tens of volts, the ideal model gives the same answer as the complete model within 1%. If R_L is small (tens of ohms), r_d matters and you must use the complete model. Also note: the offset voltage for germanium is 0.3 V, not 0.7 V. Mixing these up in a half-wave rectifier problem costs full marks.

Key Properties

• The ideal model assumes V_D = 0 in forward bias and I_D = 0 in reverse bias. Use it only when supply voltage is at least 10 times larger than 0.7 V.
• The offset model uses V_gamma = 0.7 V for silicon (1N4007, 1N914) and 0.3 V for germanium (OA79). This is accurate for most exam and lab scenarios.
• Bulk resistance r_d for small signal diodes like 1N914 is 5 to 15 Ω. For power diodes like 1N5408 it can be 1 to 5 Ω due to larger junction area.
• The complete model gives V_D = V_gamma + I_D * r_d. At high currents, V_D can rise well above 0.7 V, which is why power diodes run warm.
• PIV rating of a diode must exceed the peak reverse voltage it sees in the circuit. The 1N4007 has a PIV of 1000 V, making it suitable for mains rectifiers.
• In a piecewise linear model, the diode is treated as two linear segments: off below V_gamma and linear above it. This is the basis for SPICE Level-1 diode modeling.

Quick Revision

• Ideal model: V_D = 0, R = 0 when ON; open circuit when OFF.
• Offset model: V_D = 0.7 V (Si) or 0.3 V (Ge) when ON.
• Complete model: V_D = V_gamma + I_D * r_d, where r_d is bulk resistance.
• Use offset model for most GATE rectifier and clipper problems.
• Bulk resistance matters when R_L is comparable to r_d (low-load-resistance circuits).
• PIV for 1N4007 is 1000 V; for 1N4001 it is 50 V.
• Exam trap: Students often forget r_d when the load resistance is small, like 47 Ω, leading to a significant error in the calculated current.