Diode AC Resistance

A diode's resistance is not fixed. It changes with the current flowing through it. This property, called AC resistance or dynamic resistance, controls how much a small AC signal is distorted or limited when it passes through a diode junction in signal clippers and AM demodulators.

Core Concept

A diode's I-V curve is exponential, not a straight line. At any operating point, the slope of this curve changes. The reciprocal of that slope at a given DC bias current is the dynamic resistance r_d. It tells you how much voltage change results from a small current change around that operating point.

Mathematically, r_d comes from differentiating the Shockley equation. The result is simple: r_d equals the thermal voltage VT divided by the DC bias current I_DQ. At room temperature (300 K), VT is 26 mV. So a diode biased at 1 mA has r_d = 26 Ω, and at 10 mA it drops to 2.6 Ω.

This concept is used directly in signal detectors. In an AM radio envelope detector, the 1N60 germanium diode's r_d forms part of an RC time constant. In op-amp logarithmic amplifiers using a 1N4148, r_d determines the small signal gain. Knowing r_d lets you treat the diode as a simple resistor for AC analysis.

Key Equations

Shockley equation: I_D = I_S * (e^(V_D / (n*VT)) - 1)

Thermal voltage: VT = kT/q = 26 mV at T = 300 K where k = 1.38e-23 J/K and q = 1.6e-19 C.

AC (dynamic) resistance: r_d = dV/dI = n*VT / I_DQ where n is the ideality factor (1 for ideal, 1 to 2 in practice).

For n = 1 at room temperature: r_d = 26 mV / I_DQ with I_DQ in milliamps giving r_d in ohms.

Static (DC) resistance: R_DC = V_D / I_D — this is different from r_d and should not be confused with it.

Given:
Diode: 1N4148 (silicon, n = 1)
DC bias current I_DQ = 2 mA
Temperature T = 300 K
VT = 26 mV

Why this formula:
r_d is obtained by differentiating the Shockley equation at the operating point.

Formula:
r_d = VT / I_DQ

Substitution:
r_d = 26 mV / 2 mA
r_d = 0.026 V / 0.002 A

Calculation:
r_d = 13 Ω

Also find static DC resistance:
Assume V_D ≈ 0.65 V at 2 mA for 1N4148
R_DC = V_D / I_D = 0.65 / 0.002 = 325 Ω

Final Answer:
r_d = 13 Ω (AC dynamic resistance)
R_DC = 325 Ω (DC static resistance)
Note: r_d is 25 times smaller than R_DC at this bias point.

Exam Tip: GATE often asks students to distinguish between static resistance R_DC = V/I and dynamic resistance r_d = VT/I_DQ. They are very different numbers. At 1 mA, R_DC ≈ 700 Ω but r_d = 26 Ω. Another trap: if the ideality factor n is given as 2 (common for Schottky or some silicon diodes), use r_d = 2*VT/I_DQ = 52 mV / I_DQ. Forgetting n doubles your answer.

Key Properties

• r_d = VT / I_DQ at room temperature (300 K) with n = 1. VT = 26 mV, so a 1 mA bias gives r_d = 26 Ω.
• r_d decreases as bias current increases. At 10 mA, r_d = 2.6 Ω. At 0.1 mA, r_d = 260 Ω.
• Static DC resistance R_DC = V_D/I_D is always much larger than r_d at the same bias point. These two quantities must not be swapped.
• VT increases with temperature at 0.086 mV/K. At 350 K (warm chip), VT ≈ 30 mV, so r_d rises slightly for the same bias current.
• In small signal equivalent circuits of diodes, the diode is replaced by r_d in series with any bulk resistance r_b. For 1N4148, r_b ≈ 5 Ω.
• The ideality factor n for Schottky diodes like 1N5817 is close to 1.05, while for regular p-n junction diodes it ranges from 1.2 to 2.

Quick Revision

• r_d = VT / I_DQ = 26 mV / I_DQ at 300 K.
• VT = kT/q = 26 mV at room temperature (300 K).
• r_d falls as bias current rises. Higher current means lower AC resistance.
• Static resistance R_DC = V_D / I_D. Always much larger than r_d.
• If n is given, use r_d = n * VT / I_DQ.
• In AC equivalent circuit, diode becomes r_d (a resistor) in series with bulk resistance.
• Exam trap: Substituting R_DC instead of r_d in small signal analysis gives a completely wrong gain or impedance value. Always use r_d = VT/I_DQ for AC problems.