---
title: "Small signal model, AC resistance of diode"
subject: "Basic Electronics Engineering"
chapter: 2
key: "semester_2/basic_electronics_engineering:pn-diode-small-signal-ac-resistance"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/pn-diode-small-signal-ac-resistance
site: BCT Engineering
---

# Small signal model, AC resistance of diode

Basic Electronics Engineering · Chapter 2: Diodes

- Asked in: 2068 Bhadra, 8 marks; 2069 Bhadra, 3 marks (asked 2 times)
- Video: [AC or Dynamic Resistance of a Diode](https://www.youtube.com/watch?v=6QlFxif-JfQ) — Neso Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/pn-diode-small-signal-ac-resistance
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-2

## Question

Explain the small signal model of a PN junction diode and derive the expression for AC or dynamic resistance (AC resistance in the forward biased region).

## Short answer

The small-signal model replaces the diode at its Q-point by a dynamic resistance rd. From the exponential diode equation, the slope gives rd = dV/dI = ηVT/ID. At room temperature with η≈1 and VT≈25 mV, rd ≈ 25 mV/ID (ID in mA gives Ω).

## Answer

#### Small signal model
When a small ac signal vd (a few mV) is superimposed on a dc bias VD, the diode operates only on a very short part of its I-V curve around the bias point (the Q-point). That part is almost a straight line, so the diode behaves like a **linear resistance** called the dynamic (ac or incremental) resistance rd. In the small signal model the diode is replaced by rd (with the dc bias handled separately; the junction capacitance may be added in parallel at high frequency).

```text
 Diode I-V curve       Small-signal model
 I|      /             o---[ rd ]---o
  |     /  slope=1/rd
  |  Q /
  +---+------ V
```

#### Derivation of rd
Diode equation: ID = IS (e^(VD/ηVT) − 1), where VT = kT/q ≈ 25 mV at 300 K and η = 1 to 2.

In forward bias with VD ≫ ηVT, ID ≈ IS e^(VD/ηVT).

The conductance at the Q-point is the slope of the curve:

1/rd = dID/dVD = IS e^(VD/ηVT) / (ηVT) = ID/(ηVT)

**rd = ηVT/ID**

For η = 1 and VT = 25 mV: rd = 25 mV/ID (ID in mA gives rd in ohms).

Example: ID = 5 mA gives rd = 25 mV/5 mA = 5 Ω. At ID = 1 mA, rd = 25 Ω.

#### Result
- rd falls as the forward current rises, so it is not fixed but depends on the bias.
- The ac current is id = vd/rd, and the total current is ID + id.
- In reverse bias rd is very large (open circuit).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why can the diode be treated as a linear resistance for a small signal?
   A. A small signal covers a short, nearly straight part of the I-V curve around the Q-point
   B. The diode is reverse biased
   C. The curve is always linear
   D. The signal has no dc bias
   Answer: A. A small ac swing about the Q-point sees an almost straight line. (Key point: Small-signal idea)

2. Dynamic resistance rd is
   A. VD/ID
   B. The reciprocal of the slope dID/dVD at the Q-point
   C. The reverse resistance
   D. The barrier potential
   Answer: B. 1/rd = dID/dVD at the bias point. (Key point: Definition of rd)

3. The derived expression is
   A. rd = ID/(ηVT)
   B. rd = ηVT/ID
   C. rd = VT·ID
   D. rd = ηVT·ID
   Answer: B. Differentiating ID = ISe^(VD/ηVT) gives 1/rd = ID/ηVT. (Key point: Result of derivation)

4. For η = 1 and ID = 5 mA, rd is
   A. 25 Ω
   B. 5 Ω
   C. 125 Ω
   D. 0.2 Ω
   Answer: B. rd = 25 mV/5 mA = 5 Ω. (Key point: Numerical use)

## Related in Basic Electronics Engineering

- [PN junction diode I-V characteristics](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Apn-diode-iv-characteristics) — Basic Electronics Engineering, chapter 2, asked 5×
- [Large signal / piecewise linear diode models](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Apn-diode-large-signal-model) — Basic Electronics Engineering, chapter 2, asked 4×

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