Diode Dynamic Resistance
rd = VT / Id
Quick answer
This calculator solves rd = VT / Id (≈ 26 mV / Id) for Dynamic Resistance. With Thermal Voltage 0.6 V, Diode Current 20 mA, the result is 30 Ω. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The dynamic (AC) resistance of a forward-biased diode is the slope of its V–I curve at the operating point, equal to the thermal voltage divided by the bias current. It is what an AC signal "sees" through the diode and governs the behaviour of diode mixers, log amplifiers, temperature sensors, and the emitter junctions of transistors.
Variables
- rd — Small-signal dynamic resistance (Ω)
- VT — Thermal voltage (≈26 mV)
- Id — DC bias current (A)
Practical Notes
At 1 mA, rd ≈ 26 Ω. This is much smaller than the diode’s DC (static) resistance V/I, because the exponential I–V curve is steep at the operating point.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| rd | Dynamic Resistance | Ω | mΩ, Ω, kΩ, MΩ |
| Vt | Thermal Voltage | mV | pV, nV, µV, mV, V, kV |
| Id | Diode Current | mA | pA, nA, µA, mA, A, kA |
Step by step
- 1. What you know: Thermal Voltage 0.6 V, Diode Current 20 mA
- 2. The relation: rd = VT / Id (≈ 26 mV / Id)
- 3. Substitute: Vt = 0.6 V, Id = 20 mA
- 4. Result: Dynamic Resistance = 30 Ω
Related quantities from the same inputs
- P = V × I = 12 mW
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 27 Ω | 10% |
| E24 | 30 Ω | 0% |
Worked examples
Minimum range
Given: Thermal Voltage 10 mV, Diode Current 100 µA
Result: Dynamic Resistance = 100 Ω
Low range
Given: Thermal Voltage 100 mV, Diode Current 1 mA
Result: Dynamic Resistance = 100 Ω
Typical
Given: Thermal Voltage 0.6 V, Diode Current 20 mA
Result: Dynamic Resistance = 30 Ω
High range
Given: Thermal Voltage 0.9 V, Diode Current 0.5 A
Result: Dynamic Resistance = 1.8 Ω
Maximum range
Given: Thermal Voltage 9 V, Diode Current 5 A
Result: Dynamic Resistance = 1.8 Ω
Solving for each variable
Solve for Dynamic Resistance
Thermal Voltage 10 mV, Diode Current 100 µA → 100 Ω
Solve for Thermal Voltage
Dynamic Resistance 1 Ω, Diode Current 100 µA → 100 µV
Solve for Diode Current
Dynamic Resistance 1 Ω, Thermal Voltage 10 mV → 10 mA
How Dynamic Resistance changes with Thermal Voltage
| Thermal Voltage (input) | Dynamic Resistance (result) |
|---|---|
| 60 mV | 3 Ω |
| 150 mV | 7.5 Ω |
| 0.3 V | 15 Ω |
| 0.45 V | 22.5 Ω |
| 0.6 V | 30 Ω |
| 0.9 V | 45 Ω |
| 1.2 V | 60 Ω |
| 2.4 V | 120 Ω |
| 4.2 V | 0.21 kΩ |
| 6 V | 0.3 kΩ |
The same result in other units
| Unit | Value |
|---|---|
| mΩ | 30000 |
| Ω | 30 |
| kΩ | 0.03 |
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<p><a href="https://vbatpower.com/formulas/diode-dynamic-resistance/">Diode Dynamic Resistance</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Diode Dynamic Resistance?
Use rd = VT / Id (≈ 26 mV / Id). With Thermal Voltage 0.6 V, Diode Current 20 mA, Dynamic Resistance works out to 30 Ω.
How do you calculate dynamic resistance of diode formula rd = dv/di?
Rearrange for Dynamic Resistance: with Thermal Voltage 100 mV, Diode Current 1 mA, Dynamic Resistance is 100 Ω.
What is the formula for Diode Dynamic Resistance?
The formula is rd = VT / Id (≈ 26 mV / Id). The dynamic (AC) resistance of a forward-biased diode is the slope of its V–I curve at the operating point, equal to the thermal voltage divided by the bias current.
How do you find Thermal Voltage when you know the other values?
Rearrange for Thermal Voltage: with Dynamic Resistance 1 Ω, Diode Current 100 µA, Thermal Voltage is 100 µV.
How do you find Diode Current when you know the other values?
Rearrange for Diode Current: with Dynamic Resistance 1 Ω, Thermal Voltage 10 mV, Diode Current is 10 mA.
What units does Diode Dynamic Resistance use?
Dynamic Resistance is shown in mΩ, Ω, kΩ. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Discrete Amplifiers formulas →Need more features?
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