Formula & Calculator
Diode Small-Signal Resistance
The incremental (small-signal) resistance of a forward-biased diode at a given operating current.
Interpretation
Diode small‑signal resistance r_d = V_T / I_D, where V_T ≈ 25mV at room temperature.
It is the AC resistance of a forward‑biased diode at a given DC bias current.
Example: I_D=1mA → r_d = 25mV / 1mA = 25Ω.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| r_d | Small-signal (dynamic) resistance of the diode at a given bias point | Ω |
| V_T | Thermal voltage (≈ 25.85 mV at 300 K, varies with temperature) | V |
| I_D | DC bias (quiescent) current through the diode | A |
What it means
The small‑signal resistance of a forward‑biased diode is r_d = V_T / I_D, where V_T is the thermal voltage (≈25mV at room temperature) and I_D is the DC bias current. This is the dynamic resistance for AC signals superimposed on a DC bias. It is the slope of the diode I‑V curve at the operating point. The small‑signal resistance is used in AC analysis of diode circuits, such as rectifiers, clippers, and detectors. For a given bias current, the resistance is inversely proportional to the current; higher current gives lower resistance. Example: At I_D = 1mA, r_d = 25mV/1mA = 25Ω. At I_D = 10mA, r_d = 25mV/10mA = 2.5Ω. This small resistance affects the voltage gain of diode‑based circuits.
Worked example
Diode Small‑Signal Resistance – Practical Example
Real‑World| Parameter | Value |
|---|---|
| VT | 26 mV |
| ID | 1 mA = 1×10⁻³ A |
| Formula | rd = VT / ID |
Common mistakes
- Diode current I_D: The DC bias current through the diode.
- V_T: Thermal voltage (~25 mV).
- Small‑signal: This is the AC resistance at the operating point.
- Dynamic resistance: r_d = dV/dI – valid for small signal variations.
- Reverse bias: For reverse bias, r_d is very large (leakage).
Applications
Diode small‑signal resistance r_d = V_T / I_D is the AC resistance of a forward‑biased diode at a given DC current. It is used to model the diode's dynamic behaviour in amplifiers and rectifiers. Engineers use it to calculate the voltage gain of diode‑loaded stages, to design clipper and clamper circuits, and to analyse rectifier circuits. The resistance decreases with increasing current, which is important for linearity in mixers and detectors. By understanding this concept, professionals can accurately predict the AC response of diode circuits. This formula is essential for analog and RF circuit design.
- Rectifier and clipper circuit analysis
- Mixer and detector circuit design
- Voltage‑controlled resistance applications (PIN diodes)
- Temperature stabilisation in bias circuits
- Educational understanding of diode dynamic resistance
Frequently Asked Questions
The small‑signal resistance (incremental resistance) is r_d = V_T / I_D, where V_T is the thermal voltage (≈25 mV at room temperature) and I_D is the DC bias current. It represents the slope of the diode I-V curve at the operating point.
V_T = kT/q, approximately 25.8 mV at 300K. It is a fundamental constant in semiconductor physics.
r_d is inversely proportional to I_D. At low currents, the resistance is high; at high currents, it is low.
Common errors: 1) Using the total voltage drop across the diode instead of V_T, 2) Forgetting that the formula is for small‑signal (AC) resistance, not DC resistance, 3) Applying it to a reverse‑biased diode, 4) Using the formula without including the series resistance, 5) Assuming the diode is ideal.
Used in: 1) Small‑signal modelling of diodes, 2) Analysing rectifier circuits, 3) Designing voltage regulators, 4) RF detector circuits, 5) Temperature sensors (using V_T).
In an AC circuit, the diode behaves as a resistor of value r_d in parallel with the junction capacitance. This affects the frequency response.
DC resistance is V_D/I_D (total voltage/current). r_d is the slope at the operating point, which is much smaller than the DC resistance for a forward‑biased diode.