# How is dynamic resistance of a diode modeled for large voltage variations?

The resistance of a diode changes with the voltage across it which is called dynamic resistance. If the voltage across the diode is constant we can find the dynamic resistance from the slope of the I-V curve. So for small variations we can use that dynamic resistance value in the diode model.

But if the voltage across the diode varies a lot like in a AC to DC rectifying diode, I guess we cannot just model a diode’s dynamic resistance with a constant series resistance. If we want to formulate the diode current in such case how is the diode dynamic resistance modeled? Here aren’t we facing a non-linear resistor?

• Are you actually interested in seeing the page of mathematics involved, assuming a simple Shockley diode equation without current-crowding or surface channel effects? Or just asking, generally? If generally, yeah -- the dynamic resistance is only valid at one local spot on the curve so doesn't apply to the non-linear large scale model. – jonk May 18 at 19:13
• I was asking in general. Shockley diode equation with numerical methods are used as far as I understand from the answers. – Genzo May 19 at 13:40
• Sounds good, then. The closed solution math is a bit drawn out. – jonk May 19 at 17:37

## 4 Answers

The concept of dynamic resistance is a derivative:

$$\ r = \frac{dv}{di} \$$

As such, it only applies to variations of current and voltage that are small enough to allow us to neglect the non-linearity and use a linear model for the diode.

But if the voltage across the diode varies a lot like in a AC to DC rectifying diode,

In this case, a linear model can't be used to model the diode's behavior over the whole waveform, and the concept of "dynamic resistance" which is a part of this linear model does not exist, so you'll have to use the diode equation.

If you only look at a specific point in time on the waveform, then you can calculate dynamic resistance at this point, depending on the value of the current at this point.

• If you need a simpler approximation, you could always just use a few more terms in the taylor series, no? – Hearth May 18 at 17:55
• You could, but it won't help much with modeling the whole diode IV curve – peufeu May 18 at 19:14

You can model the DC I-V characteristics with the Shockley diode equation over a fairly wide range of currents, especially if you include an accurate ideality factor and some series resistance. It's nonlinear but still very simple and easy to solve numerically.

The diode model used in SPICE has more than a dozen parameters.

Yes, for slow enough changes in bias, a diode can be modeled as a nonlinear resistor. For faster changes you must also consider the diode's capacitance, which is also bias-dependent.

Simplifying a lot, the simulator has to keep updating the value for the dynamic resistance as the simulation evolves.

For "large" voltage variations, you might model the diode as a distortion. The coefficients of the polynomials in the series of terms will work in that model.

Look for Taylor Series Expansion of e^x, as a start.