How do I find the forward resistance of a diode using diode law?

[lilmul123]

Homework Statement

I must find the resistance of a diode inside the piecewise model using the diode law equation.

I am given variables V_D = .75V, I_s = 5*10^-13 A, and V_T = .026 A. n = 1

Homework Equations

The Diode Law equation: I_D = I_S(e^(V_D/nV_T) - 1)

The Attempt at a Solution

We were told that to find the resistance, we are to find the derivative of this equation to find the conductance, and then the inverse of this would be the resistance. I'm not sure what to derive with respect to or if even this explanation is correct. Can anyone help explain how to find resistance using this equation?

 

[gneill]

One measure of resistance is the one that describes the operating point of the device: operating voltage divided by operating current. So if you're given the voltage across the device and can calculate the resulting current, then R = V/I.

A second measure of resistance is the 'small signal resistance', which describes how a change in voltage across the device (at the operating point) affects the current: r = Δv/ΔI. This one you might find by taking the derivative of your diode law w.r.t. voltage to find di/dv, and hence dv/di.

It looks like it's the first version of resistance you're after in this case.

 

[NascentOxygen]

It looks like it's the first version of resistance you're after in this case.

Poster needs to find the small signal resistance. (Probably what you meant to say.)

The variables are I_D and V_D, being the diode current and voltage, all other terms are constants.

 

[gneill]

Poster needs to find the small signal resistance. (Probably what you meant to say.)

You're probably right!
Thanks for he catch.

 

[DeeNos]

Firstly, it is important to note that the term "resistance" is not typically used when discussing diodes. Instead, the concept of resistive behavior in a diode is often referred to as "dynamic resistance" or "incremental resistance." This is because the resistance of a diode is not constant like a typical resistor, but instead varies with the applied voltage.

To find the dynamic resistance of a diode using the diode law equation, we can rearrange the equation to solve for the dynamic resistance (RD):

RD = (1/ID)*(dVD/dID)

Where dVD/dID is the derivative of the forward voltage (VD) with respect to the forward current (ID). This can be found by taking the derivative of the diode law equation:

dVD/dID = (nVT/ID)

Plugging this back into the equation for RD, we get:

RD = (1/ID)*(nVT/ID) = nVT/ID^2

Therefore, to find the dynamic resistance of a diode, we can substitute the given values for VD, IS, VT, and n into this equation. Keep in mind that the diode law equation is an approximation and the actual dynamic resistance may vary slightly.