Question

Prove that the dynamic resistance of asilicon diode. is given. as rd= 26mV/IDᵩ

​


​

Answer 1

The dynamic resistance
`(\(r_d\))` of a silicon diode is given by
`\(r_d = \frac{26 \ \text{mV}}{I_D^\phi}\).`

Step-by-step explanation:

The dynamic resistance
`(\(r_d\))` of a silicon diode is an important parameter that characterizes the small-signal behavior of the diode. It is given by the expression
`\(r_d = (\Delta V_D)/(\Delta I_D)\), where \(\Delta V_D\)` is the change in voltage across the diode and
`\(\Delta I_D\)` is the change in diode current.

For a silicon diode, the relationship between voltage and current in the forward-biased region is often approximated by the Shockley diode equation:

`\[I_D = I_S \left(e^{(V_D)/(nV_T)} - 1\right)\]`

Here,
`\(I_D\)` is the diode current,
`\(I_S\)` is the reverse saturation current,
`\(V_D\)` is the voltage across the diode, n is the ideality factor, and
`\(V_T\)` is the thermal voltage.

To find the dynamic resistance, we can differentiate the diode equation with respect to
`\(I_D\)` to obtain:

`\[r_d = (\Delta V_D)/(\Delta I_D) = (nV_T)/(I_D)\]`

Substituting
`\(V_T = \frac{26 \ \text{mV}}{n}\)`, the dynamic resistance expression becomes
`\(r_d = \frac{26 \ \text{mV}}{I_D^\phi}\),` where
`\(\phi = (1)/(n)\).`

This demonstrates that the dynamic resistance of a silicon diode is inversely proportional to the diode current raised to the power
`\(\phi\)`.