Mathematical Expression for the Dynamic Resistance of a PN Junction Diodes

Mathematical Expression for the Dynamic Resistance

• We have seen earlier that the dynamic resistance is the reciprocal of the slope of the V‒I characteristic of a diode.

• For the incremental changes in voltage and current we can write,

 r = 1 / Slope of graph

 = 1 / [dI/dV]

• Now current equation of a diode is given by,

I = I₀ (e^V/ηVT ‒1)

Ex. 2.11.1: A p‒n junction diode has at a temperature of 125°C a reverse saturation current of 30 μ A. At a temperature of 125°C find the dynamic resistance for 0.2 V bias in forward and reverse direction.

Solution:

Now

T = 125 °C, V = ± 0.2 V, I₀ = 30 μА

V_T = kT at temperature T in °K

T= 125 + 273 = 398 °K

and k = 8.62×10^‒5 = Boltzmann's constant

and

V_T = 398×8.62×10^‒5

 = 0.034307 V = 34.3076 mV

The dynamic resistance is given by,

 r = ηV_T  / I₀e^V/ηVT

Assume germanium diode, η = 1

For forward bias, V = +0.2 V

 r_f = ( 1×0.0343076 ) / ( 30×10^‒6 × e^{0.2/0.0343076} )

 = 3.3612 Ω

For reverse bias, V = ‒ 0.2 V

 r_r = ( 1×0.0343076 ) / ( 30×10^‒6 ×e^{‒0.2/0.0343076} )

 = 389.078 ΚΩ

Review Questions

1. Derive the expression for the dynamic resistance of a diode.

2. For a silicon diode with reverse saturation current of 0.2 μA, calculate the dynamic forward and reverse resistance at a voltage of 0.72 V and ‒0.72 V respectively, applied across the diode, at room temperature of 27 °C.

[Ans. : 0.252 Ω, 2680.9 GΩ]