Electronic – Explain the equation

diodespower electronics

Explain the following equation…

r^{\prime}_d = \dfrac{26\mathrm{mV}}{I_D} + r_B

Explain from where and how this equation comes out . Also elaborate the terms used in above mentioned equation.

Best Answer

If it is the dynamic resistance of the diode, \$r_d\$ is the value of this resistance, when the diode is forward biased with a current \$I_D\$.

This starts from the analysis of the diode equation

$$ I = I_s\cdot \left(e^{\dfrac{q_e\,V}{\eta\,K\,T}} -1\right) $$

and defining the dynamic resistance as

$$ r_d = \dfrac{dV}{dI} $$

replacing \$K\$ for the Boltzmann's constant, \$T\$ the temperature, \$\eta\$ a coefficient between 1 y 2, \$q_e\$ the electron charge and \$I_s\$ the saturation current (minoritary carriers), an aproximate value is

$$ r_d \approx \dfrac{26\,\mathrm{mV}}{I} $$

You can find a more detailed explanation here