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# Rpi - Input resistance of a transistor

## Simple amplifier circuit

Equivalent scematics:

So how can a diode have resistance?

## Shockley equation:

Shockley equation is diode current as a function of diode voltage.

Id - diode current

Vd - diode voltage

Is - reverse bias saturation current

Vt - termal voltage

n - ideality factor

Diode allmoast constant current changes just a little bit under the influence of input signal.

Because this change is small, it can be approximated with a line.

Slope of this line is input resistance Rpi.

Slope of a tangent line is first derivative.

Rpi is resistance that input signal sees when it is connected to amplifier input.

We model base-emmiter junction of a transistor with a diode.

This diode inside amplifier circuit is allways biased and has current Id trough it.

Input signal will change this current just a little bit, so we can approximate

diode function with tangent line, and because amplifier has input capacitor

we are only interested in the slope of that line.

Slope of a tangent line to function at certain point, is first derivative at that point.

And this is Rpi.

By the way formula for Vt is:

k - Boltzmann constant

T - temperature of diode in Kelvins

q - elementary charge