Input and Output Impedance of a BJT
Measuring input/output impedance is little more than calculating the resistors in a voltage divider. Consider the following two situations:







simulate this circuit &ndash; Schematic created using CircuitLab

Important is that the whole circuit is not clipping, so the voltage \$U_i\$ is small in relation to the supply voltage. There should be no distortion. Also it is essential that you measure only the AC component, so in case of the output impedance you do your measurements at the right end of the output capacitor.

For the output impedance you have to do two measurements at a given frequency. For audio 1kHz is a good start, but as Andy states, you might be interested in the impedance at various frequencies.

With a known input amplitude \$U_i\$ do two measurements:


Measure the voltage amplitude \$U_{o}\$ with \$R_l\$ removed (left situation);
Measure the voltage amplitude \$U_{o}\$ with a known \$R_l\$ in place (right situation);


\$(1) R_o = \dfrac{\Delta U_{R_o}}{\Delta I} \$

\$(2) R_o = \dfrac{U_i-U_o}{\frac{U_i}{R_o+R_l}} \$

\$(3) R_o = \dfrac{R_o+R_l}{U_i} (U_i - U_0)\$

\$(4) R_o = R_o + R_l - (R_o+R_l)\dfrac{U_o}{U_i}\$

\$(5) R_l = (R_o+R_l)\dfrac{U_o}{U_i}\$

\$(6) R_l(1-\dfrac{U_o}{U_i}) = R_o\dfrac{U_o}{U_i}\$

\$(7) R_o = R_l(1-\dfrac{U_o}{U_i})\dfrac{U_i}{U_o}\$

So the resulting formula to calculate the output impedance is:

\$(8) R_o = R_l(\dfrac{U_i}{U_o}-1)\$

Calculating output impedance follows the same method as calculating input impedance, you are just calculating the other resistor in the divider.

The input impedance is identical to \$R_l\$ in (6) where \$R_o\$ is the output impedance of your signal source (optionally increased by an extra series resistor. So:

\$R_l = R_{amp,in} , U_o = U_{amp,in} , U_i = U_{generator,out} , R_o = R_{out,generator}\$

\$(6) R_l(1-\dfrac{U_o}{U_i}) = R_o\dfrac{U_o}{U_i}\$

\$(9) R_{amp,in}(1-\dfrac{U_{amp,in}}{U_{generator,out}}) = R_{generator,out}\dfrac{U_{amp,input}}{U_{generator,out}}\$

\$(10) R_{amp,in} = R_{generator,out} \cdot \dfrac{U_{amp,in}}{U_{generator,out}} \cdot \dfrac{1}{(1-\dfrac{U_{amp,in}}{U_{generator,out}})}\$

\$(11) R_{amp,in} =  R_{generator,out} \cdot \dfrac{U_{amp,in}}{U_{generator,out}-U_{amp,input}}\$