Electrical – Common collector effect of emitter resistor on output impedance

impedanceoutputtransistors

I've been trying to figure out why the expression for output impedance in a common collector configuration contains a parallel Re emitter resistor.
Looking at the classic circuit, it looks as though the Re resistor is not part of the seen output impedance (similar to the way it isn't in a common emitter configuration)

I'm a rather elderly person who has decided to take on myself to self-study analog electronics – so I would appreciate if someone more experienced and knowledgeable could enlighten me about this issue.

Thanks,
Sefer.

Best Answer

Inside the BJT transistor (and hidden from view) is a resistor called \$r_E\$. Sometimes it is called \$r_{\pi}\$ just to confuse everybody but I was brought up with \$r_E\$ so I'll refer to it as that. I'll refer to the external emitter resistor as \$R_E\$. This is what \$r_E\$ looks like in the bigger picture: -

enter image description here

The value of \$r_E\$ is inversely proportional to the current flowing from the emitter (largely the current flowing into the collector) and, proportional to a value called \$V_T\$ and \$V_T\$ is 26 mV at room temperature.

So, \$r_E\$ is about 26 ohm per mA of emitter current. If you want more evidence of this see the extract I took from here regarding what \$V_T\$ is. I've put this under the main body of my answer at the bottom of the page.

In a common-collector amplifier, the "imaginery emitter" would follow the base signal but the real emitter voltage would be the imaginery emitter voltage minus the loading effect of \$R_E\$ on \$r_E\$. In other words these two resistors form a potential divider on the "imaginary emitter".

And this is why the output from a common collector (emitter follower) BJT circuit contains both resistor values in the formula. It's also why the output impedance of a common emitter is loosely referred to as \$r_E\$ but is more accurately referred to as $$r_E || R_E$$.


Where \$V_T\$ comes from: -

enter image description here