Z(out) for the BJT emitter-follower configuration

I have a slight problem trying to understand how to determine the output impedance of a emitter-follower configuration using the re model for small signal analysis. I also added the contribution of $$\r_o\$$.

From my understanding of circuit theory and analysis theorems, to determine the output impedance, I have to set the input $$\V_i = 0\text{ V}\$$ ($$\R_b\$$ has no influence now) and keep $$\V_o\$$ at a constant value (please correct me if I am wrong, I mostly study on my own without having someone to give me feedback on my understanding). I keep the controlled current source (for there still is a current going though the base node), $$\\beta r_e\$$, $$\r_o\$$ and $$\R_e\$$.

My first instinct would be to calculate $$Zo = \beta r_e \parallel r_o \parallel R_e$$

But I find in the book that $$Zo = \frac{\beta r_e}{\beta + 1} \parallel r_o \parallel R_e$$

What exactly is it that I don't understand?

• Little r e (aka $r_E$) is the output impedance at the emitter and it is in parallel with $R_E$. Feb 17, 2021 at 17:25
• This problem was discussed recently, see here: electronics.stackexchange.com/questions/331671/…
– LvW
Feb 17, 2021 at 17:29
• @LvW, that is a different problem. I am using small signal analysis using re model. The link you gave me is about h-parameters. Feb 17, 2021 at 17:34
• OK - the question contains h-parameters. But my answer - for example - uses the re model. (By the way: You can express h-parameters with re=1/gm and vice versa).
– LvW
Feb 17, 2021 at 17:45
• @LvW, It's just that the book I am reading right now started modeling BJTs using the re model first, though I understand your point of view for I have seen a lot of books using the hybrid parameters first. Maybe I shall skip right to the part where my book addresses them and return later to this part. I asked the question because I was assured that I can do the analysis using basic circuit theorems (like source transformation). Feb 17, 2021 at 17:53