# Computing output resistance for zener power supply

I have a simple zener power supply, the schematic is below. My question is how to find the output resistance of the circuit?

I also have small signal model given, but I cannot get a proper result.

• I have tried replacing Ui with a short circuit, hfeIb with an open circuit and compute Rs as a function of R, Rz and Hie, but this didn t give me a proper result. I should get Ro = (Rz || R + hie)/(hfe + 1) – Cezar Chirila Oct 29 '17 at 11:56
• Do not open hfe, it is a dependent source. – sarthak Oct 29 '17 at 12:36

If you calculate the impedance seen across $u_s$ by shorting $u_i$, clearly R comes in parallel with $R_z$. Thus, potential at the node connected to current source becomes, $$V = -i_b(R_z||R + h_{ie})$$ Also total current will out from that node will be $-i_b(1+h_{fe})$.
The impedance becomes the ratio of these two i.e. $(R_z||R + h_{ie})/(1+h_{fe})$. This actually comes in parallel with the $R_s$.