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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.

Zener Power Supply

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  • \$\begingroup\$ 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) \$\endgroup\$ – Cezar Chirila Oct 29 '17 at 11:56
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    \$\begingroup\$ Do not open hfe, it is a dependent source. \$\endgroup\$ – sarthak Oct 29 '17 at 12:36
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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\$.

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  • \$\begingroup\$ This is the correct answer, thank you! I still do not clearly understand why the current from that node is -ib(1+hfe) and not -ib*hfe. \$\endgroup\$ – Cezar Chirila Oct 29 '17 at 13:25
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    \$\begingroup\$ It would be better to show the OP the direction rather than providing the answer directly. \$\endgroup\$ – Spehro Pefhany Oct 29 '17 at 13:25
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First find the impedance the base is being driven with. That's R in parallel with the Zener at the operating point you are using. You'll need to look in the Zener datasheet.

Next, reflect that impedance to the emitter. That's the impedance looking into the emitter. How the impedance is reflected from base to emitter is a function of the gain of the transistor, again, at the operating point it is actually used at. Put that in parallel with Rs to get the final output impedance at Us.

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