Incremental analysis to solve a circuit with a Zener diode

[pc2-brazil]

Homework Statement

The attached figure is an illustration of a crude Zener-diode regulator circuit.

a) Using incremental analysis, estimate from the graph an analytical expression for v₀ in terms of V and Δv.
b) Calculate the amount of DC and the amount of AC in the output voltage using the Zener-diode characteristic to find model values.

Homework Equations

The Attempt at a Solution

First I assume that the current i_Z in the circuit goes in the direction of the diode's arrow. v_Z, the voltage across the diode's terminals, is minus v₀. Applying KVL to the circuit in the attached figure, I find that $V+\Delta v = v_0 - i_ZR_1 = -v_Z - i_ZR_1$.

To find an expression for $v_Z$, I first have to find the operating point values $V_Z$ and $I_Z$ in terms of V, considering the case when Δv = 0 (that is, ignoring the small signal). This gives: V = -I_ZR₁ - V_Z, or V_Z = -I_ZR - V. So I think I should do a graphical analysis, plotting the line v_Z = -i_ZR₁ - V at the given graph to estimate the intersection point V_Z, I_Z.

But the graph doesn't seem to give enough details for being able to find an intersection point.

Any hints on how to proceed?

Thank you in advance.

 

[berkeman]

I think you can just eyeball the intersection point. Would you estimate it to be -4.5V or -4.4V, or a different value?

 

[rude man]

Yeah, but you can't assume the reverse voltage curve has infinite slope, otherwise there would be no ac in the output and the problem seems to want a finite ac output.

I agree it's tough to estimate the dynamic impedance of the zener from the graph. Maybe ~ 0.1V/8mA = 12.5Ω.