# Incremental analysis to solve a circuit with a Zener diode

1. Feb 6, 2013

### pc2-brazil

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. The attempt at a solution

First I assume that the current iZ in the circuit goes in the direction of the diode's arrow. vZ, 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 = -IZR1 - VZ, or VZ = -IZR - V. So I think I should do a graphical analysis, plotting the line vZ = -iZR1 - V at the given graph to estimate the intersection point VZ, IZ.

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

Any hints on how to proceed?

#### Attached Files:

• ###### fig1.PNG
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Last edited: Feb 6, 2013
2. Feb 6, 2013

### Staff: Mentor

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

3. Feb 7, 2013

### 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.