# Incremental analysis to solve a circuit with a Zener diode

• Engineering
• pc2-brazil
In summary, the conversation discusses a crude Zener-diode regulator circuit and using incremental analysis to estimate an analytical expression for the output voltage in terms of input voltage and change in voltage. It also mentions calculating the amount of DC and AC in the output using the Zener-diode characteristic. However, there is difficulty in finding the intersection point on the graph to accurately estimate the output voltage.
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.

## 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?

#### Attachments

• fig1.PNG
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Last edited:
I think you can just eyeball the intersection point. Would you estimate it to be -4.5V or -4.4V, or a different value?

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.

## 1. What is incremental analysis in the context of circuit analysis?

Incremental analysis is a method used in circuit analysis to simplify complex circuits by breaking them down into smaller, incremental sections. This allows for easier analysis and calculation of circuit parameters such as voltage, current, and resistance.

## 2. How does incremental analysis help to solve circuits with Zener diodes?

Zener diodes are non-linear components that can be difficult to analyze using traditional circuit analysis methods. Incremental analysis allows for the Zener diode to be treated as a small, incremental section of the circuit, making it easier to calculate the voltage and current across the diode.

## 3. Are there any limitations to using incremental analysis for circuits with Zener diodes?

While incremental analysis can simplify the analysis of circuits with Zener diodes, it may not provide exact results as it assumes that the Zener diode is operating in the linear region. In reality, Zener diodes can exhibit non-linear behavior at certain voltages, which may affect the accuracy of the analysis.

## 4. How is incremental analysis different from other methods of circuit analysis?

Incremental analysis differs from other methods of circuit analysis, such as nodal or mesh analysis, in that it focuses on breaking down the circuit into smaller, incremental sections rather than analyzing the circuit as a whole. This can be particularly useful for circuits with non-linear components like Zener diodes.

## 5. When is it appropriate to use incremental analysis for circuit analysis?

Incremental analysis is most useful for solving circuits with non-linear components or circuits with multiple stages. It can also be helpful in simplifying complex circuits for easier analysis. However, for circuits with only linear components, other methods of analysis may be more accurate and efficient.

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