# Pole-Zero Analysis

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## Description

Pole-Zero analysis enables you to determine the stability of a single input, single output linear system, by calculating the poles and/or zeros in the small-signal ac transfer function for the circuit. The dc operating point of the circuit is found and then linearized, small-signal models for all non-linear devices in the circuit are determined. This circuit is then used to find the poles and zeros that satisfy the nominated transfer function.

The transfer function can either be Voltage Gain (output voltage/input voltage) or Impedance (output voltage/input current).

## Setup

Pole-Zero analysis is set up on the Pole-Zero Analysis Setup page of the Analyses Setup dialog (after the dialog appears, click the Pole-Zero Analysis entry in the Analyses/Options list). An example setup for this analysis type is shown in the image below:

## Parameters

• Input Node - the positive input node for the circuit.
• Input Reference Node - the reference node for the input of the circuit (Default = 0 (GND)).
• Output Node - the positive output node for the circuit.
• Output Reference Node - the reference node for the output of the circuit (Default = 0 (GND)).
• Transfer Function Type - defines the type of ac small-signal transfer function to be used for the circuit when calculating the poles and/or zeros. There are two types available:

`V(output)/V(input)` - Voltage Gain Transfer Function.
`V(output)/I(input)` - Impedance Transfer Function.

• Analysis Type - allows you to further refine the role of the analysis. Choose to find all poles that satisfy the transfer function for the circuit (`Poles Only`), all zeros (`Zeros Only`), or both `Poles` and `Zeros`.

## Notes

Pole-Zero analysis works with resistors, capacitors, inductors, linear-controlled sources, independent sources, diodes, BJTs, MOSFETs and JFETs. Transmission lines are not supported.

The method used in the analysis is a sub-optimal numerical search. For large circuits it may take a considerable time or fail to find all poles and zeros. For some circuits, the method becomes "lost" and finds an excessive number of poles or zeros. If there is non-convergence in finding both poles and zeros, refine the analysis to calculate only poles or only zeros.

The simulation results are displayed on the Pole-Zero Analysis tab of the Waveform Analysis window.

## Examples

Consider the circuit in the image above, where a Pole-Zero analysis is defined with the following parameter values:

• Input Node = `IN`
• Input Reference Node = `0`
• Output Node = `OUT`
• Output Reference Node = `0`
• Transfer Function Type = V(output)/V(input)
• Analysis Type = `Poles and Zeros`

The entry in the SPICE netlist will be:

`*Selected Circuit Analyses: .PZ IN 0 OUT 0 VOL PZ`

Running the simulation will yield the output wave plot shown in the image below:

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