Transfer Function Analyzer

Analyze poles, zeros, DC gain, Bode samples, and time-domain response data from a polynomial transfer function.

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What This Calculator Does

This calculator analyzes a continuous-time transfer function given by numerator and denominator polynomial coefficients. It reports poles, zeros, DC gain, stability, and compact Bode, step, and impulse response sample data.

It combines Numerator Coefficients, Denominator Coefficients, Min Frequency, Max Frequency to estimate DC Gain, Stability, Poles.

Formula & Method

Core equations:

G(s)=\frac{N(s)}{D(s)}

, DC gain is

G(0)=\frac{N(0)}{D(0)}

, and the frequency response is evaluated on the imaginary axis as

G(j\omega)

with magnitude

20\log_{10}|G(j\omega)|

and phase

\angle G(j\omega)

Notation used in the formulas: $R$ = DC Gain; $x_{1}$ = Numerator Coefficients; $x_{2}$ = Denominator Coefficients; $x_{3}$ = Min Frequency; $x_{4}$ = Max Frequency; $x_{5}$ = Time Horizon.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when you need a fast control-systems read on pole-zero placement, low-frequency gain, and whether a plant or compensator looks stable before you move to a full plotting tool.

Reference Book

Modern Control Engineering

Katsuhiko Ogata · Pearson

A standard control-systems text for transfer functions, response analysis, and PID-style tuning frameworks.

View Book

Inputs Used

Numerator Coefficients: Used directly in the calculation.
Denominator Coefficients: Used directly in the calculation.
Min Frequency: Used directly in the calculation.
Max Frequency: Used directly in the calculation.
Time Horizon: Used directly in the calculation.

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