How do I make a Nyquist plot from a transfer function?

Enter numerator and denominator coefficients in descending powers of s, plus an optional gain K. The tool evaluates G(jω) on a log-spaced frequency grid and draws real versus imaginary. Download the SVG for a report or slide.

What does a Nyquist plot tell you?

It shows how the open-loop frequency response travels in the complex plane. How the curve sits relative to (−1, 0) is the geometric core of the Nyquist stability criterion. This page draws the curve. It does not output stable/unstable.

Is this the same as a Bode plot?

No. A Bode plot is magnitude and phase versus frequency. A Nyquist plot is Re(G(jω)) versus Im(G(jω)). Same transfer function, different figure. Use the Bode plot generator for the two-panel chart.

Does this run the Nyquist stability criterion?

No. It does not count clockwise encirclements of (−1, 0) and it does not know P, the number of open-loop right-half-plane poles. The printed distance to (−1, 0) is only a geometric hint.

Is this an electrochemical impedance Nyquist plot?

No. Impedance spectroscopy plots Z′ versus −Z″ from measured spectra. This page evaluates a control-system transfer function G(s). Paste EIS tables elsewhere.

Is the Nyquist plot generator free?

The precise, coefficient-driven plot is free to use and free to download as SVG, with no sign-up. Sign in only if you want AI illustrations or other ConceptViz generation tools.

Control Systems Tool

Nyquist Plot Generator for G(jω)

Free Nyquist plot generator. Enter a transfer function to draw G(jω) on the complex plane, then download SVG.

Numerator / denominator coefficientsReal vs imaginary of G(jω)Critical point (−1, 0)Download a watermark-free SVG — free

Enter numerator and denominator coefficients — renders G(jω) on the complex plane as SVG, free

Transfer function

Coefficients in descending powers of s, same as the Bode page. This tool does not run the full Nyquist N = P − Z test.

NumeratorDenominatorGain K

Title

Critical point (−1, 0)Mirror ω < 0 (real coefficients)Unit circle

n=240 · closest approach to (−1, 0) is 1.000 at ω=80.000. Distance is a diagnostic, not a stability verdict.

Nyquist Plot Examples

The first four are exact engine renders from transfer functions. The last two are AI illustrations of Illustration mode.

View:

First-order low-pass

Exact engine render — H(s) = 1/(s+1), real vs imaginary of G(jω).

nyquistlow-pass

Second-order system

Exact engine render — damped second-order plant.

nyquistsecond-order

Type-1 plant

Exact engine render — a pole at the origin sends low-ω points down the imaginary axis.

nyquisttype-1

Integrator

Exact engine render — G(jω) = −j/ω.

nyquistintegrator

AI illustration — polar

AI illustration of Illustration mode — visual mockup, not evaluated from G(s).

aiillustration

AI illustration — teaching

AI illustration of Illustration mode — visual mockup, not a stability proof.

aiillustrationteaching

What is a Nyquist plot?

A Nyquist plot is the frequency response of a transfer function drawn on the complex plane: the real part of G(jω) on x, the imaginary part on y, as ω runs from near 0 to a large value. Control engineers use it with the Nyquist stability criterion and the critical point (−1, 0). This page evaluates a continuous-time rational G(s) you type as coefficients. It is not a Bode magnitude/phase pair, and it is not the electrochemical impedance plot of Z′ versus −Z″.

How to enter G(s)

Use the same coefficient convention as the Bode plot generator: descending powers of s. 1 / (s + 1) is numerator 1 and denominator 1, 1. A type-1 plant 1 / (s(s + 1)(s + 2)) is denominator 1, 3, 2, 0.
The solid curve is ω > 0. The dashed curve is the conjugate mirror for real coefficients (ω < 0). The red dot is (−1, 0). Distance from the curve to that point is printed as a diagnostic.
This page does not count encirclements or apply N = P − Z. For a stability argument you still need the open-loop right-half-plane pole count from your notebook.

Nyquist plot versus a Bode plot

Both come from G(jω). A Bode plot splits that number into magnitude (dB) and phase (degrees) versus log frequency. A Nyquist plot keeps the complex number as one polar curve. Use this page for the complex-plane figure; use the Bode plot generator for the two-panel frequency-response figure.

Export

Download a scalable SVG with no watermark and no account required for the precise plot. The AI Illustration tab is only for slides when you do not have a transfer function yet — it will not match your G(s).

Frequently Asked Questions

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What is a Nyquist plot?

How to enter G(s)

Use the same coefficient convention as the Bode plot generator: descending powers of s. 1 / (s + 1) is numerator 1 and denominator 1, 1. A type-1 plant 1 / (s(s + 1)(s + 2)) is denominator 1, 3, 2, 0.

The solid curve is ω > 0. The dashed curve is the conjugate mirror for real coefficients (ω < 0). The red dot is (−1, 0). Distance from the curve to that point is printed as a diagnostic.

This page does not count encirclements or apply N = P − Z. For a stability argument you still need the open-loop right-half-plane pole count from your notebook.