Draw Nyquist plots online
This free online Nyquist plot tool maps a transfer function H(s) into the complex plane. Enter H(s) and it traces H(jω) as a Nyquist diagram, drawing the full contour, the −1 critical point, and the behaviour at infinity.
What is a Nyquist plot?
A Nyquist plot is the curve traced by the complex value H(jω) as the frequency ω sweeps from −∞ to +∞. Unlike a Bode plot, it shows magnitude and phase together as a single path in the complex plane.
It is the basis of the Nyquist stability criterion: by counting how many times the open-loop response encircles the −1 point, and in which direction, you can determine the number of unstable closed-loop poles without solving for them directly.
How to draw a Nyquist plot from a transfer function
- Enter the open-loop transfer function as coefficients or typed polynomials.
- The solid curve is the response for ω > 0; the dashed curve is its mirror for ω < 0.
- Watch the −1 critical point and how the contour encircles it, plus the dotted arcs at infinity for systems with poles on the imaginary axis.
- Hover the curve to read values, and follow the direction arrows for increasing ω.
Frequently asked questions
- What is a Nyquist plot?
- A Nyquist plot is the path traced by H(jω) in the complex plane as frequency ω runs from −∞ to +∞. It is used with the Nyquist stability criterion to judge closed-loop stability.
- How do you read a Nyquist plot?
- Look at how the curve encircles the −1 point. The number and direction of those encirclements, together with the open-loop poles in the right half-plane, determine the number of unstable closed-loop poles.
- Why is the −1 point important on a Nyquist plot?
- The −1 point is the critical point of the Nyquist stability criterion. Encirclements of −1 by the open-loop frequency response correspond to right-half-plane closed-loop poles.
- Is this Nyquist plotter free?
- Yes, it is completely free and runs in your browser with no signup.