Complex plane with unit circle and radial phase lines: the standard format for plotting Nyquist contours and frequency response in control systems.

Free printable Nyquist plot paper PDF. Cartesian complex plane with concentric circles and radial phase lines for control-system stability analysis.

Nyquist Plot Paper | Free Printable PDF

Nyquist Plot Paper

Before sketching the full Nyquist contour, evaluate G(jω) at ω = 0 (the DC gain on the real axis), ω = ∞ (the high-frequency limit), and the corner frequencies of any poles or zeros. Plot those points first, then sketch the curve connecting them.

Plot a few key frequencies first

The Nyquist criterion is: number of encirclements of –1 equals (closed-loop unstable poles) – (open-loop unstable poles). For most stable systems, you want zero encirclements. Trace your contour with a finger; count how many times it goes around the point (–1, 0).

Check the –1 encirclement count

Where the contour crosses the negative real axis (between –1 and the origin), the distance to –1 is the gain margin. If the crossing is at –0.5, the gain margin is 2 (you could double the open-loop gain before instability). If it crosses past –1, the system is already unstable.

Read gain margin off the negative real axis

Find where the contour crosses the unit circle. The angle from the negative real axis to that crossing point is the phase margin. A larger phase margin means more damping. Typical control-loop designs target 45–60° of phase margin.