Nyquist Plot

A Nyquist plot is the trajectory of G(iω) , where G(s) is a transfer function. This applet illustrates the dependence of the Nyquist plot on the poles and zeros of G(s) , in the particular case when G(s) is a rational function.

At right is a portion of the complex plane. On it are marked zeros (by small cyan circles) and poles (by small green x's). These can be moved by a cursor drag. They can be created or annihilated by buttons below the window. A single pole or zero is restricted to lie on the real axis. The [pole pair] and [zero pair] buttons allow creation of complex conjugate pairs of poles or zeros at the location of a cursor click. The "Annihilate" keys remove zeros or poles, or pairs of such. There is also a yellow diamond on the imaginary axis, which can be dragged along the axis the cursor. Pale line segments connect this point to the poles and zeros. The lengths of these segments contribute
to |G(iω)| . A ray directed arc around each pole and zero connects this line segment to a pale ray pointing in the positive real direction, illustrating the contribution of the pole or zero to Arg(G(iω)) . A rollover creates crosshairs and a readout.

The left window holds the Nyquist plot. A slider below this window controls the scale, logarithmically. The value of G(iω) corresponding to the marked value of i omega is marked by a yellow diamond and connected to the origin by a yellow line segment, and the magnitude and argument of G(iω) are displayed in yellow below the window.

The [Formula] button toggles display of the algebraic formula for the rational function with the given poles and zeros.

The number of poles or zeros is limited to 8.