# Bode plot and Step Response for 1 Real Pole and 1 real Zero

Cuthbert Nyack
This applet shows the Bode plot of a 1 pole and a 1 pole, 1 zero system:-
For the 1 pole system the phase(cyan) goes from 0 to -0.5p and the magnitude(orange) curve has a slope of -20dB/decade at high frequencies.
For the 1 pole, 1 zero system the phase(green) starts and ends at zero. It may go +ve or -ve in between depending on whether the zero is to the left or right of the pole. The magnitude plot starts ands with a slope of 0.
eg (1.0, 0.6, 0, 2.0, ~1.11, 5.0) shows zero to right of pole. The minimum phase occurs at (az)½ = ~1.095rad/s
(1.0, 0.6, 0, 0.2, ~0.35, 4.0) shows zero to left of pole. The maximum phase occurs at (az)½ = ~0.346rad/s
The eg parameters (1.0, 0.2, 0, 3.0, ~0.2, 1.5) show the accuracy with which the asymptote follows the magnitude curve of a single pole for frequencies greater than a.
(1.0, 0.1, 0, 10.0, ~1.0, 3.0) show the break frequencies in the magnitude plot of the 1 pole, 1 zero system coincides with the pole(x, 0.1) and zero(o, 10.0) location and the minimum phase occuring at 1rad/s.

Gif image below shows how applet should appear. 