# Z Plane Magnitude Surface Plot 1R Pole

Cuthbert Nyack
The properties of the transfer function in the Z domain of a system, with a pole at p1, is shown in the applet below for Z within the unit circle. Fn = 0 shows the Magnitude, Fn = 1 shows the Phase, Fn = 2 shows the Real part and Fn = 3 shows the Imaginary part of the transfer function.

n is the number of zeros at the origin.
eg parameters (0.5, NA, 0, 1.0, 10.0, 1.0, 0, 60.0, 40.0, 1.6)
Shows the magnitude of the transfer function inside the unit circle when there is 1 pole at 0.5. The peak of the pole is truncated at the value of mx to improve the visibility of the values around the unit circle. In fact the height of the pole is infinite.

eg parameters (0.5, NA, 3, 2.8, 2.2, 1.8, 0, 120.0, 40.0, 1.0)
Shows the magnitude of the transfer function inside the unit circle when there is 1 pole at 0.5 and 3 zeros at the origin.

eg parameters (0.5, NA, 3, 1.0, 2.2, 2.0, 0, 0.0, 90.0, 1.0)
Shows a contour plot of the magnitude of the transfer function inside the unit circle when there is 1 pole at 0.5 and 3 zeros at the origin.

eg parameters (0.5, NA, 2, 1.0, 8.0, 1.8, 1, -40.0, 60.0, 1.0)
Shows the phase plot of the transfer function inside the unit circle when there is 1 pole at 0.5 and 2 zeros at the origin. Changing n shows how zeros at the origin affect the phase.

eg parameters (0.85, NA, -1, 2.8, 4.0, 1.8, 1, 108.0, 60.0, 1.0)
Shows the phase of the transfer function inside the unit circle when there are 2 poles at 0.85 and 0 respectively.

eg parameters (0.5, NA, 0, 1.0, 8.0, 1.8, 2, 100.0, 30.0, 1.4)
Shows a plot of the real part of the transfer function inside the unit circle when there is 1 pole at 0.5. The function changes sign along the real axis.

eg parameters (0.5, NA, 0, 1.0, 8.0, 1.8, 3, -30.0, 30.0, 1.4)
Shows a plot of the imaginary part of the transfer function inside the unit circle when there is 1 pole at 0.5. The function changes sign along a line parallel to the imaginary axis.