Contents
What effect does a pole near the unit circle have on the phase response?
When the poles are close to the unit circle, the frequency response has peaks at ±0.2π. 4. The closer the poles are to the unit circle, the sharper the peak is. Poles at the origin (z = 0) have no effect on |Hf (ω)|.
What happens when poles get closer to zero?
Effects of Poles and Zeros As s approaches a zero, the numerator of the transfer function (and therefore the transfer function itself) approaches the value 0. When s approaches a pole, the denominator of the transfer function approaches zero, and the value of the transfer function approaches infinity.
What is a gain margin?
1. Gain margin. Gain margin is defined as the amount of change in open-loop gain needed to make a closed-loop system unstable. The gain margin is the difference between 0 dB and the gain at the phase cross-over frequency that gives a phase of −180°.
What causes a zero on the unit circle?
A zero on the unit circle causes a zero in the magnitude response at the corresponding frequency ( z = 1 is DC, and z = − 1 is Nyquist) For a zero at DC ( z = 1 ), the sum of all impulse response coefficients must be zero. A zero near the unit circle causes a dip in the magnitude response at the corresponding frequency.
What causes a dip in the magnitude response?
A zero near the unit circle causes a dip in the magnitude response at the corresponding frequency. The closer the zero to the circle the more pronounced the dip. A pole close to the unit circle causes a peak in the magnitude response at the corresponding frequency. The closer to the circle the sharper the peak.
Why does a pole close to a circle cause oscillation?
A pole close to the unit circle causes a peak in the magnitude response at the corresponding frequency. The closer to the circle the sharper the peak. Complex conjugate poles cause oscillation.
What are poles and zeros in signal processing stack exchange?
The plot on the left is the typical diagram we see when introduced to poles and zeros showing their location on the s-plane, noting that a pole is the value for s that makes the equation X (s) go to infinity while a zero is the value for s that makes the equation X (s) go to zero.