Frequency response analysis
• Frequency response is the steady state output of a linear
system to sinusoidal input
• Even though these responses are of same frequency as that of
input, they differ in amplitude and phase angle from the input
• These differences are functions of frequency
• Since input is sinusoidal substitute s=jω in the transfer
function
• Magnitude frequency response
• Phase frequency response
• Combination of the magnitude and phase
response is called the frequency response
frequency
Phase plot
Frequency domain specifications
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Gain margin
Phase margin
Resonant frequency
Resonant peak
Gain margin
•
It is the gain that can be varied before the system becomes just stable
•
The amount of additional open-loop gain, expressed in dB and measured at 180 degree of phase
shift, required to make a closed-loop system unstable.
Phase margin
• The phase margin is the amount of additional open-loop phase shift
required at unity gain to make the closed-loop system unstable.
Standard second order system
• Resonant Peak
• Resonant frequency
Gain margin and Phase margin from bode plot
Minimum phase system
• It is a system in which poles and zeros will not
lie on the right side of s plane
• The transfer function of the minimum phase
system can be determined from the bode plot
Polar plot