This example shows how to obtain numeric values of several frequency-domain characteristics of a SISO dynamic system model, including the peak gain, dc gain, system bandwidth, and the frequencies at which the system gain crosses a specified frequency.
Create a transfer function model and plot its frequency response.
H = tf([10,21],[1,1.4,26]); bodeplot(H)
Plotting the frequency response gives a rough idea of the frequency-domain
characteristics of the system.
H includes a pronounced
resonant peak, and rolls off at 20 dB/decade at high frequency. It
is often desirable to obtain specific numeric values for such characteristics.
Calculate the peak gain and the frequency of the resonance.
[gpeak,fpeak] = getPeakGain(H); gpeak_dB = mag2db(gpeak)
gpeak_dB = 17.7579
getPeakGain returns both the peak location
the peak gain
gpeak in absolute units. Using
gpeak to decibels shows that the gain peaks
at almost 18 dB.
Find the band within which the system gain exceeds 0 dB, or 1 in absolute units.
wc = getGainCrossover(H,1)
wc = 1.2582 12.1843
getGainCrossover returns a vector of frequencies
at which the system response crosses the specified gain. The resulting
shows that the system gain exceeds 0 dB between about 1.3 and 12.2
Find the dc gain of
The Bode response plot shows that the gain of
toward a finite value as the frequency approaches zero. The
finds this value in absolute units.
k = dcgain(H);
Find the frequency at which the response of
off to –10 dB relative to its dc value.
fb = bandwidth(H,-10);
bandwidth returns the first frequency at
which the system response drops below the dc gain by the specified
value in dB.