![]() ![]() Also, \$w_n=w_p\$, causes an infinite response (undamped system - oscillator). The meaning of \$w_n\$ for the Butterworth response is the same as for the first-order case, that is, \$w_n\$ represents the -3 dB frequency, also called cuttoff frequency. The magnitude curve is sais to be maximally flat (no peak). In filter theory, that special value for \$\zeta=0.707\$ corresponds to a Butterworth response. Note on figure below: When varying the damping ratio \$\zeta\$, the peak follows a specific curve. Where \$\omega_n\$ is the natural frequency (also called corner frequency when considering assymptotes), the peak Frequency is the logarithmic axis on both plots. Peaks in the frequency response can only exist in systems with conjugate complex poles.įor an underdamped (\$\zeta 0.5\$) second-order system, the peak appears specifically for \$\zeta<1/\sqrt$$ Bode plots consist of two individual graphs: a) a semilog plot of gain vs frequency b) a semilog plot of phase shift vs frequency. ![]()
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