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It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. As originally conceived by Hendrik Wade Bode in the 1930s, the plot is an asymptotic approximation of the frequency response, using straight line segments .
The Bode plot of a first-order low-pass filter. The frequency response of the Butterworth filter is maximally flat (i.e., has no ripples) in the passband and rolls off towards zero in the stopband. [2] When viewed on a logarithmic Bode plot, the response slopes off linearly towards negative
Magnitude transfer function of a bandpass filter with lower 3 dB cutoff frequency f 1 and upper 3 dB cutoff frequency f 2 Bode plot (a logarithmic frequency response plot) of any first-order low-pass filter with a normalized cutoff frequency at =1 and a unity gain (0 dB) passband.
If the transfer function of a first-order low-pass filter has a zero as well as a pole, the Bode plot flattens out again, at some maximum attenuation of high frequencies; such an effect is caused for example by a little bit of the input leaking around the one-pole filter; this one-pole–one-zero filter is still a first-order low-pass.
It is also possible to perform Monte Carlo sensitivity analysis. The plotting tool is capable of generating frequency spectrums and performing frequency analysis to generate Bode diagrams and Nyquist plots. Hopsan models can be exported to Simulink. Plot data can be exported to XML, CSV, gnuplot and Matlab.
A Bode plot of displacements in the system with (red) and without (blue) the 10% tuned mass. The Bode plot is more complex, showing the phase and magnitude of the motion of each mass, for the two cases, relative to F 1. In the plots at right, the black line shows the baseline response (m 2 = 0).
Bode's sensitivity integral, discovered by Hendrik Wade Bode, is a formula that quantifies some of the limitations in feedback control of linear parameter invariant systems. Let L be the loop transfer function and S be the sensitivity function .
A straight-line approximation of its Bode plot when normalized with = and =-is: For the above plot: Below ω 1 {\displaystyle \omega _{1}} , the circuit attenuates, and well below ω 1 {\displaystyle \omega _{1}} acts like a differentiator.