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Figure 2 shows the Bode magnitude plot for a zero and a low-pass pole, and compares the two with the Bode straight line plots. The straight-line plots are horizontal up to the pole (zero) location and then drop (rise) at 20 dB/decade. The second Figure 3 does the same for the phase.
Hendrik Wade Bode (/ ˈ b oʊ d i / BOH-dee, Dutch:; [1] December 24, 1905 – June 21, 1982) [1] was an American engineer, researcher, inventor, author and scientist, of Dutch ancestry. As a pioneer of modern control theory and electronic telecommunications he revolutionized both the content and methodology of his chosen fields of research.
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.
This page was last edited on 19 July 2005, at 14:41 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may ...
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 .
The imaginary part of a response function describes how a system dissipates energy, since it is in phase with the driving force. [ citation needed ] The Kramers–Kronig relations imply that observing the dissipative response of a system is sufficient to determine its out of phase (reactive) response, and vice versa.
In this expanded plane, we define the polar of the point O to be the line at infinity (and O is the pole of the line at infinity), and the poles of the lines through O are the points of infinity where, if a line has slope s (≠ 0) its pole is the infinite point associated to the parallel class of lines with slope −1/s. The pole of the x-axis ...
For a rational and continuous-time system, the condition for stability is that the region of convergence (ROC) of the Laplace transform includes the imaginary axis.When the system is causal, the ROC is the open region to the right of a vertical line whose abscissa is the real part of the "largest pole", or the pole that has the greatest real part of any pole in the system.