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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 .
Phase margin and gain margin are two measures of stability for a feedback control system. They indicate how much the gain or the phase of the system can vary before it becomes unstable. Phase margin is the difference (expressed as a positive number) between 180° and the phase shift where the magnitude of the loop transfer function is 0 dB.
Figure 5: Bode gain plot to find phase margin; scales are logarithmic, so labeled separations are multiplicative factors. For example, f 0 dB = βA 0 × f 1. Next, the choice of pole ratio τ 1 /τ 2 is related to the phase margin of the feedback amplifier. [9] The procedure outlined in the Bode plot article is followed. Figure 5 is the Bode ...
Bode's ideal control loop frequency response has the fractional integrator shape and provides the iso-damping property around the gain crossover frequency. This is due to the fact that the phase margin and the maximum overshoot are defined by one parameter only (the fractional power of s {\displaystyle s} ), and are independent of open-loop gain.
Tools include the root locus, the Nyquist stability criterion, the Bode plot, the gain margin and phase margin. More advanced tools include Bode integrals to assess performance limitations and trade-offs, and describing functions to analyze nonlinearities in the frequency domain.
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.
# set terminal svg enhanced size 875 1250 fname "Times" fsize 25 set terminal postscript enhanced portrait dashed lw 1 "Helvetica" 14 set output "bode.ps" # ugly part of something G(w,n) = 0 * w * n + 100000 # 1 / (sqrt(1 + w**(2*n))) dB(x) = 0 + x + 100000 # 20 * log10(abs(x)) P(w) = w * 0 + 200 # -atan(w)*180/pi # Gridlines set grid # Set x axis to logarithmic scale set logscale x 10 set ...
In signal processing, linear phase is a property of a filter where the phase response of the filter is a linear function of frequency.The result is that all frequency components of the input signal are shifted in time (usually delayed) by the same constant amount (the slope of the linear function), which is referred to as the group delay.