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In electrical engineering and control theory, a Bode plot (/ ˈboʊdi / BOH-dee) is a graph of the frequency response of a system. 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 ...
You can use Bode plots to graphically determine the gain margin and phase margin of a system. [3] A Bode plot maps the frequency response of the system through two graphs – the Bode magnitude plot (expressing the magnitude in decibels) and the Bode phase plot (expressing the phase shift in degrees).
For the design of control systems, any of the three types of plots may be used to infer closed-loop stability and stability margins from the open-loop frequency response. In many frequency domain applications, the phase response is relatively unimportant and the magnitude response of the Bode plot may be all that is required.
Bode magnitude plot for the voltages across the elements of an RLC series circuit. Natural frequency ω0 = 1 rad/s, damping ratio ζ = 0.4. Sinusoidal steady state is represented by letting s = jω, where j is the imaginary unit. Taking the magnitude of the above equation with this substitution: and the current as a function of ω can be found from
For approximately linear phase, it is sufficient to have that property only in the passband (s) of the filter, where |A (ω)| has relatively large values. Therefore, both magnitude and phase graphs (Bode plots) are customarily used to examine a filter's linearity. A "linear" phase graph may contain discontinuities of π and/or 2π radians.
Figure 5: Bode gain plot to find phase margin; scales are logarithmic, so labeled separations are multiplicative factors. For example, f0 dB = βA0 × f1. Next, the choice of pole ratio τ1 / τ2 is related to the phase margin of the feedback amplifier. [9] The procedure outlined in the Bode plot article is followed.
Bode was one of the great engineering philosophers of his era. [3] Long respected in academic circles worldwide, [4][5] he is also widely known to modern engineering students mainly for developing the asymptotic magnitude and phase plot that bears his name, the Bode plot.
The magnitude Bode plot for a first-order filter looks like a horizontal line below the cutoff frequency, and a diagonal line above the cutoff frequency. There is also a "knee curve" at the boundary between the two, smoothly transitioning between the two straight-line regions.