Bode plot

From Academic Kids

A Bode plot, named for Hendrik Wade Bode, is usually a combination of a Bode magnitude plot and Bode phase plot:

A Bode magnitude plot is a graph of log magnitude against log frequency often used in signal processing to show the transfer function or frequency response of an LTI system. It makes multiplication of magnitudes a simple matter of adding distances on the graph, since

<math>

\log(a \times b) = \log(a) + \log(b) <math>

The Bode plot describes the output response of a frequency-dependent system for a normalised input. The magnitude axis of the Bode plot is often converted directly to decibels.

A Bode phase plot is a graph of phase against log frequency, usually used in conjunction with the magnitude plot, to evaluate how much a frequency will be phase-shifted. For example a signal described by: A×sint) may be attenuated but also phase-shifted. If the system attenuates it by a factor x and phase shifts it by -Φ the signal out of the system will be A/x×sint-Φ). The phase shift Φ is generally a function of frequency.

The magnitude and phase Bode plots can seldom be changed independently of each other—if you change the amplitude response of the system you will most likely change the phase characteristics as well and vice versa.

A typical application of a Bode plot is to show the frequency response of a filter. It is especially useful in this case because the complex curves that appear in a linear magnitude-frequency plot can often be approximated by straight lines in a Bode plot.

These asymptotic approximations are useful because they can be drawn by hand following a few simple rules. Simple plots can even be predicted without drawing them. A lowpass RC filter, for instance, requires only one calculation. It has an asymptote at 0 dB and an asymptote with a slope of -20 dB per decade, which meet at the point fc:

<math>

f_c = {1 \over {2\pi RC}} <math>

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