Five Things Every Engineer Should Know About Bode Plots

Bode Plot of DC/DC Converter

In 1938 Hendrik Wade Bode, who worked at Bell Labs, published his asymptotic assessment of phase margin and gain margin, bearing his name [2]. The Bode plot is recognized for its simplicity and the simple asymptotic approach makes the method useful for both design and assessment of power system control loops.  There have been many other methods introduced since, including Nathaniel Nichol’s stability charts in 1947 [4] and root locus introduced by Walter Evans in 1948 [5].  In 1974 R.D. Middlebrook introduced minor loop gain stability assessment as a method of assessing the stability of an input filter combined with the negative input resistance of a switching regulator [5].

During the early 1980s, Dean Venable popularized the Bode plot with the introduction of a low-cost frequency response analyzer (‘FRA’) that allowed power engineers to directly measure the phase margin using Bode plots.  Since then, most power supply engineers have relied on the Bode plot for the assessment of stability.  While there have been several articles discussing the shortfalls of the Bode plot, this article presents an excellent case study on the shortfalls, as well as a simpler alternative.[6]

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1.   H. Nyquist, Regeneration theory, BSTJ, vol. 11, pp. 126–147, 1932.

2.   H. W. Bode, Variable equalizers, BSTJ, vol. 17, pp. 229-244, 1938.

3.   N. Nichols, in Theory of Servomechanisms, H. M. James et al., Eds. New York, NY: McGraw-Hill, 1947.

4.   W. R. Evans, Control System Dynamics, New York, NY: McGraw Hill, 1954.

5.   R. D. Middlebrook, Input filter considerations in design and application of switching regulators, Proc. IEEE Industry

6.  S.M. Sandler When Bode Plots Fail Us, Power Electronics, April 30, 2012

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