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Blog
What is a Bode plot?
September 17, 2007
Bode plots are a way of visually representing the transfer functions of electronic circuit elements, such as amplifiers and filters. In mechatronics, they also can represent system components, such as motors, flexible couplings, and even entire control loops. All that is required is that the transfer functions be single-valued with respect to frequency.
Bode plots are important for mechatronic analysis because they instantly signal any resonance conditions visually. They then aid analysis and remediation efforts by providing clear indications of what may be wrong and how to correct it.
Generally, two graphs are included in a set of Bode plots: response magnitude vs. frequency and phase vs. frequency. Typically, the frequency (horizontal) axis is plotted logarithmically. The vertical axis may be plotted logarithmically or linearly.
Bode plots for an electronic amplifier, for example, include a gain vs. log frequency graph, and a phase-shift vs. log frequency graph. Plots for a simple filter often include a log filter response vs. log frequency graph because a one-pole filter transfer function plots as a straight line on a log/log graph.
Logarithms have no units, while frequencies have units of Hertz or cycles per second. To make a logarithmic frequency axis, we need a comparison frequency. Any comparison frequency will do, but one typically likes to use something that makes sense in the problem. Amplifier characteristics, for example, are often published with 1 Hz being the comparison frequency, since in the sub-Hertz range, most amplifiers have effectively flat frequency responses.
Bode response plot of a low pass filter looks like the profile of a cliff.
As another example, low-pass filters typically have a characteristic, or cutoff, frequency at which the filter’s phase shift is 45º. At that frequency, the filter response is 0.7071. Using this frequency as the comparison frequency and plotting positive and negative log values puts the interesting part of the graph in the center.
Another class of system elements that are important in mechatronics is resonant elements. For mechatronics, resonance in the entire control loop is most important. The Bode plot for a resonant system generally consists of a sharp peak at the resonant frequency in the response graph, and a sinuous line passing through zero at the resonant frequency in the phase graph.
Bode phase plot of a low pass filter passes through zero at the cutoff frequency.
Additional important Bode plots include a response showing multiple peaks or nulls indicating multiple resonant frequencies. These may or may not be harmonics. Phase plots for multiple resonances show curves that pass back and forth between positive and negative phase shifts, with zero crossings at each resonant frequency.
Bode response plot of a resonant element peaks at the resonant frequency, where the system becomes unstable.
For more from Control Engineering on this topic, read:
Bode phase plot of a resonant element crosses zero at the resonant frequency.
"Bode plots solve frequency domain problems."
Posted by Charlie Masi on September 17, 2007 | Comments (0)