Why Use Magnitude and Phase Plots?

• Overview
• Freq Domain
• Why Bode?
• Asymptotic plots
• Making Plot
• Examples
• BodePlotGui
• Rules Table
• Printable

Why choose the Bode Plot representation?

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The previous document made the case that the study of sinusoidal inputs is important, and showed how phasor representations of the input and the system transfer function can be used to easily determine system output.  This document will explain why the standard way of representing the transfer function is with two plots: magnitude vs. frequency and phase vs. frequency. 

The difficulty in representing the transfer function comes about because we need to plot a complex number, H(s) or H(jω), as a function of frequency.  Consider the transfer function

To graph this, the most straightforward way (with a computer) might be to plot the value of H(s) as the frequency changes.  This yields the blue line in the three-dimensional plot shown below.

It would obviously be hard to get accurate information about the real and imaginary parts of H(s) from such a plot.  It is easier if we plot the real and imaginary parts as a function of frequency (the red and green projections of the blue line).  Clearly, in this case, two 2-dimensional graphs (one for real and one for imaginary) are superior to a single 3-dimensional graph.

However, in the last document we showed that to easily determine the output given the input, we would like to have the transfer function in phasor notation.  This means that we should make a plot of magnitude and phase.  Again, we could make a single 3-dimensional plot (the blue line), but it would be easier to interpret the results if we make two 2-dimensional plots (the magenta and cyan lines).

To clarify further, lets make separate plots of the magnitude and phase.

Note:  Standard Bode plots are logarithmic on the frequency axis, and plot the magnitude in dB's (deciBels).  We'll explore that in the next installment.

Consider the examples from the previous document. 

By examining the plots above, the magnitude and phase from the diagrams, the phasor representation of the transfer function at any frequency is immediately obvious.

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