- before creating the Bode magnitude and phase
plots, check the form of H(s). Poles and zeros (except for
"s" or "1/s" terms) must be of the form (1+s/a). before
canceling out any constants or terms, make sure you've maintained
an equivalent expression to the original (e.g. if you multiply all
factored constants and roots back together, you should get the
original transfer function).
- roots of the form 1+s/a have two asymptotes--one at constant 0 dB before the -3dB frequency and one with +/- 20 dB/dec slope starting at the -3dB frequency (+20 for zeros, -20 for poles). the special case (zero "s" or pole "1/s") will have only one asymptote with the mentioned +/- 20 dB/dec roll-off starting at omega = 1.
- poles have a constant phase of 0° until one decade before the -3dB frequency, where the phase shifts with -45°/dec slope and ends with constant phase of -90° one decade after the -3dB frequency. for zeros, the behavior is similar except the phase shift is +90°. the special case ("s" or "1/s") will be different...it may help to think about them in terms of "jw" instead of "s".
- these are all approximations, of course, but you can verify the behavior by manually calculating the magnitude and phase angle of each root at different frequencies. you will see that the approximated curves match the actual curves very closely.
- the following document is a helpful quick reference for drawing Bode plots: http://lpsa.swarthmore.edu/Bode/BodeRules.pdf
- please include and label ALL individual contributions (asymptotes, constants, etc.) to the total magnitude and phase responses on your final plots. you can use the graph paper provided on the assignment sheet.