Bode plot: Difference between revisions

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Capitalization of 1st word in bullet point
Capitalization of 1st word in bullet point
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To draw the phase plot, for '''each''' pole and zero:
 
* ifIf <math>A</math> is positive, start line (with zero slope) at <math>0^\circ</math>
* ifIf <math>A</math> is negative, start line (with zero slope) at <math>-180^\circ</math>
* ifIf the sum of the number of unstable zeros and poles is odd, add 180° to that basis
* atAt every <math> \omega = |x_n| </math> (for stable zeros <math>-\operatorname{Re}(z) < 0</math>), '''increase''' the slope by <math>45 \cdot a_n</math> degrees per decade, beginning one decade before <math> \omega = |x_n| </math> (E.g.: <math display="inline"> \frac{|x_n|}{10} </math>)
* atAt every <math> \omega = |y_n| </math> (for stable poles <math>-\operatorname{Re}(p) < 0</math>), '''decrease''' the slope by <math>45 \cdot b_n</math> degrees per decade, beginning one decade before <math> \omega = |y_n| </math> (E.g.: <math display="inline"> \frac{|y_n|}{10} </math>)
* "unstableUnstable" (right half plane) poles and zeros (<math>\operatorname{Re}(s) > 0</math>) have opposite behavior
* flattenFlatten the slope again when the phase has changed by <math>90 \cdot a_n</math> degrees (for a zero) or <math>90 \cdot b_n</math> degrees (for a pole),
* After plotting one line for each pole or zero, add the lines together to obtain the final phase plot; that is, the final phase plot is the superposition of each earlier phase plot.