Excel Formula To Test If Number Is Positive Or Negative How To Draw a Bode Plot

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How To Draw a Bode Plot

There are two ways to draw a Bod plot. Calculating the magnitude and phase of the system transfer function at each frequency and drawing a plot with those points. Next, called asymptotic bode plot, considers straight lines between poles or zeros and has some simple rules for the slopes of those lines. Given its simplicity, these can be drawn by hand. This article focuses on the asymptotic bode plot.

A transfer function is expressed by a DC gain, rooted at the numerator (zero) and rooted at the denominator (pole):

H(s) = DC gain * (s/z1 + 1) *… * (s/zn + 1) / ((s/p1 + 1) *… * (s/pm + 1))

with zeros from z1 to zn and poles from p1 to pm. We can have negative and positive poles and zero.

Magnitude plot

The rules for drawing a magnitude plot are:

  • The plot starts with a horizontal line at magnitude equal to the DC magnitude of the system (H(0) = A).

  • For each pole, the slope of the line decreases by 20 dB/decade frequency at that pole’s frequency.

  • For each zero, the slope of the line increases by 20 dB/decade of the frequency at that zero’s frequency.

  • For each pole or zero at zero frequency, the plot starts with the effect of that pole/zero on the slope. Poles and zeros at zero frequency Zero: H(s) = s Pole: H(s) = 1/s Which means that at a frequency of 1 rad/s, the magnitude must be equal to the DC magnitude A . The trace of the plot should cross A at 1 rad/s and move back to the starting frequency of the plot.

  • For multiple zeros or poles at the same frequency, the slope of the line changes according to that number

Phase plot

The rules for step plotting are as follows:

  • Start the plot with a horizontal line at 0º phase if the gain is positive or -180º if the gain is negative (a negative gain corresponds to a 180º phase between input and output)

  • For each negative pole or positive zero, decrease the slope by 45º/decade one decade before the pole/zero, and increase by the same amount one decade after the pole/zero. After two decades, the phase will be -90º from before for each pole/zero.

  • For each positive pole or negative zero, increase the slope by 45º/decade one decade before the pole/zero, and decrease by the same amount one decade after the pole/zero. After two decades, the phase will be +90º for each pole/zero than before.

  • For each pole or zero at zero frequency, the plot starts with the effect of that pole/zero on the phase. This means poles subtract 90º from the initial phase and zeros add 90º to the initial phase.

For detailed diagrams, visit the complex root case and the bode plot on OnMyPhd, an online bode plot generator.

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