This page demonstrates the techniques described previously to take a transfer function defined by the user, identify the constituent terms, draw the individual Bode plots, and then combine them to obtain the overall transfer function of the transfer function. Finally, an example is given of how to use the Bode plot to find the time domain response of the system to a sinusoidal input.
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We start with the transfer function (note: the process here follows that on the second page of the file BodeRules.pdf):
We rewrite it by factoring into real poles & zeros, complex poles & zeros and poles & zeros at the origin.
Next we write all the poles and zeros is our standard form.
Rewrite the constant:
Now the transfer function is in the form we need to apply our rules to draw the Bode plot.
In this section we draw the Bode plots of each of the indivuidual termas enumerated above. Select one of the terms by selecting the corresponding radio button. The selected term will be highlighted on the graphs with a thicker line. An explanation that describes how to draw the asymptotic magnitude and phase plots for the selected term is written out below.
The graphs below show the individual plots (with the same color scheme as above), along with the combined plot (a thicker gray line) which is the sum of the individual plots for both magnitude and phase; in other words the asymptotic plot of the complete transfer function. This addition of terms can be complicated, but is conceptually quite easy.
On the Bode plot, the gray lines represent the asymptotic plot, adn the black line is the exact solution.
The pink dots show the magnitude and phase of the Bode plot at a frequency chosen by the user (see below).
(Note: it can take several seconds to refresh after changing variables.)
The input to the system is A·cos(ω·t + φ°)
Input = 1.0 · cos(1.0 · t + 0°); replace this.
The output is M·A·cos(ω·t +(φ + θ)°).
We get M and θ from the Bode plot.
cos(ω · t + (φ + θ)°); replace this.