Summation of Bode Plots

Questions
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1

Can anyone explain how I can create a plot of the summation of two or more bode plots. I have created 3 bode plots named G1, G2, and G3. I would like to create a bode plot called G4 which is the Magnitude of the previous 3 summed, and the Phase of the previous 3 summed. Each Bode plot was created using the following notation:

G1 = TransferFunctionModel[{"my function"},s];
G2 = ...
G3 = ...

Somehow I would like G4 to be the bode plot of G1+G2+G3… but this notation is clearly incorrect.

Then I did

BodePlot[{G1,G2,G3,G4},{10,10^(10)}]

Can someone please advise!!!
Thank you!!

2

I’ll have a think about this one and get back to you later.

3

Hi DJ,

It depends on what you mean by sum. On a Bode plot gains are in dB, so summing is equivalent to multiplication of gains, which is a series connection for transfer functions. (Or multiplication in the s-domain.) Such multiplication also sums phase response. Below tf1 has DC gain 1 and a single pole at -10; tf2 has gain 2 and a pole at -1000; tfSum is the series connection.

tf1 = TransferFunctionModel[{{{{}}}, {{{-10}}}, {{1 10}}}, s]

tf2 = TransferFunctionModel[{{{{}}}, {{{-1000}}}, {{2 1000}}}, s]

tfSum = SystemsModelSeriesConnect[tf1, tf2]

BodePlot[{tf1, tf2, tfSum}, PlotLegends -> {"TF1", "TF2", "Sum"}]

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4

That sounds right to me. I just did not know the syntax for doing what I wanted to do. Appreciate the help!!!

5

I have mathematica 8 and it doesn’t seem to recognize the SystemModelSeriesConnect function. Am I missing something obvious?

6

missed the “s” sorry.