# Bode Plot When Adding Two Transfer Functions in Parallel

#### KevinB12345

Joined Mar 26, 2020
1
Hello,

If I have two transfer functions in series G1(s) and G2(s) where G3(s) = G1(s)*G2(s), I know that following holds true:
-for any given frequency, the magnitude in dBs of G3(s) is equal to the sum of the magnitude of G1(s) and the magnitude of G2(s)
-for any given frequency, the phase of G3(s) is equal to the sum of the phase of G1(s) and the phase of G2(s)

If instead G1(s) and G2(s) are connected in parallel where G3(s) = G1(s)+G2(s), is there any such shortcut for determining the magnitude and phase of G3(s) at a given frequency based on the magnitude and phase of G1(s) and G2(s) at that frequency?

Thanks,
Kevin

Joined Mar 10, 2018
4,057

#### MrAl

Joined Jun 17, 2014
7,748
Hello,

If I have two transfer functions in series G1(s) and G2(s) where G3(s) = G1(s)*G2(s), I know that following holds true:
-for any given frequency, the magnitude in dBs of G3(s) is equal to the sum of the magnitude of G1(s) and the magnitude of G2(s)
-for any given frequency, the phase of G3(s) is equal to the sum of the phase of G1(s) and the phase of G2(s)

If instead G1(s) and G2(s) are connected in parallel where G3(s) = G1(s)+G2(s), is there any such shortcut for determining the magnitude and phase of G3(s) at a given frequency based on the magnitude and phase of G1(s) and G2(s) at that frequency?

Thanks,
Kevin
I am not sure where you are getting that information, but it does not look right at all.

Try these...

For the following cases use these:
G1:1/(s+2)
G2:1/(s+3)

Find the amplitude and phase of both of those.

Now investigate the series case G1*G2,
then investigate the parallel case G1+G2.

Check the amplitude and phase of both of those.
Compare results to whatever you think is right for the combination of the individual transfer function gains and phases.

In one case the amplitudes multiply, in the other case the amplitudes approximately add but you should strive for the more exact result in which they differ slightly from the pure addition of the two.
However, the phases are quite different. Try the G1*G2 first that's the easiest.

What else you can do is see if you can find out how to combine these two sine functions:
ft1=sin(t+ph1)+sin(t+ph2)

See what it takes to combine those into just one single sine term:
ft2=A*sin(t+ph3)

by finding A and ph3. Note if you get everything right when you plot ft1 and ft2 from t=0 to 10 both graphs should be exactly the same. If there is even a small noticeable difference then something is not right yet.

EDIT:
I made a mistake with the parallel combo but is corrected now.

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