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I am trying to generate a Bode plot for a transfer function of a high pass circuit.

It's part of a solution to another question but this is the part that is confusing me. I have a transfer function:

Transfer Function

When I use a standard Bode plot table I get three lines and they sum to the function in purple:

enter image description here

When I plot the same transfer function in Matlab I get a similar function but it is shifted higher and I'm unsure why:

enter image description here

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While your expansion is correct, the issue is your 1st plot is in Hz while the Matlab plot is in Radians, ~ 10x different

num = [1 0];
den = [(1/(4000000*pi*pi)) 101/(20000*pi) 1];
G = tf(num,den);
bode(G)

enter image description here

However, a couple of extra commands can switch the units to Hz (you can do it from the UI as well)

num = [1 0];
den = [(1/(4000000*pi*pi)) 101/(20000*pi) 1];
G = tf(num,den);
bode(G);
h = gcr;
setoptions(h,'FreqUnits','Hz');

enter image description here

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