I've forgotten how to get the frequency response function out of a Bode Plot. The phase component of $H(j\omega) = e^{j\pi/2}$, right? But I am having trouble finding $|H(j\omega)|$. How would I get it from decibels?

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  • 1
    $\begingroup$ That's a differentiator. $\endgroup$
    – Matt L.
    Mar 2, 2017 at 7:06

1 Answer 1


Your Bode plot is a straight line. As we are on a semilog-scale, the equation is given by

$$y = m \log(x) + b$$

In this case, $y$ would be the magnitude of the frequency response $|H(j\omega)|$ in $\mathrm{dB}$, and $x$ would be the frequency $\omega$. Taking two points of the plot and solving the $2\times2$ equation system should give you the function you're looking for.

As you didn't put the values of the $\omega$-axis, I'm going to assume that the plot starts at $\omega=1$. In this case, when $\omega = 1$ the magnitude is $0 \ \mathrm{dB}$, so:

$$0 = m \log(1) + b\implies b=0$$

Also, when $\omega = 10$, the magnitude is $20 \ \mathrm{dB}$:

$$20 = m \log(10) +0\implies m=20$$

So the function is:


Note that if your plot doesn't begin at $\omega=1$ (what I just assumed to be true), the reasoning would be the same but $b$ would not be zero.


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