# Magnitude of a Transfer Function

So I have an unknown circuit with a plot like this:

From this I have to determine a likely transfer function model. It looks to me like there is a pole at 50 rad/sec and a zero at 1500 rad/sec, with a dc gain of 1.

When I plug those into a transfer function I get: H(s)= (S+1500)/(S+50) or as H(f) = (j2πf+1500)/(j2πf+50)

How do I find the magnitude of this transfer function?

I've been doing |H(f)| = √((2πf)^2+1500^2) / √((2πf)^2+80^2) but I am not getting the same magnitude as my plot.

• I assume 80 is a typo. Are you entering in radians and Hz properly? Oct 24, 2021 at 22:54
• Curiously same plot found in Russian site , 5fan-ru.translate.goog/files/13/… Oct 25, 2021 at 0:54
• It's j $2\pi f$, not $2\pi f$. You're not calculating the complex absolute value correctly. Oct 25, 2021 at 7:26

For one, you are not expressing the magnitude in $$\dB\$$, $$\20log10(H)\$$ as in your plot. Try plotting in this form.
$$|H(w)_{dB}| = 20log10(\sqrt{(1+(w/1500)^2)/(1+(w/50)^2)})$$
$$H(s=jw) = \frac{1}{30}\frac{(s+1500)}{(s+50)}$$ $$= \frac{50}{1500}\frac{1500}{50}\frac{(\frac{s}{1500}+1)}{(\frac{s}{50}+1)}$$