# How to find transfer function looking bode plot

I have some Bode plot (only in amplitude) as these:

Now, I must to find their transfer functions, in particular the exact value of their zeros and poles.

It is clear that their are a low pass filter and a high pass filter.

I'm looking for a method for extract the numerical value of their transfer function.

Thank you and bye,
Giacomo

• This might help: en.m.wikipedia.org/wiki/Bode_plot . Have you already tried to reconstruct the transfer function applying the same rules you use when drawing the plot? – Rhei Feb 16 '15 at 16:46
• Yes, I have read that page. I'm asking if for the first one which is a low pass filter, i.e., $H(s)=\frac{k}{p+j\Omega}$ there are some tools for extract the values of $k$ and $p$. – Giacomo Alessandroni Feb 16 '15 at 16:56

locate the 3db point. (The point where the line before and after the curve would meet.) Take note of the magnitude and frequency f.

Find the angular frequency at this point. w = 2 * pi * f

If the graph is going up then it's a zero. H(s) = w + s

If it's going down then it's a pole. H(s) = 1 / ( w + s )

Once you've got that. check the slope. If it's 20dB/decade then you're set. If it is 40, you'll need to square it, 60 and you'll cube it etc.

Finally you'll need to find the gain constant to make it correct at low frequency (or DC)

So you're answers will look like this:

H(s) = Gain * ( w + s )
H(s) = Gain / ( w + s )