# Magnitude characteristic of H(s)

I have a question about drawing a magnitude characteristics of H(s).

So my transmittance function is for example:

and in the book the magnitude characteristics is shown as:

And my question is - how to count the value of abs(H(jΏ) ?

I understand that s = 1 is a zeros (local minima), and this function has two poles: -1-j and -1 +1 (local maxima), but I can't count the values highlighted in yellow.

The most direct way is to turn your transfer function into frequency response by setting $$s = j\Omega$$ and then $$H(j\Omega) = \frac{j\Omega - 1}{-\Omega^2 + 2j\Omega + 2}$$ So for $$\Omega = 0$$, you get $$H(0) = -\frac{1}{2}$$ which gives $$|H(0)| = \frac{1}{2}$$ and is in agreement with your figure. Similarly, for $$\Omega = \pm 1$$, you get $$H(\pm j1) = \frac{\pm j - 1}{-1 \pm 2j + 2} = \frac{\pm j -1}{1 \pm 2j}$$ You can show that $$|H(\pm j1)| = \sqrt{2/5}$$, which also agrees with your magnitude response plot.
• Taking the modulus of each complex number: it's $|H(\pm j1)| = \frac{|\pm j - 1|}{|1 \pm 2j|} = \frac{\sqrt{2}}{\sqrt{5}} = \sqrt{2/5}$ – GKH Jan 28 at 23:19