# Phase from transferfunction

#### Chrill3

Joined Mar 8, 2010
9
I try to calculate the bode-plot from this transferfunction that I derived:

1/((1+s)^2+1)

I got stuck on this problem and dont know how to calculate phase or amplitude. Any help is appreciated.

#### jp1390

Joined Aug 22, 2011
45
I try to calculate the bode-plot from this transferfunction that I derived:

1/((1+s)^2+1)

I got stuck on this problem and dont know how to calculate phase or amplitude. Any help is appreciated.
$$H(s) = \frac{1}{(s+1)^{2} + 1} = \frac{1}{s^{2} + 2s + 2}$$

To take the magnitude you are going to have to bring the transfer function back in terms of 'w', by s = jw.

$$H(jw) = \frac{1}{-w^{2} + 2jw + 2}$$

$$|H(jw)| = \frac{1}{\sqrt{(2 - w^{2})^{2} + (2w)^{2}}}$$

$$= \frac{1}{\sqrt{w^{4} + 4}}$$

As for the phase:

$$Phase(H(jw)) = \arctan{(\frac{0}{1})} - \arctan{(\frac{2w}{2 - w^{2}})}$$

$$= -\arctan{(\frac{2w}{2 - w^{2}})}$$