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.

 

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:

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

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

 

I always find this site a good way to review my results quickly:
http://www.williamsonic.com/BodePlot/