determinant of transfer function

[Bhuvanesh123]

i am studying control system i crossed this transfer function

H(jw)=(1-jw/1+jw)

now taking determinant of this

|H(jw)|=1

My question in what way the determinant is usefull to learn about the systrem.Here the determinant of transfer function is 1,so the 1 saying anything about the system

 

[LvW]

A transfer function like the one you have shown belongs to a so called "allpass", which has a magnitude of unity (for all frequencies) and a frequency-dependent phase shift.
The phase function is phi(w)=-2arctan(w*T); in your case T=1.

 

[Bhuvanesh123]

Thank you sir,yes it is unity for all frequency. Does magnitude of 1 for all frequency mean , it is "allpass" or does a magnitude is non zero for all frequency mean "allpass" .i am poor in basics ,help me please.

 

[LvW]

Thank you sir,yes it is unity for all frequency. Does magnitude of 1 for all frequency mean , it is "allpass" or does a magnitude is non zero for all frequency mean "allpass" .i am poor in basics ,help me please.

Yes - an allpass always has a fixed amplitude of non-zero.

 

[Bhuvanesh123]

if suppose the determinant gives decreasing amplitude value for giving increasing frequency value .is that low pass?
if suppose the determinant gives increasing amplitude value for giving increasing frequency value .is that high pass?