# frequency response in control systems

Thread Starter

#### avyan reddy

Joined Oct 30, 2020
7
can some one explain why we substitue s by jw in frequency response

#### ericgibbs

Joined Jan 29, 2010
18,840
hi avyan.
This explains
E
The reason why S=jω is chosen to evaluate AC signals is that it allows to convert the Laplace transform into Fourier transform. The reason is that while S is a complex variable, what's used in the Fourier representation is just the rotational (imaginary) component, hence σ=0.

#### Papabravo

Joined Feb 24, 2006
21,225
Setting s=jω allows us to evaluate the magnitude of a transfer function along the jω axis as a function of frequency alone. We could also evaluate it along another path in the left half plane which would then have an exponential decay as well as a dependence on frequency. We can of course do the same thing with phase. When you do this you get the familiar Bode plots.

Thread Starter

#### avyan reddy

Joined Oct 30, 2020
7
hi avyan.
This explains
E
The reason why S=jω is chosen to evaluate AC signals is that it allows to convert the Laplace transform into Fourier transform. The reason is that while S is a complex variable, what's used in the Fourier representation is just the rotational (imaginary) component, hence σ=0.
thank you

Thread Starter

#### avyan reddy

Joined Oct 30, 2020
7
Setting s=jω allows us to evaluate the magnitude of a transfer function along the jω axis as a function of frequency alone. We could also evaluate it along another path in the left half plane which would then have an exponential decay as well as a dependence on frequency. We can of course do the same thing with phase. When you do this you get the familiar Bode plots.
thank you