Transfer function in frequency domain

A transfer function defines the relationship between the input to a system and its output. It is typically written in the frequency domain (S-domain), rather than the time domain (t-domain). The Laplace transform is used to map the time domain representation to frequency domain representation.

1. How do you use the transfer function in time domain?
2. What is the frequency of transfer function?
3. How can we convert our transfer functions from the Laplace domain to the frequency domain?
4. What is the difference between a general transfer function and a frequency transfer function?

How do you use the transfer function in time domain?

To find the transfer function, first take the Laplace Transform of the differential equation (with zero initial conditions). Recall that differentiation in the time domain is equivalent to multiplication by "s" in the Laplace domain. The transfer function is then the ratio of output to input and is often called H(s).

What is the frequency of transfer function?

In fact the frequency response of a system is simply its transfer function as evaluated by substituting s = jω. The frequency response H(jω) is in general is complex, with real and imaginary parts. This is often more useful and intuitive when expressed in polar coordinate.

How can we convert our transfer functions from the Laplace domain to the frequency domain?

The Laplace transform can be viewed as an extension of the Fourier transform where complex frequency s is used instead of imaginary frequency jω. Considering this, it is easy to convert from the Laplace domain to the frequency domain by substituting jω for s in the Laplace transfer functions.

What is the difference between a general transfer function and a frequency transfer function?

A transfer function is a more general concept than frequency response. For instance, you could have a transfer function for a magnetic core with the hysteresis. A frequency response is more specific and we qualify the response with a transfer function using Laplacian expressions.