So, how to make one? What kind of skills are needed for this task to
be performed? Can it be done easily or does it require some higher
How to make a transfer function? you need to know the poles and zeros of your system. Normally this is done by physical modelling and converting the physical model to a model in the frequency space. For example: A low pass filter has one pole and one zero.
In the case of physical modeling it really helps to have an understanding of the frequency space, and more specifically the laplace domain. I would say this is required. The next higher math that helps is differential equations because the physical systems are really differential equations that have been simplified to laplace notation.
At minimum you need to understand polynomial algebra because that's what transfer functions consist of.
For example, LTSpice draws a Bode plot (magnitude/phase) for a given
circuit for free. So, is there any good in studying and understanding
It helps to understand the math because instead of spending hours if there is some criterion that you are working to design, the transfer function that is needed can be predicted and they physically realized.
In control theory it is important to make sure the system is stable (ie that it will not oscillate or rail out and that it will move to the desired control input), in this case the physical system is modeled and then a controller is developed with a specific transfer function to maintain that stability.
This is more of a design question, there are two ways to design:
1) Simulate simulate simulate! or s^3 keep changing things until they work. There are many engineers that do this, the problem with designing this way is the systems they develop don't always work under all conditions, in part because they didn't adequately simulate the system. I've also seen software\firmware engineers use this strategy and play wack a mole with a problem until it goes away, only to return later or break something else.
2) Design, Build, Test. Sit down and actually understand what the problem is and what others have done to design systems as the one you want to build, this means spending time and educating yourself which takes effort. You build a list of requirements. The requirements are used to generate a design, on paper or on a computer. This may include checking it with a simulation to see if it meets the requirements. Then you build the design and check it against the requirements.