Designing a system with desired transfer function

Question

Suppose we have a transfer function H(s) = 1/s+1. Is there a general method by which using electric components we can construct such a system?

Answer 1

It is not so common passing from transfer functions to circuits. Maybe it is more common han usual in time discrete circuits. I guess you are referring to time continues circuits.

However, It depends if your transfer function will amplify the signal or just attenuate.Active components for the former, passive ones for the latter.

At that point you have to decompose your transfer functions as product of monomial terms and use the well-known circuits to realize your transfer function. During the design you have to keep in mind this rule: The product of transfer function is the cascade interconnection of electrical circuits only if the output impedance of the first filter is lower than the input impedance of the second filter and so on. That's the only way to avoid unwished interface effects between two circuits.

For example, you would find a configuration like that:

\$H(s)=\frac{1}{(s^2a^2+2sa+1)}=\frac{1}{(1+sa)(1+sa)}\$

It is the product of two RC filter.

Let's consider basics configurations: 1)RC filter with \$H(s)=\frac{1}{1+sRC}\$ 2)RL filter with \$H(s)=\frac{sL}{R+sL}\$ 3)RLC, LR, CR etc

Does it work?