Positive real transfer function

1. What do you mean by positive real function?
2. Which of the following is positive real function?
3. What is positive realness?
4. Which of the given network functions satisfy the condition of a positive real function?

What do you mean by positive real function?

Positive-real functions, often abbreviated to PR function or PRF, are a kind of mathematical function that first arose in electrical network synthesis. They are complex functions, Z(s), of a complex variable, s.

Which of the following is positive real function?

Therefore Z₄ (s) is a positive real function.

Also note that this is for the 2021 cycle.

What is positive realness?

Definition of positive realness is originally introduced in circuit theory Otto Brune in 1930 [1, 2]. In fact, it is shown that the driving point impedance of each one-port passive electrical network is positive real (PR) transfer function and vice versa.

Which of the given network functions satisfy the condition of a positive real function?

Any function which is in the form of F(s) will be called as a positive real function if fulfill these four important conditions: F(s) should give real values for all real values of s. P(s) should be a Hurwitz polynomial.