Question

A Hurtwiz polynomial D(s) must satisfy two conditions. One is the polynomial is real when s is real. What is the other condition?
1. Roots of D(s) have real parts which are positive and non-zero
2. Roots of D(s) have imaginary parts which are negative
3. Roots of D(s) have real parts which are either zero or negative
4. Roots of D(s) have real parts which are positive or zero

Answer 1

Correct Answer - Option 3 : Roots of D(s) have real parts which are either zero or negative

Hurwitz Polynomial:

If we have a stable network function, then the denominator of the F(s) is called the Hurwitz polynomial.

Let, \(F\left( s \right) = \frac{{P\left( s \right)}}{{Q\left( s \right)}}\)

Where Q(s) is a Hurwitz polynomial.

Properties of Hurwitz Polynomial:

• For all real values of s, the value of the function P(s) should be real.
• The real part of every root should be either zero or negative.
• Let us consider the coefficients of the denominator of F(s) is b_n, b_(n-1), b_(n-2), … b₀. Here it should be noted that b_n, b_(n-1), b₀ must be positive and b_n, and b_(n-1) should not be equal to zero simultaneously.
• The continued fraction expansion of Even/Odd or Odd/Even part of the Hurwitz polynomial should give all positive quotient terms.