# Pole and zero of a transfer function

1. Jul 12, 2010

### mdnazmulh

A transfer function H(S) in s-domain has been obtained as
H(s) = 5.0625/(0.0008s^2 + 0.0882s + 5.0625). I’m interested in finding its poles and zeros.

I found that denominator polynomial 0.0008s^2 + 0.0882s + 5.0625 has complex conjugate roots. Roots are -55.13 + i 57.35 and -55.13 - i 57.35. I was expecting real valued poles but they are complex poles and it made me doubtful about the correctness of my solution for the poles.
And what about the zeros? Are the zeros at infinity because numerator is a constant quantity?
Would anybody help me in this regard?
Thanks

2. Jul 12, 2010

### xcvxcvvc

There isn't anything wrong with a transfer function that has complex roots. In fact, they are very common and lead to damped or exponentially growing sinusoids. As for the zeros, they are at plus or minus infinity like you've said.

Though, what you've said is a little specific. You could more generally say that if a transfer function is a proper fraction in terms of s, meaning the numerator's highest power is lower than the denominator's highest power, then there are zeros at +/- infinity.

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