Transfer function from poles and zeros

1. How do you find the transfer function of zeros?
2. What do you mean by poles and zeros of a given network transfer function?
3. How do you determine stability from poles and zeros?

How do you find the transfer function of zeros?

This is just a constant term (b₀/a₀) multiplied by a ratio of polynomials which can be factored. In this equation the constant k=b₀/a₀. The z_i terms are the zeros of the transfer function; as s→z_i the numerator polynomial goes to zero, so the transfer function also goes to zero.

What do you mean by poles and zeros of a given network transfer function?

Zeros are defined as the roots of the polynomial of the numerator of a transfer function and. poles are defined as the roots of the denominator of a transfer function.

How do you determine stability from poles and zeros?

If all the poles lie in the left half of the s-plane, then the system is stable. If the system has two or more poles in the same location on the imaginary axis, then the system is unstable. If the system has one or more non-repeated poles on the imaginary axis, then the system is marginally stable.