Problem 2
When we write a Transfer Function as
(s-p1)(s-p2)..(s-pn)
difference of two complex numbers, s = a + bj, z = x + jy and p = pr + jpi. If we take the magnitude of T(s) we get: Each term on the right inside the bars is a distance from the location s to a zero zi or |s-p|ls-p21..|s-pn| a pole p.. SO, the magnitude of the Transfer Function at any complex frequency s is directly proportional to the product of its distance from all the zeroes, and inversely proportional to the product of its distance from all the poles.
s+a
(HINT: sketch it in the s-plane.)
constant as o. (HINT: sketch it in the s-plane.)
KS
reaches a peak at , and goes to zero as o. (HINT: sketch it in the s-plane.)
Similarly, the phase of T(s) is the sum of the phases in the numerator minus the sum of the phases in the denominator: ((d - s)7+.+ (d -s)7+(d -s)) - (z - s)7 +..+(z - s)+(z -s)>)= (s7 We will look at this later when we learn about the sinusoidal steady state.