Question

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A2. Find the Transfer function of the following pole - zero plot. FB,

Answer 1

are Generally we represent transfer function as H(s). Suppose the transfer function is HCS) MCs) D(S) where N(s) is Nomenat bolynomia D(S) is Denominat bolynomial Zeros of H(s) the roots of NCs) → Poles of H(s) are the roots of DCs). For any polynomial, if its roots are L, t. In then the polynomial is equal to: f(x) = (x2-x)(x-4) (X-23) ... (x-2). polynomial. In the given figure, we can observe that they are two crosses and Co) * In a pole-Zero plot: X denotes dendes a zero of H(s) So H(s) has one zero and two poles. 4 Coordinate of zero is obtjo) Coordinates of poles are (q+jo), (-2, +jo) As we discussed, Jeros roots of NCs) and poles are roots of DCs). Hence -b) is root of NCs) -A2, -a, are roots of Dls) one dot a pole and OUR are

so Сде ean write. N(s) s-(-6) stb 06) - [S-C-a.)][S-C-00] - [Sta2] [sta] (sta,) (sta) Therefore, If we N(s) stb HCS) D(S) (5+1)(s+a) want to express HCs) in terms of a,, A, B, B, then from figure - bz Bi = -a b= a + BI A₂ = a +A - 2 + A = -9 > Replace b=a+B and a=GTA. in above result.