Fall 2001 16.3115-8 Note that the poles tending to infinity do so along very specific paths so that they form a Butterworth Pattern At high frequency we can ignore all but the highest powers of s in the expression for A(s)=0 T 0 b The 2(n-m) solutions of this expression lie on a circle of radius (6/r)12-m) at the intersection of the radial lines with phase from the neg- ative real axis: m0一 土 (n-m)odd (+1/2)丌 Z=0.1 n-m even n-7 Examples n- m Phase 1 0 2 丌/4 3 0,土丌/3 4±丌/8,±3丌/8 Note: Plot the SRL using the 180 rules(normal)if n-m is even and the oo rules if m ddFall 2001 16.31 15—8 • Note that the poles tending to infinity do so along very specific paths so that they form a Butterworth Pattern: — At high frequency we can ignore all but the highest powers of s in the expression for ∆(s)=0 ∆(s)=0 ; (−1) ns2n + r−1 (−1) m(bosm) 2 = 0 ⇒ s2(n−m) = (−1) n−m+1 b2 o r • The 2(n − m) solutions of this expression lie on a circle of radius (b 2 0/r) 1/2(n−m) at the intersection of the radial lines with phase from the neg￾ative real axis: ± lπ n − m , l = 0, 1,..., n − m − 1 2 , (n − m) odd ±(l + 1/2)π n − m , l = 0, 1,..., n − m 2 − 1 , (n − m) even • Examples: n − m Phase 1 0 2 ±π/4 3 0, ±π/3 4 ±π/8, ±3π/8 • Note: Plot the SRL using the 180o rules (normal) if n − m is even and the 0o rules if n − m is odd