IQ Bode Plots 252 plot W P recognise that at, U = there i h a resoilant point iTfe thus calcuiak the riiagnituutlr for this point from H ( s ) As the rrunher of poles is by one grratcr than the nunlher of zeros, the magnitude frequency response lar >> fah at 20 dU/clrcnde To confirni this w~ determincl the rringnitudc at d = 10 In order to apyroximatc tlw path more accurateiy we ~ a l c i i l a lthe ~ tdur fm L 8s wrll The cli-;lmces in equation (10 ) are calciilatcd from the pole-zero plot As is evident in Figure 10.9, the lollowirrg apprtrxiniatte v;zhies are yielded, if the - 1,2 c U (I *t w=0 (I w-1 ul=2 w = L0 Fipirr 10 9: Estimating the lengths €or various w distances of the zeros are multiplicd and divided by thc distmce of t h c p o l ~ s : (10.5) For the pliase plot wc need the phase at J = and recognise from the pole-zero diagram that diie to the pole s = + j the phrtsc changes sharply around w -= I/'lirtlncxr, the phase of H ( s ) for w >> t,akes a value of -90" Considering this, we c m est,irrtat,e the phase a t the following points with the pole-zero diagram, as shown in Figure 10.10 We obtain -4 t7(.?0) = ~('1) M x 60" - 30" + 90' - 90" == 90" p(j2) =c: x 80" - 50" - 0" 90" = " (10.6)