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Error analysis of arctan Bode approximation

Error analysis of arctan Bode approximation - phase(degrees...

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Unformatted text preview: phase (degrees) Accuracy of the Bode phase approximation (phase (degrees) vs. frequency (rad/sec) 90 my 80 7O 60 tan“1 50 40 30 w=10gspace(’2,2,100); x=atand(w); 20 w1=10gspace(-2,0,IOO); xneg=57.3*w1; w2=logspace(0,2,100); xpos=57.3*((pi/2)—(l./W2)); 1 O plot(10g10(w),x,log10(w1),xneg,log10(w2),xpos); grid 0 -.01 -.1 1 1 O 1 00 14 T"T"””':TT‘”’"T‘§T """"" ITT‘T‘E """"""""""""""""""" TT ' T Max phase error occurs within the 12 w- a), (0 <1 ----------------- ‘ ««««««««««« w two octivcs astride the break frequency 10 w ,,,,,,,,, error = tan‘1 60 —~ g _ _1_ 7 a) >1wm§pww «Him? .......... gmww WWW»; ........................ g ,,,,,,,,,,,,,,,,,,,,,,,,, 8 . ,,,,,,,,,, a) ,5 , w1=logspace(-2,0,100); xexact1=atand(w1); xneg=57.3*w1; W2=1ogspace(0,2, 1 00); xexact2=atand(w2); xpos=57.3*((pi/2)—(1./W2)); eneg=xexact1-xneg; eposzxexath—xpos; p10t(10g10(w1),eneg,log10(w2),epos); grid —.5 1 2 5 frequency (rad/sec) 20 50 100 ...
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