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By Robert Pease

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6 rad/sec) 0 Ϫ20 Ϫ40 Ϫ60 Ϫ80 Ϫ100 Ϫ100 Ϫ150 Ϫ200 Ϫ250 Ϫ300 Ϫ350 104 105 Frequency (rad/sec) Figure 1-29: Plot of the loop transmission magnitude and phase, Attempt #2, showing crossover frequency of 3993 radians/second and a phase margin of 85°. The results of a MATLAB crossover frequency and phase margin test are shown in Figure 1-29. Note that by adding the low-pass filter, we’ve significantly improved the gain margin of this circuit. Results show: • • • Crossover frequency: 3993 radians/sec (635 Hz) Phase margin: 85° Better-behaved step response, as shown in Figure 1-30.

W ww. 6 Figure 1-46: Step response of compensated Maglev example. m; REACTIVE LOAD EXAMPLE’) w ww. com 40 Chapter 1 % MOSFET OCTC calculation Rgs=(rout+Rsense)/(1+gm*Rsense); Tgs=Rgs*Cgs; GM=gm/(1+gm*Rsense); Rgd=rout+RL+(GM*rout*RL); Tgd=Rgd*Cgd; T=Tgs+Tgd % sum of OCTCs mosfetpole=1/T mosfet=tf(Ao,[T 1]) % Find loop transmission LT=series(opamp,mosfet) margin(LT); title(‘moscursource. FREQUENCY RESPONSE OF UNCOMPENSATED MOSFET CURRENT SOURCE’)figure; % close the loop f=tf(1,1) uncomp=feedback(LT,f,-1); step(uncomp); grid; title(‘moscursource.

Stability So far, we haven’t discussed the issue regarding the stability of closed-loop systems. There are many definitions of stability in the literature, but we’ll consider BIBO stability. In other words, we’ll consider the stability problem given that we’ll only excite our system with bounded inputs. The system is BIBO stable if bounded inputs generate bounded outputs, a condition that is met if all poles are in the left-half plane (Figure 1-6). w ww. c om Review of Feedback Systems 7 jv Poles in left-half plane for BIBO stability s Figure 1-6: Closed-loop pole locations in the left-half plane for bounded input, bounded output (BIBO) stability.

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