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This paintings is aimed toward practitioners wishing to achieve a broader systems-based viewpoint of phase-locked loops; and is additionally compatible as a graduate textual content for engineering scholars. It offers precise assurance of electronic sampling results in glossy phase-locked frequency synthesizers from a structures viewpoint, and discusses all facets of part noise, its mathematical modelling and its impression upon assorted electronic conversation structures.
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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.