By Nikolaos I. Margaris
This publication develops for the 1st time a whole and hooked up nonlinear conception for the analog Phase-Locked Loop (PLL) which clarifies the imprecise issues of its advanced non-linear behaviour. The booklet indicates new non-linear types for the PLL parts and applies the averaging way to examine PLL. The e-book offers the actual interpretation of the PLL operation, locates the problems provided through its operation and indicates recommendations to beat those difficulties. eventually it presents closed shape expressions for all of the vital measures of the PLL and proposes new layout standards.
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Extra resources for Theory of the Non-linear Analog Phase Locked Loop
4-1b) = ȝ » º dĳ 2 « ª 1 2 «+ « Șo 2 (2vcont + ȝvcont )» >1+ cos2(z + ĳ)@» ȍm «¬ ¬ »¼ ¼ where vcont = 1 ª cos > z șr ĳd2 + (1 N)(ĳ ĳd1 )@ +º kr « ». 4-2) In Fig. 4-1 and Fig. 4-2 the comparison of simulation results between the exact and averaged equations is shown, referring to the main synchronization for various values of the parameters. We conclude that the approximation of the exact equations with the averaged ones is totally satisfactory, since the time evolution of corresponding variables cannot be distinguished, even in the case of a long lasting simulation, as in Fig.
1. Effect on the amplitude of the VCO signal (a) Effect of parameter k. 3-8) the parameter k de- pends on the multiplier gain and the amplitude of the reference signal k = k m ar . 3-8) Since the multiplier gain is usually constant, parameter k depends mainly on the amplitude of the reference signal. 1-6), the steady state amplitude of the VCO is equal to unity in the absence of a reference signal (k 0). In contrast, when the reference signal is present, the amplitude depends significantly on the parameter h and the ripple.
Minorski N (1962) Non-linear Oscillations. E. Krieger, Malabar, Florida, ch 20 10. Stensby JL (1997) Phase-Locked Loops. CRC Press, Boca Raton, Florida 11. Viterbi AJ (1966) Principles of Coherent Communication. McGraw-Hill, New York 4. Main synchronization In this chapter the main synchronization of the first order PLL is discussed. At first, we perform the local stability analysis of the main synchronization, which results in closed mathematical expressions for the limits of the synchronization (hold-in) region.
Theory of the Non-linear Analog Phase Locked Loop by Nikolaos I. Margaris