Digital Clocks for Synchronization and Communications
This text explains important phase-lock circuit design techniques, and how to select commercially available equipment for a variety of projects in the field.
TABLE OF CONTENTS Digital Clocks for Synchronization and Communications
Chapter 6: Simulation of a Digital PLL
Simulation is an effective tool for analyzing the characteristics of digital PLL constructions, since it is often difficult to find any closed-form arithmetic relationships in their behavior. In addition, because of increased computer power, simulation is an attractive and precise alternative if we are interested in a characteristic whose measurement is difficult or would take a lot of time. This chapter describes the validity of PLL simulation.
6.1 Transfer Function Analysis
Let us consider a basic digital PLL that is composed of a digital filter (described in Section 5.4.2), a digital phase comparator, and a digital controlled oscillator, as shown in Figure 6.1. A complete transfer function is hard to obtain, but a reasonable analysis is possible through an equivalent analog PLL in the region where the quantization effect can be ignored.
Figure 6.1: Example of a digital PLL.
Let us compare the transfer function of an analog PLL calculated according to (5.36) with the measured data of the digital PLL, which uses the following coefficients:
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Phase comparator:
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Phase difference detection resolution: 6 ns;
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Sampling: 8 kHz and 0th hold;
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Filter:
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Type: complete second-order filter as expressed in (5.42);
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Proportional coefficient of multiplication: A = 32;
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Integration coefficient: B = 6 10 ?5;
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Sampling period in integration: 8s;
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Controlled oscillator:
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Resolution of digital frequency control: 1 10 ?12.
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Figure 6.2(a) shows the transfer function for a variation in the input phase of the PLL. This is the characteristic of a general lowpass filter. Figure...
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