Phase locked system design and measurement tutorial consisting of physical hardware and co-simulation environment

International Journal of Electrical Engineering Education, Oct 2004 by Burbidge, Martin John

Simulation model explanation and key equations

The circuitry depicted in Fig. 1 represents a mixed-signal model of the 74HCT4046(15) charge-pump phase-locked loop that is used for the practical exercises. The key elements of the simulation model are explained below along with their respective parameters. The information in this section is only intended to provide a brief overview of the key PLL sub-sections. Further, more detailed information on PLL operation is provided in Refs [2] and [3].

Phase detector and charge pump (PD CP)

This part of the circuit models the phase detector and charge-pump respectively.

Phase detector. The purpose of the phase detector is to produce correction signals at its outputs (see M2 and Ml) that are proportional to the difference at its inputs (see A1 elk and A2 elk). Note that the phase detector in this circuit only operates on rising edges of the input signals. Also this type of phase detector has a detection range of ±2π (360°). This statement can be proved by experimentation with the provided simulation models.

Charge pump. The charge pump circuit converts the outputs from the phase detector into voltage signals that are directly proportional to the phase difference on the PLL inputs.

MATLAB files are included as part of the course material that allow calculation of eqns (8) and (9) directly from the loop filter component values. The natural frequency and damping of the loop will control the transient response of the loop (including settling time and overshoot) and will also have direct control over the loop bandwidth. More information about the natural frequency and damping is provided in the hardware-based course modules.

The key equations required to carry out the course material adequately are eqns (3), (4), (5), (6), (8), and (9). Other equations are included for completeness and to provide more advanced students with an initial point of reference for Laplace-based representations of control systems. The main reason for this approach is that the material should be applicable to a wide range of students and prior knowledge of Laplace domain calculations could not be guaranteed. An important focus of the course is to show a qualitative relationship between component values, natural frequency and damping and to allow the student to observe corresponding output response changes.

Examples of analytical response curves

In many situations the initial part of the design phase starts with a specification for desired final system performance. With a PLL, typical design issues centre on bandwidth, and transient response of the final system when it is subjected to certain inputs. Commonly used inputs that can allow frequency and transient response to be calculated are sinusoidal frequency modulation and frequency steps, respectively. It is common to find normalised frequency response plots and transient response plots of systems reproduced in PLL and control system texts.

A normalised transfer function plot included in the course material is shown in Fig. 2. The plot of Fig. 2 shows the magnitude and phase response of the output signal of a second-order PLL when it is subjected to an increasing input modulation frequency. That is, the continuous periodic input signal is phase- or frequencymodulated at increasing modulation frequencies. Plots are created in MATLAB using eqn (7). A copy of the code listing that will generate the normalised transfer function plots is included as part of the course material.