Title:

A frequency control for digital switching networks

Pulse code modulation is being introduced into telephone networks to increase the capacity of existing multipair cables. It is possible to use a switched digital communications network for data as well as for p.c.m. telephone traffic if all the clock oscillators in the network operate in phase at all times. Various control systems have been proposed to achieve the required clock synchronisation without the use of a central reference. These control systems are based on the application of phase locking to a large number of interconnected oscillators. Some proposals are for nonlinear systems, but this Thesis is largely restricted to the discussion of linear systems. Two main types of linear system have been proposed. The first, known as the singleended system, minimises the amount of buffer storage needed at the inputs to the exchanges. These stores allow for the variation of line delay with temperature, as well as accommodating small phase errors. The resulting network operating frequency is substantially dependent on the line delays. The alternative is the doubleended system. This eliminates the interdependence of frequency and line delay, but involves a rather more complicated stability condition. Filters, which are an essential part of the system hardware, affect the stability of both systems. Their effects are examined in the Thesis. The system equations derived in this Thesis include the line delays, the effects of hnnped filters and the starting conditions. They are obtained for both the singleand doubleended systems. A continuous model is assumed, but the systems are in fact sampled at a high rate c· . 'An alternative 'set of equations has been derived to allow the 'effects of the sampling rate to be investigated. The behaviour of the systems is examined' by means of the mathematics of multivariable control systems. This has allowed many important results to be deduced without exact knowledge of the connections between the exchanges, or even the number of exchanges. The stability criteria in this Thesis are all sufficient, but, not generally necessary. As a result, it has been possible to give the criteria in forms which may be checked at each exchange independently of the rest of the network. It is possible to add to the network without disturbing remote exchanges. The criteria are given in terms of the basic system parameters, such as gains and filter time constants. This Thesis includes a full treatment of the doubleended system, including some of the effects Q£ unbalanced gains in the error paths. The results are more comprehensive than any others published to date. and include the effects of sampling on both classes of system. The factors determining the final frequency of the synchronised network are examined. The doubleended system is treated in a general manner, which yields a formula for unbalanced systems as well as the more usual balanced system. An extreme case of this is the singleended system. This general formula is expressed in terms of the basic system parameters, which are easily measured. It is shown that the frequency depends upon the variations of the line delays from integer multiples of one frame period, and not their absolute values. The phase comparators used in the locked oscillators are by nature periodic; a piecewiselinear form is considered to be most suitable. The periodicity causes a number of stable states to exist with different phase differences. Some of these differences may cause the buffer store capacities to be insufficient. A new set of system equations, in terms of principle phase differences, is evolved. This leads to a phasespace representation of the system state, Which has links with the method used to examine transient behaviour. Although it is not possible to give a general method for finding all the possible modes for a given network, a necessary condition for a 'wrong mode', with some large phase differences, can be found. This has suggested a technique tor the detection of such modes and their release to the desired mode with substantially zero phase dlfferences. The investigation of transients and the effects of noise is not complete. There is as yet no quantitative analysis of the noise spectrum at the lower frequencies which will affect the control system, Some indlcations of the crltical frequencies are given, to allow such measurements to be made. The investigation of transients shows that in most networks some phase differences will be increased before the network relaxes. Liapunov estimate isused, but this is limited to systems without filters or line delays. The results reported in this Thesis allow the system designer to determine the values of the controllable parameters, Some recommendations are given, and suggestions are made for the design of equipment to automatically set the network in the requlred mode of synchronised operation. A field trial of these systems is required, and proposals being studied by the British Post Office are based on results given in this Thesis. Such a trial should take place over lines carrying signals of the same statistical form as live telephone traffic. This will allow the deduction of further results concerning the transient response of the systems.
