M.Ing. (Electrical and Electronic Engineering) / This research project sets out to investigate passive L-C coupling circuits as an alternative to transformer-capacitor couplers, with the prime intention to reduce the cost of coupling in power-line communications, hence the title “Compact, Economical Coupling Circuits for Low-Voltage Power-line Communications”. This chapter first presents a short introduction to Power-Line Communications, and then briefly reviews relevant topics surrounding this project. Also discussed, in general, are the standards and regulations for power-line communications i.e. the CENELEC EN50065.1 Standard and the IEEE 1901.2 Standard. This information intends to give the reader guidelines and relevant protocols and/or rules when designing and building communication devices for PLC. This information will also help us in our designs and experimental set-ups as we proceed with this project. The reader will also be introduced to the concept of filtering and impedance matching in communication systems. Emphasis will be laid on the required output signal frequency profile of a coupling band-pass filter. The chapter will define filtering in terms of communications and also discuss the more significant and important parameters in filter circuits. The last section of this chapter will touch on impedance matching and the concept of maximum power transfer, so as to attain maximum signal transfer to the receiver-end.

A FORTRAN program has been developed in order to investigate the process of modal parameter estimation and non-parametric system identification. The theory underlying the process of modal parameter estimation is reviewed and the decoupling of a MIMO system into several SISO systems is demonstrated. Modal filtering is shown to be useful in the field of non-parametric system identification and it is shown that it may also be of some use in the field of signal processing. The program is documented. It simulates the output of a n-th order system from which a smaller order subsystem can be decoupled. The modal parameters of a subsystem output signal and its first two derivatives and the modal parameters of a second subsystem output and its first derivative are calculated. The unit step response of the theoretical system and the subsystem are then calculated. The signals are then modal filtered to produce the periodic unit step response and the periodic unit square wave response. Finally, the discrete Fourier coefficients of the periodic unit step response are calculated. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

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Two common classes of filter functions in use today, Butterworth functions and Chebyshev functions, are based upon solutions to special cases of the Sturm-Liouville equation. Here, solutions to several other special cases of the Sturm-Liouville equation were used to develop filter functions, and the properties of the resulting filters were examined. The following functions were explored: Chebyshev functions of the second kind, untraspherical functions of the second and third kinds, Hermite functions, and Legendre functions. Filter functions were developed for each of the first five polynomials in each series of functions, and magnitude and phase responses were tabulated and plotted. One of the classes of functions, the Hermite functions, led to filters which have a significant advantage over the commonly used Chebyshev filters in passband magnitude response, and were essentially the same as Chebyshev filters in stopband magnitude response and phase response.

A computer program, which realizes monolithic crystal filters with constant group delay, is developed. This program analyzes and synthesizes a class of transfer functions developed by J.D. Rhodes called equidistant linear phase transfer functions. Using cascade synthesis, the program calculates the values of the inductor and capacitors of the ladder sections which realizes these functions. The ladder sections are implemented using monolithic crystal filters.

The closed form error expression of optimum Wiener filter was first introduced by M. C. Yovit and J. L. Jackson in 1955. Since then, a number of people have proved the validity of this form using almost similar technique but no one has succeeded to extend the Yovit-Jackson's original formula for the other cases such as prediction and delay filters. It is understood that the main reason to fail in the extension can be summarized as: (1) The starting point that most of other authors have chosen is for the special case that confines itself to the zero delay filtering system. (2) The derivation procedure depends too much on cancellation among terms. To compensate the above two points, an alternative method utilizing Parseval's theorem was presented. The major problems in the extension of Yovit-Jackson's form are summarized as: (1) To find a new method of derivation from generalized starting point such as Y. W. Lee's error expression. (2) To find mathematical relations between the original spectrum and factorized component spectra. (3) To find the closed form expression of generalized transfer function of optimum operator. / M.S.

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