Signals which are quantized both in time of occurrence and in magnitude are in fact quite old in the communications art. Printing telegraph is an outstanding example. Here, time is divided into equal divisions, and the number of magnitudes to be distinguished in any one interval is usually no more than two, corresponding to the closed or open positions of a sending switch. It is only in recent years, however, that the development of high speed electronic devices has progressed sufficiently to enable quantizing techniques to be applied to rapidly changing signals such as produced by speech, music, or television. Quantizing of time, or time division, has found application as a means of multiplexing telephone channels.1 The method consists of connecting the different channels to the line in sequence by fast moving switches synchronized at the transmitting and receiving ends. In this way a transmission medium capable of handling a much wider band of frequencies than required for one telephone channel can be used simultaneously by a group of channels without mutual interference. The plan is the same as that used in multiplex telegraphy. The difference is that ordinary rotating machinery suffices at the relatively low speeds employed by the latter, while the high speeds needed for time division multiplex telephony can be realized only by practically inertialess electron streams. Also the widths of frequency band required for multiplex telephony are enormously greater than needed for the telegraph, and in fact have become technically feasible only with the development of wide-band radio and cable transmission systems. As far as any one channel is concerned the result is the same as in telegraphy, namely that signals are received at discrete or quantized times. In the limiting case when many channels are sent the speech voltage from one channel is practically constant during the brief switch closure and, in effect, we can send only one magnitude for each contact or quantum of time. The more familiar word “sampling” will be used here interchangeably with the rather formidable term “quantizing of time”.

Spectra of quantized signals

Two independent equations relating the average powers at the different frequencies in nonlinear inductors and capacitors are derived. These equations are a consequence only of the assumption of a single-valued characteristic for the nonlinear element. They are independent of the particular shape of this characteristic, of the power levels at the various frequencies, and of the external circuit in which the nonlinear reactor is connected. These general energy relations give information regarding the gain and stability of nonlinear reactor modulators and demodulators, and consequently of magnetic and dielectric amplifiers, without requirng detailed information about these devices. The utility of these equations is illustrated by discussing the gain and stability of the simplest types of nonlinear reactor modulators and demodulators and harmonic generators. This analysis for nonlinear inductors and capacitors is extended to include the effects of hysteresis in the nonlinear characteristic in the special case where the operating hysteresis loop is no more than double-valued. A similar analysis applied to nonlinear resistors yields two equations relating the reactive powers at the different frequencies, rather than the real powers as above. The interpretation of reactive power under these conditions is not clear.

Some General Properties of Nonlinear Elements-Part I. General Energy Relations

The multicell converter topology is said to possess a natural voltage balancing property. This paper is the first of a two-part series in which multicell converters are modelled for the general case of p-cells. This paper focuses on the development of the natural balancing theory for the two-cell case. An understanding of the two-cell case is fundamental to understanding the general balancing theory. The switching functions used in switching these converters are mathematically analyzed. Equivalent circuits are derived and presented. The switching and balancing properties of these converters are mathematically analyzed. The main conclusion of the analysis is that the natural balancing of these converters are influenced by three factors namely, the harmonic content of the reference waveform, the switching frequency and the load impedance. Mathematical tools are presented that can help designers to predict if balancing problems would occur for a particular set of operating conditions. As a result of the detailed understanding of the balancing mechanism that is gained through this theory it is shown that by adding a balance booster, the load impedance can be manipulated to improve the natural balancing of the converter. Simulation results are included to verify the presented balance theory and properties

http://digitalknowledge.cput.ac.za/bitstream/11189/1768/1/Wilkinson_Richardt%20H_Meynard_Thierry%20A_Mouton_Hendrik%20du%20Toit_.pdf

Natural Balance of Multicell Converters: The Two-Cell Case

It is axiomatic that frequency changing, whether it be in communications or power convertors, can only be achieved by a process of modulation. The paper presents a powerful method of analysing and synthesising these complex modulation processes using a 3-dimensional modulation-model approach, which provides a lucid geometric interpretation of the processes involved. The application of the new approach is demonstrated by deriving new frequency-spectra results for the p.w.m. and p.a.m. convertors, thereby providing essential design information.

Novel approach to the analysis and synthesis of modulation processes in power convertors

This paper discusses the generalized theory of phase-shifted carrier pulsewidth modulation (PSC-PWM) for cascaded H-bridge (CHB) converters and modular multilevel converters (MMCs), provides a reasonable classification of the PSC-PWM, and extends the possible phase-shift angles to full range. First, the PSC-PWM for CHB converter is classified into two categories by phase-shift pattern. In addition, by rigorous mathematical derivation, the impact law of the full-range phase-shift angles on harmonic minimization is obtained. And then, it is proved that the generalized theory is equally applicable to MMC, which also merges the former proposed PSC-PWM for MMCs into itself. Moreover, the harmonic analysis of the dead-time error voltage is discussed, which is found to have the same harmonic distribution as the ideal voltage, except for the emerging of odd-order harmonics. In summary, this generalized theory offers a general perspective of the PSC-PWM for CHB converter and MMC, and builds up a scientific and comprehensive understanding for researchers from both academia and industry. Finally, the analytical findings are sufficiently validated by simulation and experimental results.

Generalized Theory of Phase-Shifted Carrier PWM for Cascaded H-Bridge Converters and Modular Multilevel Converters

A new method of computing modulation products by means of multiple Fourier series is described. The method is used to obtain for the problem of modulation of a two-frequency wave by a rectifier a solution which is considerably simpler than any hitherto known.

W. R. Bennett

Papers

New results in the calculation of modulation products