| In recent years, pulse width modulation (PWM) has become important in efficient energy processing and management in all types of communication systems and audio applications. Since a PWM signal has only a few (most often two) discrete levels, it can be amplified easily via switching mode amplifiers. PWM is also an essential control technique used for power management in microprocessors and portable communications. The high efficiency provided by the PWM technique allows the reduction of the sizes of the power supplies and heat sinks, and also increases the battery life in portable devices.; The determination of the frequency spectrum of a general pulse width modulated signal with band-limited input has been an open problem for many years. When the input is a single tone sinusoidal signal, a double Fourier series method can be applied to obtain the spectrum of the PWM signal. However, it is difficult to extend this method to study the general PWM signals. In this thesis, we describe a new approach that gives exact analytical expressions for the spectra of the two common forms of PWM, namely, uniform-sampling and natural-sampling PWM signals. It is shown that for natural-sampling PWM, there is no harmonic distortion in the baseband. The results for the special case of a single tone input signal match those obtained from the double Fourier series method.; When the input to a PWM modulator is a sequence of uniformly spaced samples of the original signal, the resulting uniform-sampling PWM signal has high distortion. It is possible to eliminate the distortion completely by converting the uniform-sampling input sequence into a natural-sampling sequence before applying it to the PWM modulator. In this thesis, it is shown that it is possible to express the natural-sampling sequence exactly in terms of the derivatives of the input signal raised to various powers. Since the input signal is known only through its sample values, numerical methods are used to devise high-accuracy, low-computational-complexity, methods for computing the natural-sampling sequence from the uniform-sampling sequence. To simplify the implementation of real applications, the noise shaping technique is employed to reduce the resolution of quantization without compromising the signal to quantization noise ratio. |
