Theory Based on Device Current Clipping to Explain and Predict Performance Including Distortion of Power Amplifiers for Wireless Communication Systems

Power amplifiers are critical components in wireless communication systems that need to have high efficiency, in order to conserve battery life and minimise heat generation, and at the same time low distortion, in order to prevent increase of bit error rate due to constellation errors and adjacent channel interference. This thesis is aimed at meeting a need for greater understanding of distortion generated by power amplifiers of any technology, in order to help designers manage better the trade-off between obtaining high efficiency and low distortion. The theory proposed in this thesis to explain and predict the performance of power amplifiers, including distortion, is based on analysis of clipping of the power amplifier device current, and it is a major extension of previous clipping analyses, that introduces many key definitions and concepts. Distortion and other power amplifier metrics are determined in the form of 3-D surfaces that are plotted against PA class, which is determined by bias voltage, and input signal power level. It is shown that the surface of distortion exhibits very high levels due to clipping in the region where efficiency is high. This area of high distortion is intersected by a valley that is ‘L’-shaped. The 'L'-shaped valley is subject to a rotation that depends on the softness of the cut-off of the power amplifier device transfer characteristic. The distortion surface with rotated 'L'-shaped valley leads to predicted curves for distortion versus input signal power that match published measured curves for power amplifiers even using very simple device models. The distortion versus input signal power curves have types that are independent of technology. In class C, there is a single deep null. In the class AB range, that is divided into three sub-ranges, there may be two deep nulls (sub-range AB(B)), a ledge (sub-range AB(A)) or a shallow null with varying depth (sub-range AB(AB))

New Investigation on the Spheroidal Wave Equations

Changing the spheroidal wave equations into new Schro$dinger's form, the super-potential expanded in the series form of the parameter$\alpha$are obtained in the paper. This general form of the super-potential makes it easy to get the ground eigenfunctions of the spheroidal equations. But the shape-invariance property is not retained and the corresponding recurrence relations of the form (4) could not be extended from the associated Legendre functions to the case of the spheroidal functions

On the Diophantine Equation 2^a3^b + 2^c3^d = 2^e3^f + 2^g3^h

This paper is a continuation of [1], in which I studied Harvey Friedman's problem of whether the function f(x,y) = x^2 + y^3 satisfies any identities; however, no knowledge of [1] is necessary to understand this paper. We will break the exponential Diophantine equation 2^a3^b + 2^c3^d = 2^e3^f + 2^g3^h into subcases that are easier to analyze. Then we will solve an equation obtained by imposing a restriction on one of these subcases, after which we will solve a generalization of this equation.Comment: This 6-page paper is the second part of an honors thesis I have written as an undergraduate at UC Berkele