| This thesis is intended as an investigation of the use of non-uniform transmission lines as impedance matching networks. Numerous attempts have been made by scholars to show the limits of non-uniform transformer designs as regards the minimum of the return loss, the total length of the lines and the required bandwidth. Although a large number of studies have been made on numerical design methods, little is known about using analytical solutions for direct synthesis. Our method can provide simple mathematical interpretations and form the basis of possible extensions of this work to more complicated cases.;First of all, a mathematical derivation of the optimization procedures will be presented, together with a number of conditions to simplify the problem. These conditions include: the characteristic impedance function is continuous at both ends, the specified input and output impedances are resistive and frequency-independent, and the transmission lines are lossless and transverse electromagnetic (TEM).;Second, some general properties of this theory will be stated with mathematical explanations and observations based on a number of examples. The results using other independent numerical methods, such as the ABCD matrix method, Ansoft Designer and Ansoft HFSS, will be compared with our earlier results. Then, we will introduce an approximation to adapt our method for non-transverse electromagnetic (non-TEM) lines. This adaptation will offer the ability to extend our designs to microstrip lines, examples of which will then be fabricated and measured. All these comparisons show substantial agreement with our theory.;Lastly, our theory will be extended to a more general situation: allowing discontinuities at both ends of the impedance profile. It will become clear at this point that we are able to obtain further improvement in performance, in the sense that it has lower input reflected power over a given range of design frequencies than traditional "optimized" designs, such as Klopfenstein's taper. With this new degree of freedom, we can extend the method to handle the complex matching impedances. |
