Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: In this dissertation a number of techniques to design multi-band filters, with specific focus on coupled resonator implementations, is presented. Multi-band transfer functions are constructed from single-band transfer functions using frequency mapping methods. A general class of rational mapping functions is presented that can accommodate arbitrary bandwidth specifications. Multi-band circuits are synthesised directly from multi-band transfer functions and are obtained by applying reactance transformations to single-band prototype circuits. For the direct synthesis of multi-band filters from multi-band transfer functions coupling matrix synthesis methods are employed. The circuits that result from matrix synthesis methods tend to have topologies that are undesirable from a practical perspective and must be simplified using rotations of the coupling matrix. The synthesis of multi-band filters through reactance transformations is both simple and result in filters that have practical topologies for realisation as coupled resonator circuits. Multiple filters are designed using different design methodologies and different transmission line technologies to illustrate the various design possibilities. The designs include both all-pole and cross-coupled filters and employ single-layer stripline, multi-layer stripline as well as coaxial resonators as transmission line technologies for the implementations. / AFRIKAANSE OPSOMMING: In hierdie proefskrif word verskeie ontwerpstegnieke vir multi-band filters aangebied en word daar spesifiek klem gelê op filters wat as gekoppelde resoneerder strukture geïmplimenteer kan word. Multi-band oordragsfunksies word geskep uit enkelband oordragsfunksies deur gebruik te maak van wiskundige afbeeldingstegnieke. ’n Spesiale klas van rasionale funksies word voorgestel wat spesifiek gebruik kan word om multi-band funksies te skep wat ’n arbitrêre bandwydte spesifikasie het. Multi-band stroombane word direk gesintetiseer vanuit multi-band oordragsfunksies en word ook verkry deur die toepassing van reaktansietransformasies op enkelband stroombane. Vir die direkte sintese van multi-band stroombane vanuit multi-band oordragsfunksies word stroombane gesintetiseer as koppelmatrikse. Stroombane wat op hierdie wyse gesintetiseer word is geneig om topologieë te hê wat nie baie gesog is vanuit ’n praktiese perspektief nie en matriks rotasies word dan hier ingespan om die stroombane se topologieë te vereenvoudig. Die sintese van multi-band stroombane deur gebruik te maak van reaktansietransformasies is beide eenvoudig en lei tot stroombane wat praktiese topologieë het vir implimentering as gekoppelde resoneerder strukture. Die ontwerpsmoontlikhede wat die verskillende metodieke bied word geïllustreer deur die ontwerp van verskeie filters op verskillende maniere waar daar gebruik gemaak word van verskeie transmissielyn tegnologië. Die filter ontwerpe sluit filters in waar alle transmissienulle by oneidige frekwensies is, sowel as gevalle waar somige transmissienulle by eindige frekwensies is. Die filters word geïmplimenteer deur gebruik te maak van koaksiale resoneerders sowel as enkellaag en multilaag strooklyn.