Development of a FEM waveguide code, incorporating Fast Frequency Techniques, for numerical synthesis

Clarke, Samuel R. (Samuel Robert) (2002-12)

Thesis (MScEng)--University of Stellenbosch, 2002.

Thesis

ENGLISH ABSTRACT: A computational tool for numerical synthesis via optimization is developed. Only two port waveguide devices are considered. The Finite Element Method (FEM) is used for the electromagnetic analysis. Specifically, the frequency domain electric field FEM is used with vector curl-conforming constant tangential/linear normal brick-shaped elements. Special boundary conditions are used at the ports. These boundary conditions only consider dominant mode propagation. The issues surrounding the implementation of this formulation are discussed. The results generated using this code compare favorably to examples from independent sources. A parametric mesher that is used in conjunction with the FEM is developed. This is done to eliminate the need for human intervention during each iteration of the synthesis procedure. Fast Frequency (FF) techniques are presented to reduce the computational requirements of the synthesis. FF techniques reduce the cost of calculating many frequency samples in a specified band and do not reduce the computational requirements of computing a FEM solution at a single frequency. The FF techniques presented are: Asymptotic Waveform Evaluation (AWE), Model Based Asymptotic Waveform Evaluation (MB-AWE) and Model Based Parameter Estimation (MBPE) . The results obtained using these techniques are compared and the most suitable technique for the synthesizer is selected. MBPE is selected as the most suitable technique for this application. An adaptive sampling algorithm for Model Based Parameter Estimation is presented. The algorithm relies on the difference between multiple models generated from the same samples to determine the sample locations. The use of this algorithm enables a model of a narrow band filter at X-band to be determined using only fourteen FEM solutions. The difference between the model- and the FEM solutions is less then -lOOdBacross the band. A sample synthesis using generalized simulated annealing is presented. A single pole filter in X-band waveguide is successfully synthesized to illustrate the usefulness of the code. The use of FF techniques results in a computational cost saving of a factor of forty times.

AFRIKAANSE OPSOMMING: 'n Rekenaar werktuig vir numeriese sintese deur middel van optimering word ontwikkel. Slegs twee-poort golfleierkomponente word beskou. Die Eindige Element-metode (EEM) word vir die elektromagnetiese analise gebruik. Meer spesifiek, die frekwensiegebied, elektriese-veld EE-formuleering word gebruik, met eurl-ondersteunende, konstant-tagensiaaljlineêr-normaal, baksteenvormige vektorelemente. Spesiale grensvoorwaardes word by die poorte gebruik. Hierdie grensvoorwaardes neem slegs voortplanting van die dominante modus in ag. Die kwessies rondom die implementering van hierdie EEM word bespreek. Resultate wat met hierdie kode verkry word, vergelyk goed met dié vanuit onafhanklike bronne. 'n Parametriese diskretisasie prosedure in ontwikkel, vir gebruik saam met die genoemde EEM, met die doelom menslike interaksie uit die weg te ruim, tydens die sintese proses. Vinnige Frekwensie (VF) tegnieke word beskryf, met die doelom die berekeningskoste van die sintese te verminder. VF tegnieke verminder die berekeningskoste verbonde aan 'n reeks EEM oplosings binne 'n gegewe frekwensieband, maar verminder nie die koste verbonde aan 'n enkel-frekwensie EEM oplossing nie. Die VF tegnieke wat beskryf word, is die volgende: Asimptotiese Golfvorm Evaluasie (AGE), Model Gebaseerder Asimptotiese Golfvormevaluasie (MGAGE) en Model- Gebaseerde Parameterekstraksie (MGPE). Die resultate wat met hierdie metodes verkry word, word vergelyk om sodoende die mees toepaslike VF tegniek te kies. MGPE word gekies as die mees toepaslike tegniek. 'n Aanpasbase monsteringsalgoritme vir MGPE word beskryf. Die algoritme berus op die verskil tussen twee modelle wat vanaf dieselfde stel punte geskep word, om monsterfrekwensiewaardes te bepaal. Die gebruik van hierdie algoritme lei tot 'n model van 'n nou-, X-band filter, vanuit slegs veertien EEM oplossings. Die verskil tussen hierdie model en enige EEM oplossings binne die band, is kleiner as -lOOdB. 'n Voorbeeld sintese, wat gebruik maak van veralgemeende, gesimuleerde versmelting, word beskryf. 'n Enkel-pool filter by X-band word suksesvol gesintetiseer om die bruikbaarheid van die kode te illustreer. 'n Faktor veertig vermindering III berekeningskostes word behaal deur gebruik te maak van VF tegnieke.

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