Beam ripple modelling in wideband dual-reflector antenna systems

Wolmarans, Jacques (2022-04)

Thesis (MEng)--Stellenbosch University, 2022.

Thesis

ENGLISH ABSTRACT: Efficient modelling of the rapid far-field frequency variations found in the radiation of electrically small dual reflector antennas is of high interest due to their increasing use in array configurations for interferometry. These rapid variations, most discernible in broadside directivity across frequency, are a result of internal field interference between the radiation from the feed and reflector apertures causing chromatic aberration. Their quasi-sinusoidal nature presents a significant challenge from a modelling perspective, as computationally expensive samples at the Nyquist rate or above are required to capture the ripple during frequency interpolation. This thesis presents the design of a physics based surrogate model able to reconstruct the ripple with a sparse set of samples independent of its frequency, and therefore, at a mere fraction of the Nyquist rate, significantly reducing the computational cost of wideband characterisation. The model is designed to assist during the evaluation of reflector geometry and feed suitability through interpolation of MoM or PO solutions with the characteristic basis function expansion method (CBFP). An adaptive sampling approach is adopted to minimise the number of direct antenna simulations needed for the generation of an accurate global model able to facilitate rapid design and analysis. The surrogate model implementation shown here is able to capture the chromatic aberration ripple inherent to reflector surfaces of several tens of wavelengths with a sample density ≈ 1 10 th of the Nyquist rate per octave bandwidth, for analytical Gaussian primary patterns. Prediction error is typically less than 10 % of the ripple amplitude, provided enough samples are used such that the CBFP expansion successfully isolates geometric beam features. A higher sampling density is required for primary patterns from practical antennas due to their effects on the macro behaviour of the secondary pattern across frequency, however, this is typically below 1 4 of Nyquist density. Overall, far-field radiation pattern prediction error is tied to the number of frequency samples available to train the CBFP expansion, therefore, any modelling limitation previously imposed by the chromatic aberration ripple is removed.

AFRIKAANSE OPSOMMING: Die effektiewe modellering van vinnige ver-veld variasies gevind in die radiasie patroon van elektriese klein dubbel reflektor antennas is van groot belang a.g.v. die toenemende gebruik van antenna samestellings vir interferometrie. Hierdie vinnige variasies, mees prominent in die bre¨ekant gerigtheid oor frekwensie is a.g.v. die interne veld interferensie tussen die voer- en reflektor openinge se radiasie, veroorsaak deur chromatiese afwyking. Vanaf ‘n modellerings perspektief bied die kwasi-sinusvormigheid van die variasies ‘n groot uitdaging, omrede duur berekenings monsters nodig is, teen die Nyquist-koers of ho¨er, vir suksesvolle opvang van die rimpel tydens frekwensie interpolasie. Hierdie tesis handel oor die ontwerp van ‘n fisika-gebaseerde surrogaat model, in staat daarvan om die rimpel vanaf ‘n stel yl monsters onafhanklik van die frekwensie te rekonstrueer, teen ‘n blote breukdeel van die Nyquist-koers, voor, wat gevolglik tot ‘n groot afname in die berekenings koste vir bre¨eband karakterisering lei. Die model dien as ‘n hulpmiddel tydens die evaluering van reflektor geometrie en voer geskiktheid deur interpolasie van die moment metode en fisiese optika oplossings met die karakteristieke basis funksie uitbreidings (KBFU) metode te kombineer. ‘n Aanpasbare steekproef benadering word aangeneem om die aantal direkte antenna simulasies, nodig vir die generasie van akkurate globale modelle vir vinnige prototipering en kalibrasie, te minimeer. Die surrogaatmodel implimentering wat hier voorgelˆe word, is daartoe instaat om die chromatiese aberrasie rimpel, inhirent tot reflektoroppervlakte van verskeie tientalle golflengtes met ’n monster digtheid ≈ 1 10 th van die Nyquist koers per oktaaf bandwydte vir analitiese Gauss primˆere patrone, op te vang. Die voorspellingsfout is tipies minder as 10% van die rimpelamplitude, mits genoeg monsters gebruik word sodat die KBFU die geometriese balk kenmerke suksesvol kan isoleer. ’n Ho¨er steekproefdigtheid word benodig vir primˆere patrone van praktiese antennas a.g.v. hul effek op die makro gedrag van die sekondˆere patroon oor frekwensie, alhoewel dit tipies onder 1 4 van die Nyquist-digtheid is. Algemene ver-veld radiasie patroon voorspellingsfout is gekoppel aan die aantal frekwensie monsters beskikbaar om die KBFU op te lei, daarom is enige modellerings beperkinge voorheen opgelˆe deur die chromatiese aberrasie verwyder.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/124689
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