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2 years ago in Computational Electromagnetics , Microwave Engineering By Pranav

I’m designing a horn antenna from scratch. How do I determine the initial aperture dimensions (width and height) based solely on my target operating frequency?

I need to create a simple pyramidal horn for a basic gain standard at 10 GHz. Before optimizing for gain or beamwidth, I need the correct starting point: what should the approximate aperture (A x B) be to ensure the horn actually functions efficiently at that frequency? I recall rules of thumb involving multiples of wavelength, but I'm unsure of the exact derivations from the condition for efficient radiation versus a waveguide cutoff. Is there a straightforward formula or a minimum aperture size criterion based on frequency alone?

InputImpedanceCalculation ModalExpansion FeedProbeReactance DesignOfExperiments(DOE)

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By Karkuvel Answered 1 year ago

You've pinpointed the core design step. The critical equation is the modal expansion for the input impedance, derived from the cavity model's Green's function. For a rectangular patch (L x W) fed by a coaxial probe at (x?, y?), it's an infinite sum over TM?? modes:
Z_in(x?,y?) = jωμt ∑? ∑? [ψ??²(x?,y?) / (k² - k??²) ]
where ψ?? are the modal eigenfunctions (cosines for ideal magnetic walls), k is the wavenumber, k?? is the modal wavenumber, μ is permeability, and t is substrate thickness. In practice, you truncate after the dominant (1,0) mode and maybe (3,0), as higher modes contribute negligibly near resonance. You must also add a series inductive term to model the probe. I use this equation in a script, sweeping (x?,y?) along the patch's centerline (y?=W/2) to find where Re(Z_in) ≈ 50Ω, then fine-tune with a full-wave solver. Remember, this model assumes perfect magnetic walls, so it's a superb starting point, but dielectric and radiation losses will slightly shift the optimal point in practice.

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I’m designing a horn antenna from scratch. How do I determine the initial aperture dimensions (width and height) based solely on my target operating frequency?

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