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Volterra series formula for RF power amplifiers — kernels, memory, and nonlinearity

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RF nonlinearity path: Volterra PA model → π/2-BPSK PAPR → EVM → SNR In one sentence: A Volterra series formula extends a Taylor polynomial with memory kernels so the PA output depends on the present input and recent past samples — the regime of wideband 4G/5G waveforms. Matlab/Python simulation: Use this model when you move … Read more

Array pattern multiplication of phased array antennas

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Antenna models — reading order Maxwell’s equations Retarded potentials Near-field / far-field boundary Far-field retarded potentials Array pattern multiplication (this article) Dipole power gain patterns Introduction Take one element’s radiation vector \(\mathbf{F}\), place \(N\) identical copies at positions \(\mathbf{l}_i\) with weights \(a_i\), and the far-field total factors as \(\mathbf{F}\,A\). That is pattern multiplication: the step … Read more

Near-field – far-field : Where is the boundary ?

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Antenna models — reading order Maxwell’s equations Retarded potentials Near-field / far-field boundary (this article) Far-field retarded potentials Array pattern multiplication Dipole power gain patterns Introduction Antenna fields change character with distance: reactive storage near the element, Fresnel diffraction at intermediate range, and spherical-wave radiation farther out. Link-budget and pattern formulas almost always assume that … Read more

From Maxwell’s equations to antenna array – part 1

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Antenna models — reading order Maxwell’s equations (this article) Retarded potentials Near-field / far-field boundary Far-field retarded potentials Array pattern multiplication Dipole power gain patterns Introduction Antenna theory is Maxwell’s equations plus boundary conditions and a far-field approximation. Before retarded potentials and array factors, write the four laws carefully—especially Ampère’s law with Maxwell’s displacement current. … Read more

Normalized power gain of dipole antennas

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Antenna models — reading order Maxwell’s equations Retarded potentials Near-field / far-field boundary Far-field retarded potentials Array pattern multiplication Dipole power gain patterns (this article) Introduction You have almost certainly seen the short-dipole pattern: nulls along the wire, maximum broadside. We will derive the normalised power patterns for the Hertzian dipole, the half-wave dipole, and … Read more

Bayes’ theorem

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Key focus: Bayes’ theorem is a method for revising the prior probability for specific event, taking into account the evidence available about the event. Introduction In statistics, the process of drawing conclusions from data subject to random variations – is called “statistical inference”. Usually, in any random experiment, the observations are recorded and conclusions have … Read more