From first principles to advanced beamforming — our library of guides, tutorials, and deep-dives is free for engineers, students, and enthusiasts worldwide.
Structured topic guides — each covers a complete subject area with articles, equations, and worked examples.
Wave propagation on guided structures — characteristic impedance, reflection, standing waves, and microstrip design.
A practical guide to the most common antenna types — how each works, where it's used, and how to choose the right one for your application.
From electric and magnetic fields to the four equations, electromagnetic waves and boundary conditions — and how they shape lines, waveguides and antennas.
From impedance, reflection coefficient and VSWR to reading the Smith chart and designing L-network and stub matches for real antennas.
Part 8: constant-resistance circles, constant-reactance arcs, constant-conductance and susceptance circles, constant-VSWR circles, the wavelengths-toward-generator scales, radially scaled parameters and constant-Q curves.
Read guide →Part 9: a step-by-step method for plotting impedance on a Smith chart, reading Γ, VSWR and return loss, finding admittance, and following an impedance along a transmission line, with calculator screenshots.
Read guide →Part 10: impedance matching with the Smith chart — conjugate matching, how series and shunt components move the impedance, step-by-step L-network design, four solutions for one load, component values, bandwidth and π/T networks.
Read guide →Part 11: single-stub and double-stub impedance matching — stub position and length on the Smith chart and analytically, short vs open stubs, microstrip lengths on FR-4, the double-stub forbidden region, and stub bandwidth.
Read guide →Part 12: practical Smith chart applications — matching a measured antenna from a Touchstone .s1p file, reading VNA sweeps, how cable loss hides a mismatch, port extension, and stability, gain and noise circles in amplifier design.
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