RF & Antenna Education

From first principles to advanced beamforming — our library of guides, tutorials, and deep-dives is free for engineers, students, and enthusiasts worldwide.

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Structured topic guides — each covers a complete subject area with articles, equations, and worked examples.

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Showing 48 articles  ·  Page 3 of 4
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Beginner
RF Fundamentals

Understanding Characteristic Impedance of Transmission Lines

Part 2: what a transmission line is, the definition of characteristic impedance Z₀ = √(L/C), voltage and current on a line, Z₀ of coaxial cables and microstrip lines, why 50 Ω and 75 Ω systems are used, and the factors that change Z₀.

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Beginner
RF Fundamentals

Understanding Load Impedance and Reflection Coefficient

Part 3: load impedance and reflections, the reflection coefficient Γ = (Z_L − Z₀)/(Z_L + Z₀), its magnitude and phase, short, open and matched loads, return loss, S11 and reflected power, with Smith Chart Calculator examples.

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Intermediate
RF Fundamentals

Standing Waves and Voltage Standing Wave Ratio (VSWR)

Part 4: how standing waves form on a mismatched line, voltage maxima and minima, the definition of VSWR, conversions between VSWR, Γ, return loss and mismatch loss, the VSWR circle on the Smith chart, and why VSWR matters.

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Intermediate
RF Fundamentals

Impedance Transformation Along Transmission Lines

Part 5: the input impedance of a transmission line, impedance transformation as rotation on the Smith chart, λ/8, λ/4 and λ/2 lines, the quarter-wave transformer, short- and open-circuited stubs, and physical line lengths.

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Intermediate
RF Fundamentals

Introduction to the Smith Chart

Part 6: the purpose and history of the Smith chart, how it is constructed from the reflection-coefficient plane, its regions and special points, the impedance and admittance charts, and how to read the combined Z/Y chart.

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Intermediate
RF Fundamentals

Understanding Normalized Impedance on the Smith Chart

Part 7: normalised impedance and admittance (z = Z/Z₀, y = Y·Z₀), denormalising chart readings, changing the reference impedance from 50 Ω to 75 Ω, and converting normalised values into inductor and capacitor values.

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Intermediate
RF Fundamentals

Understanding Smith Chart Parameters and Circles

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.

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Intermediate
RF Fundamentals

How to Plot Impedance on a Smith Chart

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.

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Intermediate
RF Fundamentals

Impedance Matching Using the Smith Chart

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.

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Advanced
RF Fundamentals

Single-Stub and Double-Stub Impedance Matching

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.

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Advanced
RF Fundamentals

Practical Applications of Smith Charts in RF and Microwave Engineering

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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Beginner
Antenna Fundamentals

Introduction to Antennas

Part 1 of the Antenna Fundamentals series: what an antenna is, why wireless needs one, radiation from accelerating charges, radiation resistance, receiving antennas and effective aperture, reciprocity, the antenna equivalent circuit and the main antenna families.

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