Electromagnetics and Antennas
This domain covers Maxwell's equations, plane-wave propagation, transmission lines and Smith-chart use, and antenna parameters such as gain, directivity and effective aperture.
Core rules
- Free-space intrinsic impedance η0 = 377 Ω; propagation constant γ = α + jβ = √((R + jωL)(G + jωC)).
- Reflection coefficient Γ = (ZL − Z0)/(ZL + Z0); VSWR = (1 + |Γ|)/(1 − |Γ|); return loss = −20 log|Γ|.
- A half-wave dipole is about 0.48λ long with 2.15 dBi gain and 73 Ω radiation resistance; a short dipole gives 1.76 dBi. Gain = directivity × efficiency.
- Friis: Pr = Pt Gt Gr (λ/4πd)², valid only in the far field, d > 2D²/λ.
Worked example
A 50 Ω line feeds a 100 Ω load. Γ = (100 − 50)/(100 + 50) = 1/3, so VSWR = (1 + 1/3)/(1 − 1/3) = 2. The fraction of incident power delivered to the load is 1 − |Γ|² = 1 − 1/9 = 0.889, i.e. 88.9%, with 11.1% reflected; the return loss is −20 log(0.333) = 9.54 dB. A quarter-wave transformer of √(50 × 100) = 70.7 Ω would match the load at that single frequency only.
Traps
Quoting VSWR as |Γ|; expecting a quarter-wave transformer to be broadband; applying Friis inside the near field; and treating directivity as gain when the antenna has losses.