Radio wave propagation and antennas
Radio wave propagation and antennas
This domain tests how you translate a radio link into power, loss, and antenna terms. Expect free-space and terrestrial path loss, Fresnel clearance, polarization, gain, EIRP, impedance match, and link margin.
Core rules
- Free-space path loss: FSPL(dB)=32.44+20log10 f(MHz)+20log10 d(km). Friis in dB: Pr=Pt+Gt+Gr-Loss-FSPL.
- First Fresnel radius r1=17.32 sqrt(d1 d2/(f_GHz d_km)) m; aim for at least 60% clearance.
- Antenna gain and effective aperture are linked by Ae=G lambda^2/(4 pi). EIRP=Pt+Gt; ERP=EIRP-2.15 dB for a dipole reference.
- Reflection coefficient Gamma=(ZL-Z0)/(ZL+Z0), VSWR=(1+|Gamma|)/(1-|Gamma|), return loss=-20log|Gamma|.
- Linear polarization mismatch loss is -20log(cos theta); circular-to-linear mismatch costs about 3 dB.
Worked example
A 2.4 GHz link is 5 km. Pt=20 dBm, Gt=10 dBi, Gr=2 dBi, 1 dB cable loss at each end, receiver sensitivity -85 dBm. FSPL=32.44+20log2400+20log5=32.44+67.60+13.98=114.02 dB. Pr=20+10+2-1-1-114.02=-84.02 dBm. Margin=(-84.02)-(-85)=0.98 dB, so the link is only just closed. Rain and fade margin are not included.
Traps
Mixing MHz with km in the constant, forgetting connector/cable losses, treating ERP as EIRP, using antenna gain twice, and ignoring near-field or Fresnel obstruction. VSWR is not loss; convert it to mismatch loss before adding it to the budget.