Radio Frequency Fundamentals and Spectrum Concepts
What this domain tests
Domain 1 asks you to move confidently between watts, dBm, dBd, dBi and ERP, and to explain why a portable hears a site at one distance but not another. Expect unit conversions, bandwidth calculations and items that hinge on the difference between transmitter power and radiated power.
Rules worth memorising
- Wavelength: lambda (m) = 300 / f (MHz). 150 MHz is a 2 m wave; 750 MHz is 0.4 m.
- Decibels are ratios: +3 dB is about x2 power, +10 dB is x10 power, -3 dB is half. For voltage or field strength, 20 dB is x10.
- dBm is absolute: 0 dBm = 1 mW, 30 dBm = 1 W, 40 dBm = 10 W, 50 dBm = 100 W.
- dBd and dBi differ by 2.15 dB: dBi = dBd + 2.15.
- ERP(dBm) = transmitter power(dBm) - feedline and connector loss + antenna gain(dBd). EIRP = ERP + 2.15 dB.
- Free-space path loss grows about 6 dB per doubling of distance and about 6 dB per doubling of frequency.
- FM occupied bandwidth follows Carson's rule: BW is roughly 2 x (peak deviation + highest audio frequency). That is why 5 kHz deviation with 3 kHz audio lands near 16 kHz, and why 2.5 kHz deviation fits a 12.5 kHz channel.
- Thermal noise floor = -174 dBm/Hz + 10 log10(bandwidth) + receiver noise figure.
Worked example
A 40 W base transmitter (46 dBm) feeds a duplexer and 60 m of hardline with 2 dB total loss into an antenna rated 6 dBd. ERP = 46 - 2 + 6 = 50 dBm, which is 100 W. EIRP = 50 + 2.15 = 52.15 dBm, about 164 W. If a plan limits you to 100 W EIRP instead, drop 2.15 dB: about 61 W ERP.
Traps that cost marks
Mixing dBd and dBi, quoting transmitter power as ERP, ignoring feedline loss, treating dBm as a linear unit, and assuming free-space loss rates hold on cluttered urban paths.