Characteristic Impedance: 50Ω vs. 75Ω
Coaxial cable characteristic impedance Z₀ is determined by the ratio of outer to inner conductor diameters and the dielectric constant of the insulating medium:
Z₀ = (138 / √εᵣ) · log₁₀(D/d)
A complete engineering reference for coaxial transmission lines and RF passive components: cable types, attenuation tables, impedance, connectors, splitters, directional couplers, PIM, and weatherproofing standards.
Coaxial cable characteristic impedance Z₀ is determined by the ratio of outer to inner conductor diameters and the dielectric constant of the insulating medium:
Z₀ = (138 / √εᵣ) · log₁₀(D/d)
where D is the inner diameter of the outer conductor, d is the outer diameter of the inner conductor, and εᵣ is the relative permittivity of the dielectric. The 50Ω standard arose as a practical compromise between minimum attenuation (achievable around 77Ω in air-dielectric) and maximum power handling (achievable around 30Ω). 50Ω is universally used in RF communications, test equipment, and broadcast transmitters. 75Ω cable (e.g., RG-59, RG-6) minimises attenuation in video and cable television distribution systems and is not interchangeable with 50Ω systems without impedance matching. Mismatching 75Ω cable into a 50Ω system causes a VSWR of 1.5:1 and an 8% power reflection — acceptable for test purposes but not for permanent installations.
Selection guide for common RF coaxial cables:
Coaxial cable attenuation increases with frequency due to the skin effect in the conductors (proportional to √f) and dielectric loss (proportional to f). The combined effect means attenuation roughly doubles for each quadrupling of frequency. Designers must run the link budget at the highest operating frequency to determine the worst-case insertion loss. For a 50 m run of LMR-400:
Temperature de-rating is important for outdoor installations. Most cable specifications are at 25°C; attenuation increases approximately 0.2% per °C above this. In a desert environment at 60°C, attenuation may be 7% higher than rated — worth accounting for in tight link budgets.
The velocity factor (VF) is the ratio of signal propagation velocity in the cable to the speed of light in vacuum. VF = 1/√εᵣ. Solid PE dielectric: VF ≈ 0.66. Foam PE: VF ≈ 0.80–0.85. Air dielectric (HELIAX): VF ≈ 0.92–0.93. VF affects electrical length calculations critical for phased array feeding, impedance matching stubs, and delay equalisation in simulcast systems. For simulcast timing alignment, cable electrical lengths must match to within ±100 ns — equivalent to ±15 m of LMR-400.
A 2-way splitter divides input power equally between two output ports: each port receives −3 dB (one-half) of input power, plus typical excess insertion loss of 0.5 dB, giving a total of 3.5 dB per port. A 4-way splitter is two 2-way splitters in series: −6 dB + 1 dB excess = 7 dB per port. An 8-way adds another stage: 10.5 dB per port. Splitters are reciprocal — they function identically as combiners (joining multiple signals), with the same insertion losses.
A directional coupler samples a fixed fraction of power from a through-line with high port-to-port isolation, useful for monitoring or distributing a small tap of the main signal. Coupling values: −10 dB, −15 dB, −20 dB, −30 dB. The through-line has minimal insertion loss (0.5–1.5 dB depending on coupling value). Used in DAS for unequal power splitting where one antenna needs less power than the trunk path.
Fixed attenuators (pads) reduce signal level to prevent receiver overload, equalise levels in a distribution network, or improve return loss by padding impedance mismatches. Values: 1, 2, 3, 6, 10, 20 dB. Power ratings: 1 W to 100 W for standard pads; high-power versions to 1 kW for transmit applications. Circulators (3-port ferrite devices) route signals in one direction only: port 1 → port 2 → port 3 → port 1. Used to isolate transmitter from antenna VSWR reflections — reflections from a mismatched antenna exit port 3 (a dummy load) rather than re-entering the transmitter output stage.
Coaxial lightning arrestors (surge protectors) are installed at every cable entry point where an outdoor antenna cable enters a building or equipment enclosure. They provide a low-impedance path to ground for lightning-induced surges while presenting low RF insertion loss (< 0.2 dB) and low VSWR (< 1.2:1) during normal operation. Gas discharge tube (GDT) and hybrid (GDT + TVS diode) types are available; hybrid types provide better response to fast transients. Arrestors must be bonded to the building grounding electrode system per NEC Article 810 and TIA-222 requirements.
Outdoor connector weatherproofing is critical for long-term reliability. Unsealed N-type connectors in outdoor environments allow moisture ingress, oxidation, and eventually connector failure within 1–3 years. Methods:
Power handling de-rating in weatherproofed assemblies: connector body temperature rise due to I²R loss limits the maximum continuous power. LMR-400 with N-type connectors: continuous power limit at 450 MHz is approximately 1,100 W at 40°C ambient. For most LMR and DAS applications (< 50 W per port), power handling is not the limiting design constraint — signal level and loss are.
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