The Short Answer
50 Ω is a historical compromise between two optimums in coaxial cable: minimum loss (77 Ω) and maximum power handling (30 Ω). Since RF engineers in the 1940s needed both low loss AND reasonable power capability (for military radar), they chose 50 Ω as the practical middle ground.
Physics: Why These Two Numbers?
For air-dielectric coaxial cable with outer diameter D and inner diameter d:
Minimum loss at: Z₀ = (60/√εr) · ln(D/d)
Minimize when D/d ≈ 3.59 → Z₀ ≈ 77 Ω (air)
(more space between conductors → less skin-effect loss)
Maximum power at: largest inner conductor d (holds more current)
D/d ≈ 1.65 → Z₀ ≈ 30 Ω
(better heat dissipation in high-power TX)
Compromise: geometric mean ≈ √(77 × 30) ≈ 48 Ω → rounded to 50 Ω
Why 75 Ω for Cable TV?
Cable TV systems (CATV) distribute signals over hundreds of meters of coaxial cable at modest power levels (milliwatts). Minimum attenuation is the priority — so 75 Ω (closest to the 77 Ω optimum) was standardized. The lower power handling of 75 Ω cable is fine for TV distribution.
Mixing 50 Ω and 75 Ω Systems
Connecting 50 Ω source to 75 Ω load:
Γ = (75 − 50)/(75 + 50) = 25/125 = 0.2
Return Loss = 14 dB, VSWR = 1.5:1, Mismatch Loss = 0.18 dB
This is tolerable for casual use but significant for precision RF work.
Proper interface: use a 50Ω/75Ω minimum-loss pad:
75Ω series arm = 43.3 Ω, 50Ω shunt arm = 86.6 Ω
Are There Any Other RF Impedance Standards?
| Impedance | System | Application |
|---|---|---|
| 50 Ω | RF/microwave instruments | VNA, spectrum analyzer, lab gear |
| 75 Ω | CATV, video, broadcast | Cable TV, satellite, video monitoring |
| 300 Ω | Balanced twin-lead | Legacy TV antenna feeds |
| 93 Ω | RG62 coax (legacy) | ARCnet, early LAN systems |
RF View: All RF View analysis uses 50 Ω reference impedance. Smith chart center = 50 Ω perfect match. The VSWR Calculator shows the mismatch loss when working between 50 and 75 Ω systems.