Free Coaxial Cable Characteristic Impedance Calculator
Design custom rigid coax and analyze coaxial cables. Calculate Z0 impedance, distributed capacitance, inductance, and TE11 cutoff frequency.
🖲️ Coax Geometry & Dielectric Properties
Velocity Factor (VF): 69.0% (c • 0.69)
• Maximum Single-Mode Frequency: 34.1 GHz (Cutoff frequency for non-TEM waveguide modes).
• Safe Operating Limit: ≤ 30.7 GHz (90% of TE_11 mode).
Why 50 Ω and 75 Ω? Green in 1929 proved that an air-filled coax achieves minimum RF attenuation loss at $77,Omega$, while achieving maximum RF voltage power handling at $30,Omega$. $50,Omega$ was selected as the optimal international compromise.
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Electromagnetics of Coaxial Cables
A coaxial transmission line guides energy in the fundamental Transverse Electro-Magnetic (TEM) mode. Its characteristic impedance $Z_0$ depends strictly on the logarithm of the ratio of the conductor diameters and the dielectric constant of the insulator:
Governing Transmission Line Formulas
Velocity Factor: VF = 1 / √ε_r
Capacitance per meter: C = (2π × ε_0 × ε_r) / ln(D / d)
Inductance per meter: L = (μ_0 / 2π) × ln(D / d)
TE_11 Cutoff Frequency: f_c ≈ c / (π × (D + d) / 2 × √ε_r)
The Waveguide Cutoff Limit
At extremely high microwave frequencies where the mean circumference $pi(D+d)/2$ exceeds the guided wavelength $lambda_g$, the coaxial cable ceases to behave as a pure TEM line. It begins supporting waveguide modes ($TE_{11}$ and $TM_{01}$), which causes severe mode dispersion, signal distortion, and erratic insertion loss. To prevent mode hopping, thinner cables (e.g. 0.086" or 0.047" semi-rigid) must be used at higher GHz frequencies.
Frequently Asked Questions
Why does dielectric constant reduce the physical propagation speed?
The phase velocity of an electromagnetic wave in a medium is v = c / sqrt(epsilon_r). In solid Teflon (epsilon_r = 2.1), the velocity factor is VF = 1 / sqrt(2.1) = 0.69, meaning the wave travels at 69% the speed of light, shrinking the electrical wavelength by 31%.
What happens if I connect a 50 Ohm cable to a 75 Ohm TV antenna?
The impedance mismatch causes an SWR of 75 / 50 = 1.50:1. This produces a return loss of 14 dB (~4% of transmitted power reflected). While minor for receiving television broadcasts, in high-power transmitters this reflection causes standing wave heating in the output stage.
How does braiding coverage affect coax impedance and shielding?
The nominal impedance formula assumes an unbroken continuous outer tube. Real braided shields have tiny interstitial apertures that introduce transfer impedance (leakage). Double-braided or foil-plus-braid cables reduce RF leakage by over 40 dB compared to single-shield economy cables.