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Coaxial Cable Impedance Calculator

Calculate coaxial cable characteristic impedance (Z0), capacitance, inductance per meter, and TE11 cutoff frequency from conductor dimensions. Free, instant results.

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Formula

Z0=60εrln⁡ ⁣(Dd)Z_0 = \frac{60}{\sqrt{\varepsilon_r}} \ln\!\left(\frac{D}{d}\right)

Reference: Wadell, "Transmission Line Design Handbook" 1991, Chapter 3

D— Inner diameter of outer conductor (mm)
d— Outer diameter of inner conductor (mm)
εᵣ— Relative permittivity of dielectric

How It Works

Coaxial cable characteristic impedance determines signal transmission quality in RF systems — telecommunications engineers, broadcast technicians, and test equipment designers rely on this parameter for impedance matching and minimizing reflections. The impedance Z0 = (60/sqrt(er)) * ln(D/d) derives from Maxwell's equations for TEM-mode propagation, where D is the outer conductor inner diameter, d is the inner conductor outer diameter, and er is the dielectric constant (IEEE Standard 287-2007).

For air-dielectric coax, minimum attenuation occurs at 77 ohms while maximum power handling occurs at 30 ohms — the 50-ohm standard represents an engineering compromise adopted by military specifications (MIL-C-17) in the 1940s. According to Pozar's 'Microwave Engineering' (4th ed.), 75-ohm cable minimizes signal loss and is preferred for video/CATV applications where power handling is secondary.

Practical impedance tolerance is typically +/-2 ohms for quality coax (per MIL-C-17 specifications). At 10 GHz, even 1% impedance variation causes 0.04 dB additional loss from reflections. Temperature coefficients range from 50-200 ppm/C depending on dielectric material — PTFE exhibits approximately 100 ppm/C while polyethylene shows 200 ppm/C variation.

Worked Example

Problem: Design a 50-ohm coaxial cable for a 2.4 GHz WiFi system using PTFE dielectric (er = 2.1).

Solution per IEEE 287-2007 methodology:

  1. Rearrange impedance equation: D/d = exp(Z0 * sqrt(er) / 60)
  2. Calculate ratio: D/d = exp(50 * sqrt(2.1) / 60) = exp(1.21) = 3.35
  3. For standard 0.9 mm center conductor: D = 0.9 * 3.35 = 3.02 mm outer diameter
  4. Verify: Z0 = (60/sqrt(2.1)) ln(3.35) = 41.4 1.21 = 50.1 ohms
This matches RG-402 semi-rigid specifications. The velocity factor is 1/sqrt(2.1) = 0.69, meaning signals travel at 69% of light speed. At 2.4 GHz, wavelength in cable = 86 mm versus 125 mm in free space.

Practical Tips

  • ✓Use time-domain reflectometry (TDR) to verify impedance uniformity along cable length — IEEE 1785.1 specifies maximum deviation of +/-2 ohms for precision measurements
  • ✓Select cable impedance to match system requirements: 50 ohms for RF/wireless (optimal power transfer), 75 ohms for video/CATV (minimum loss), 93 ohms for digital buses (reduced capacitive loading)
  • ✓For impedance-critical applications above 6 GHz, specify phase-stable cable with temperature coefficient < 50 ppm/C and use torque wrenches (8 in-lb for SMA) per IEEE 287 connector care guidelines

Common Mistakes

  • ✗Using outer jacket diameter instead of shield inner diameter — error of 10-20% in calculated impedance; always measure shield ID with precision calipers (0.01 mm resolution required per MIL-STD-348)
  • ✗Ignoring skin effect at frequencies above 100 MHz — current flows only in the outer 2.1 micrometers of copper at 1 GHz, making surface finish critical; Ra < 0.4 micrometers specified for precision coax
  • ✗Neglecting temperature effects in outdoor installations — 50-meter LMR-400 run varies by +/-1.5 ohms across -40C to +85C temperature range, causing VSWR to increase from 1.05:1 to 1.12:1

Frequently Asked Questions

The 50-ohm standard emerged from 1940s military research as a compromise: air-dielectric coax achieves minimum loss at 77 ohms and maximum power at 30 ohms. With solid polyethylene dielectric (er = 2.3), the geometric mean sqrt(77 * 30) = 48 ohms, rounded to 50 ohms. MIL-C-17 standardization ensured connector interoperability. For comparison, 75-ohm cable (CATV/video) optimizes for loss at the expense of power handling — attenuation is 8% lower than 50-ohm cable of the same diameter.
Characteristic impedance is independent of length for uniform cable per transmission line theory (Pozar, 'Microwave Engineering'). However, practical factors introduce variations: connector discontinuities add +/-0.5 ohms per connection, manufacturing tolerance is typically +/-2 ohms per MIL-C-17, and cable bending below minimum bend radius (typically 10x outer diameter) can cause local impedance bumps of 1-3 ohms detectable by TDR.
This calculator applies to solid and air-dielectric coaxial cables where TEM mode propagates. For foam dielectric, use effective dielectric constant (typically 1.3-1.5 for foam PE). Semi-rigid cable follows these equations exactly. Corrugated/heliax cable requires manufacturer specifications due to complex geometry — Andrew LDF4-50A achieves 50 ohms through helical corrugations not captured by the simple D/d ratio.
Temperature causes dimensional changes in conductors (copper: 17 ppm/C) and dielectric constant shifts (PTFE: -400 ppm/C for er). Combined effect on impedance is typically 50-200 ppm/C. For a 50-meter precision measurement cable operating from 0C to 50C, impedance may shift by 0.5-1.0 ohms. Phase-stable cables use composite dielectrics to achieve < 50 ppm/C — critical for phase-coherent measurement systems.
Impedance sensitivity to diameter is dZ0/Z0 = dD/D - dd/d. For 50-ohm cable, a 1% error in either diameter causes approximately 0.4-ohm impedance error. Professional RF measurements require 0.01 mm caliper resolution (0.5% accuracy on 2 mm conductors). For production testing, use calibrated TDR with 10 ps risetime to detect impedance variations of +/-1 ohm with spatial resolution of 1.5 mm.
RG-58/U has characteristic impedance of 50 +/-2 ohms per MIL-C-17, using 0.9 mm solid copper center conductor and solid polyethylene dielectric (er = 2.3, velocity factor 0.66). Attenuation is 10.6 dB/100m at 100 MHz and 21.5 dB/100m at 400 MHz — acceptable for runs under 30m at VHF. For comparison, RG-59 (75 ohms) and RG-6 (75 ohms) are CATV standards with 0.6 dB/100m less attenuation but 1.5:1 VSWR mismatch to 50-ohm systems.
Historical analysis (Bell Labs, 1929) showed air-dielectric coax has minimum attenuation at 77 ohms (optimum E-field distribution) and maximum power handling at 30 ohms (optimum current distribution). The geometric mean is 48 ohms; practical dielectrics shifted this to 50-52 ohms. Military adoption in WWII radar systems established 50 ohms as the RF standard. 75 ohms became the video standard because minimum attenuation matters more than power for distribution systems. 93 ohms (RG-62) minimizes input capacitance for high-impedance digital buses — IBM 3270 terminals used this standard.

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