Cable Impedance Calculator

• Coaxial line: Z₀ = (60 / √ε_r) · ln(b/a), where a is inner radius, b is outer inner radius.
• Two-wire line: Z₀ = (120 / √ε_r) · acosh(D/(2r)), where r is wire radius and D is center spacing.
• Per‑length parameters: Z₀ = √(L′/C′), with L′ and C′ derived from geometry and ε_r.
• Wave velocity: v_p ≈ c/√ε_r, velocity factor ≈ 1/√ε_r.
• Input impedance (lossless): Z_in = Z₀(Z_L + jZ₀tanβl)/(Z₀ + jZ_Ltanβl), β = 2πf/v_p.

1. Select a cable type that matches your installation geometry.
2. Choose a dielectric preset or enter a custom ε_r value.
3. Enter diameters and spacing using your selected units.
4. Provide run length to estimate delay and wavelength.
5. Optionally enter frequency and load to compute Z_in and VSWR.
6. Export your saved history to CSV or create a PDF report.

Impedance planning for mixed‑use construction cabling

Consistent characteristic impedance reduces reflections and signal loss across long runs in buildings. This calculator estimates Z₀ from geometry and dielectric constant, helping you align field selections with typical 50 Ω, 75 Ω, 100 Ω, and 300 Ω systems. Use it early to compare options before ordering reels, connectors, and termination hardware.

For quick checks, compare computed Z0 to your system target and keep connector families consistent. Mixing 50 Ω and 75 Ω components often causes ghosting, dropouts, and poor return loss. If TDR traces are available, confirm sections affected by splices, tight bends, or moisture during punchlist walks.

Geometry tolerance and installation reality

Small dimensional changes can shift Z₀ noticeably. Coax depends on ln(b/a), so oval jackets, braid compression, or rework at bends can alter the effective ratio. For twin‑lead and balanced pairs, spacing and conductor diameter drive acosh(D/2r). Maintain gentle routing, avoid crushing, and protect spacing near clamps and trays.

Dielectric selection and velocity factor

The dielectric constant ε_r affects both impedance and propagation speed. Lower ε_r increases Z₀ and raises velocity factor, reducing delay per meter. Foam insulations often provide higher velocity than solid polymers, while higher‑ε_r materials increase capacitance. Capture the specified insulation type from cut sheets to match commissioning assumptions.

Frequency, wavelength, and reflection risk

When run length becomes a meaningful fraction of wavelength, mismatches create standing waves. The optional load model reports Z_in and VSWR using the lossless transmission‑line relationship, which is useful for predicting tuning sensitivity at RF and high‑speed signaling frequencies. For low‑frequency control wiring, Z₀ matters less than resistance and shielding.

Documentation outputs for QA and handover

Use the CSV export to log assumptions and compare alternatives across floors or risers. The PDF report packages the latest calculation plus session history for submittals, audits, sitewide records, and troubleshooting notes. Pair these exports with labeling details, connector part numbers, and test measurements (TDR or network certification) to close the loop from design to verification.

1) What does characteristic impedance mean on a jobsite?

It is the cable’s natural impedance for fast signals. Matching it with connectors and terminations minimizes reflections, improves signal integrity, and reduces intermittent issues during commissioning and turnover.

2) Why does εr change the result so much?

εr changes capacitance and wave velocity. A higher εr lowers Z0 and slows propagation, increasing delay. Using the correct insulation type from the cable datasheet keeps estimates aligned with installed performance.

3) Should I enter shield thickness for coax?

No. This model uses the inner conductor diameter and the inner diameter of the outer conductor. Shield thickness mainly affects loss and mechanical strength, not the primary Z0 geometry ratio.

4) When is the input‑impedance (Zin) section useful?

Use it when frequency and length are significant, such as RF feeders, video distribution, or high‑speed data. It helps predict mismatch behavior with a specified load and highlights likely VSWR issues.

5) Does the calculator include attenuation or skin effect?

No. Results assume a lossless line for Zin and ideal geometry for Z0. Real cables have frequency‑dependent losses and tolerances. Validate with manufacturer specs and field testing when accuracy is critical.

6) How can I use outputs for submittals?

Export CSV to document assumptions and comparisons, then generate a PDF for the record set. Attach cable datasheets, routing notes, and test results to provide traceable evidence for quality control.