Cable Impedance: Definition and Significance
Characteristic impedance is the resistance a transmission line presents to an electromagnetic wave propagating along it. Unlike DC resistance, which opposes steady current, impedance accounts for both resistive and reactive effects in AC circuits.
In practical terms, impedance mismatches cause signal reflections at junctions—connectors, terminations, or component interfaces. A reflection coefficient depends on the impedance ratio; even small mismatches degrade signal quality, introduce jitter, and reduce bandwidth. High-speed digital circuits, RF systems, and video distribution all demand precise impedance control.
Two cable families dominate:
- Coaxial cables: Central conductor surrounded by a shield, separated by dielectric. Used in RF, video, and some data applications.
- Twisted pairs: Two insulated wires twisted together, often in bundles. Standard for Ethernet, telephony, and differential signalling.
Impedance Formulas for Coaxial and Twisted-Pair Cables
The characteristic impedance of a transmission line depends on its inductance per unit length (L) and capacitance per unit length (C). For coaxial and twisted-pair geometries, closed-form expressions simplify calculation:
Coaxial cable:
Z₀ = (60 / √εᵣ) × ln(D / d)
Twisted pair:
Z₀ = (120 / √εᵣ) × ln(2S / D)
Propagation delay:
t = 84.72 × √εᵣ × 10⁻³ ns/m
Cutoff frequency (transverse EM mode):
f_c = 11.8 / (√εᵣ × 1000 × r_mean × π) GHz
Z₀— Characteristic impedance in ohmsεᵣ— Relative permittivity (dielectric constant) of the insulationD— Outer conductor inner diameter (coax) or wire-to-wire separation (twisted pair)d— Inner conductor diameter (coax) or individual wire diameter (twisted pair)S— Separation between wire centres in twisted pairt— Propagation delay in nanoseconds per metrer_mean— Mean radius of the transmission line cross-section
How to Use the Calculator
Select your cable type—coaxial or twisted pair—from the dropdown menu. The calculator automatically displays the required geometry parameters.
Enter the physical dimensions in millimetres or your preferred unit. For coaxial cables, provide the inner conductor diameter and the inner diameter of the outer shield. For twisted pairs, input the individual wire diameter and the centre-to-centre spacing between them.
The dielectric constant depends on the insulation material: typical polyethylene is around 2.25, polyimide approximately 3.5, and air-core cables approach 1.0. Leave this at the default value unless you have a datasheet specifying otherwise.
The calculator computes impedance, capacitance per metre, inductance per metre, propagation velocity, and the dominant-mode cutoff frequency. Use these results to verify component compatibility and signal propagation times in your circuit design.
Common Pitfalls and Design Considerations
Watch for these mistakes when working with transmission line impedance.
- Dielectric constant variability with frequency — The relative permittivity of an insulator is not truly constant—it varies with frequency, temperature, and manufacturing tolerances. Always check the cable manufacturer's specification sheet for the frequency range of interest. At high frequencies (GHz range), dissipation factors also become significant.
- Ignoring the entire transmission line — Impedance mismatch matters only if the cable length is comparable to or longer than the signal rise time (or wavelength at the signal frequency). Short stubs or patch cords on a logic board may tolerate poor impedance, but a 10-metre Ethernet run demands strict 100 Ω matching. Use the propagation delay to estimate round-trip transit time.
- Mixing measured and nominal dimensions — Manufacturing tolerance on cable diameter can be ±0.1–0.2 mm. Measure actual dimensions if precision matters—especially in high-speed systems. A 5% variance in diameter translates to roughly 10% change in impedance due to the logarithmic relationship.
- Overlooking launch and termination losses — Even a perfectly matched transmission line exhibits losses if connectors are corroded, solder joints are cold, or termination resistors have poor tolerances. High-frequency applications demand gold-plated contacts and 1% resistor tolerance.
Inductance and Capacitance Per Unit Length
The calculator also returns inductance (L) and capacitance (C) per unit length. These are useful for impedance verification and for computing characteristic impedance directly:
Z₀ = √(L / C)
For coaxial cables:
- L = 5.08 × ln(D / d) µH/m
- C = 1.41 × εᵣ / ln(D / d) pF/m
For twisted pairs:
- L = 10.16 × ln(2S / D) µH/m
- C = 0.7065 × εᵣ / ln(2S / D) pF/m
These parameters are essential for transient analysis, EMI filtering, and time-domain reflectometry (TDR) measurements. They also determine the cable's ability to support low-loss, high-bandwidth signalling.