Coaxial Cable Impedance Calculator
Calculate characteristic impedance, velocity factor, propagation velocity, and other transmission line parameters of a coaxial cable.
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Inputs
Live
Math
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Related
Enter parameters and click Calculate to view results
Formula & Theory
Z₀ = (60 / √εr) × ln(D/d)This formula is used to calculate antenna parameters for coaxial cable impedance calculator.
Overview
The Coaxial Cable Impedance Calculator determines the characteristic impedance ($Z_0$), distributed capacitance (pF/m), velocity factor ($VF$), and signal delay for coaxial transmission lines. By entering the inner shield diameter ($D$), center conductor diameter ($d$), and insulator dielectric constant ($epsilon_r$), RF engineers and cable designers can quickly evaluate custom coaxial geometries.
Input Guide
Enter Inner Shield Diameter, Centre Conductor Diameter, Dielectric Constant (εr) exactly in the units shown by this coaxial cable impedance. Check the operating band, unit prefix, and decimal position before calculating; these are the inputs used by the formula.
- Inner Shield Diameter — use mm.
- Centre Conductor Diameter — use mm.
- Dielectric Constant (εr).
Output Guide
The results describe the calculated coaxial cable impedance values for the inputs you entered. Check each value against the available space, selected components, feed system, and operating conditions before making a final design decision.
How This Calculator Works
The Coaxial Cable Impedance uses Z₀ = (60 / √εr) × ln(D/d). Supply Inner Shield Diameter (mm), Centre Conductor Diameter (mm), Dielectric Constant (εr) in the displayed units, then use the calculated values as the first engineering target for this waveguide & feedline design or analysis.
Design Notes
Coaxial cable characteristic impedance is determined solely by physical dimensions and insulator dielectric permittivity: $Z_0 = \frac{60}{\sqrt{\epsilon_r}} \ln\left(\frac{D}{d}\right)\;\Omega$. Standard $50\;\Omega$ coax represents an optimal trade-off between maximum power handling capability (which peaks near $30\;\Omega$) and minimum voltage breakdown/attenuation (which peaks near $77\;\Omega$). Television and broadband CATV distribution networks utilize $75\;\Omega$ coax because it minimizes signal attenuation per unit length.
Build and Tuning Notes
When manufacturing or selecting custom coaxial cables, ensure concentric alignment of the center conductor within the shield dielectric—eccentricity introduces unwanted higher-order modes and lowers voltage breakdown ratings. Validate characteristic impedance and return loss ($S_{11}$) across operating frequencies using a Vector Network Analyzer (VNA) or Time-Domain Reflectometer (TDR).
Frequently Asked Questions
Why is 50 Ω the standard impedance for RF and amateur radio?
For an air-dielectric coaxial line, minimum attenuation occurs at $77\;\Omega$, while maximum RF power handling occurs at $30\;\Omega$. $50\;\Omega$ was chosen as an ideal commercial compromise between high power handling and low signal attenuation.
Why is 75 Ω used for TV and video signals?
Because video receiver systems prioritize low signal attenuation over high RF power handling, $75\;\Omega$ is chosen for CATV, satellite downlinks, and video distribution to minimize signal loss over long cable runs.
How does dielectric permittivity (εr) affect characteristic impedance?
Increasing dielectric constant ($epsilon_r$) reduces characteristic impedance ($Z_0 \propto 1/\sqrt{\epsilon_r}$) while simultaneously decreasing propagation velocity ($VF = 1/\sqrt{\epsilon_r}$) and increasing distributed capacitance per meter.
How is coaxial capacitance per meter calculated?
Capacitance per unit length is calculated using $C = \frac{2\pi \epsilon_0 \epsilon_r}{\ln(D/d)} \approx \frac{55.63 \cdot \epsilon_r}{\ln(D/d)}\text{ pF/m}$. Lower $D/d$ ratios increase capacitance.
Alex Warren
B.Sc. in Electrical & Electronic Engineering (EEE)
Alex specialises in antenna design and wave propagation. His expertise helps ensure these calculators present practical RF concepts, useful design estimates, and clear engineering guidance for students, HAM operators, and wireless professionals.