For estimating and education only. Results come from the simplified models described below, are provided as is with no warranty, and are not a substitute for engineering analysis, simulation or measurement. Check them before relying on them in a design, purchase or safety decision. See the terms of use.
Equations
Z_0 = \frac{60}{\sqrt{\varepsilon_r}}\,\ln\frac{D}{d}Ω
D = d\,\exp\!\left(\frac{Z_0\sqrt{\varepsilon_r}}{60}\right)
C^{\prime} = \frac{2\pi\varepsilon_0\varepsilon_r}{\ln(D/d)}F/m
L^{\prime} = \frac{\mu_0}{2\pi}\,\ln\frac{D}{d}H/m
\mathrm{VF} = \frac{1}{\sqrt{\varepsilon_r}}, \qquad t_d = \frac{\sqrt{\varepsilon_r}}{c}delay, s/m
f_c(\mathrm{TE}_{11}) \approx \frac{2c}{\pi\,(D + d)\sqrt{\varepsilon_r}}first higher-order mode
Variables
| Symbol | Meaning | Unit |
|---|
d | Center conductor diameter | m |
D | Inner diameter of the outer conductor (dielectric diameter) | m |
\varepsilon_r | Relative permittivity of the dielectric | — |
Z_0 | Characteristic impedance | Ω |
\mathrm{VF} | Velocity factor, v / c | — |
c | Speed of light, 299 792 458 | m/s |
\varepsilon_0,\ \mu_0 | 8.854 187 8128 × 10⁻¹², 4π × 10⁻⁷ | F/m, H/m |
Common dielectrics
| Material | εr | Velocity factor |
|---|
| Air | 1.0006 | 0.9997 |
| Foam polyethylene | 1.3 – 1.6 (varies by foaming) | 0.79 – 0.88 |
| PTFE (Teflon) | 2.1 | 0.69 |
| Solid polyethylene | 2.25 | 0.67 |
Worked example
| Input | Value |
|---|
| Center conductor d | 0.91 mm |
| Dielectric diameter D | 2.95 mm |
| Dielectric | PTFE, εr = 2.1 |
| Result | Value |
|---|
| Characteristic impedance | 48.7 Ω |
| D / d | 3.242 |
| Velocity factor | 0.6901 |
| Capacitance | 99.33 pF/m |
| Inductance | 235.2 nH/m |
| Signal delay | 4.834 ns/m |
| First higher-mode cutoff (TE11) | 34.12 GHz |
These are close to the dimensions of 0.141 in semi-rigid PTFE cable, which is 50 Ω.
Load this example in the calculator
Validity
- TEM propagation only: operate below the TE11 cutoff shown in the results.
- Ideal conductors and a lossless, uniform dielectric. Loss and braid effects are not included.
- εr is taken as constant with frequency.
Sources
- D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2012. Chapter 2 (transmission lines) and §3.5 (coax higher-order modes).
- Dielectric values: typical published figures, e.g. Pozar, Appendix; polyethylene 2.25, PTFE 2.08–2.1.