How do I calculate the cutoff frequency for higher order modes in a coaxial cable?
Coaxial Mode Cutoff Calculation
The fundamental TEM mode in a coaxial line has no cutoff frequency and propagates at all frequencies from DC upward. The first higher-order mode (TE11) requires the average circumference of the coaxial cross-section to be approximately one wavelength in the dielectric medium for propagation. Below this cutoff frequency, the TE11 mode is evanescent (decays exponentially with distance) and does not propagate.
| Parameter | Semi-Rigid | Conformable | Flexible |
|---|---|---|---|
| Loss (dB/m at 10 GHz) | 0.8-2.5 | 1.0-3.0 | 1.5-5.0 |
| Phase Stability | Excellent | Good | Fair |
| Bend Radius | Fixed after forming | Hand-formable | Continuous flex OK |
| Shielding (dB) | >120 | >90 | >60-90 |
| Cost (relative) | 2-5x | 1.5-3x | 1x |
Frequently Asked Questions
Is the formula exact?
The simple formula is approximate (within 5%) for b/a ratios between 2 and 5. The exact solution requires solving a transcendental equation involving Bessel functions. For practical engineering purposes, the simple formula is sufficient.
Can I extend the range with air dielectric?
Yes. Air-dielectric cables (εr=1) have cutoff frequencies √2.1 = 1.45× higher than PTFE-filled cables of the same diameter. This is why precision airline standards (used for VNA calibration) operate to higher frequencies than PTFE-filled cables.
What about the next mode after TE11?
The next modes are TM01 and TE21, which have cutoff frequencies approximately 1.3-1.7× the TE11 cutoff. There is a narrow usable band above the TE11 cutoff but below TM01 where only two modes propagate; this is sometimes exploited in mode-selective systems but is not practical for general use.