Cables or other metal (antenna-like) structures often couple to sources of common-mode currents and end up radiating, causing product failures during compliance testing. During the troubleshooting process, it would be helpful to determine the resonance of these cables or structures to confirm they are the source of certain harmonic signals.
We could certainly measure the length of the cables or metal structures, but often, they are connected to other conductive assemblies, such as circuit boards or brackets. Because of these system inter-relationships, it’s not always easy to predict the resonances within a system, and so there’s always a little uncertainty as to where to start the troubleshooting process. These simple techniques may help quickly identify potential resonances within your system or product.
There are times when an increase in harmonic content can’t completely be explained by circuit or PC board design. If you’ve already done a good EMC design and are still getting radiated emission problems, then perhaps resonances in the product enclosure are, in effect, amplifying the internal harmonics. This internal amplification can cause a myriad of mysterious couplings internally to your product with resulting radiated emissions.
Any metal structure can become resonant if driven by a noise source. For example, I’ve seen the tines on a microprocessor heat sink resonate in the 2+ GHz region. More commonly, you’ll discover resonant modes created by the product enclosure. For example, for a rectangular enclosure, we have:
Where: epsilon = material permittivity, mu = material permeability and m, n, p are integers. Cavity resonance can only exist if the largest cavity dimension is greater, or equal, to one-half wavelength. Below this cutoff frequency, cavity resonance cannot exist. In this configuration (where a < b < c), the TE011 mode is dominant, because it occurs at the lowest frequency at which cavity resonance can exist.
The resonant frequency of the circular cavity is 1.225 GHz, very close to the calculated 1.274 GHz.
To read more about constructing a simple demonstration of resonance, click here…