# Demonstrating enclosure resonance

- July 11, 2012

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.

For my seminars, I use a simple demonstration of resonance, borrowing the idea from colleague, Lee Hill (www.silent-solutions.com). I found a seven-inch diameter round metal tin at the local Goodwill Store. Mount two BNC chassis-mount connectors in the lid about two inches apart. I soldered short wire “stubs” to the center connector, totaling about 1/2-inch long. These will provide a coupling path. Drive one connector with a swept RF signal and pick up the resulting resonance profile from the other. It doesn’t matter which connector is driven.

The demonstration tin used to show a resonance plot.

Here are the equations for a circular cavity, where a = radius (9 cm) and h = height (6 cm). As long as a > h/2, these equations are valid.

The easiest way to show the resonance is to connect a network analyzer as an s21 measurement. You can also use a spectrum analyzer with tracking generator. In this case, I’ll use a Rigol DSA815TG (15 kHz to 1.5 GHz) spectrum analyzer with built-in tracking generator. We see the calculated resonant frequency is 1,274 MHz. Let’s see how close the actual cavity resonates to this frequency.

The resonant frequency of the circular cavity is 1.225 GHz, very close to the calculated 1.274 GHz.

To measure the actual resonance of your enclosure, simply mount a couple chassis-mount coaxial connectors in an open area of the enclosure and drive them in a similar manner. If these resonances appear very close to the harmonics created by the electronics, then you may need to dampen these resonances.

A good troubleshooting technique is to place a ZipLok® bag filled with a few ferrite chokes inside the enclosure. Remeasure the resonances to demonstrate they’ve been dampened and check the product for any improvement in radiated emissions. You can also use a crumpled up ESD protective bag (semi-conductive) or wide bandwidth ferrite-loaded adhesive sheets, such as Emerson & Cuming MCS material or NEC/Tokin “Flex-Suppressor”, which would be more of a permanent solution.

With a large ferrite choke added in the tin, the resonance was dampened by 20 dB.

With the lid open, you can see the short stubs attached to each BNC connector. The large ferrite choke is also shown, which serves as a dampener.

This is an easy way to demonstrate cavity resonance to your designers or clients and is easy to make.