Resonant Cavity

Resonant cavities have the advantage of being high-0 structures. The cavities are usually an easily-analyzed geometry, such as a rectangle or a cylinder, where the resonant modes can be determined as functions of the dimensions and €_r. The general idea is to extract the permittivity, knowing the resonant frequency and the dimensions. The dimensions are measured to within an acceptable level of error (error analysis will be discussed in a later section), while the frequency sweep is usually measured with a vector network analyzer. Subsequently, from the bandwidth of the measured peak, the material's loss tangent or Q may also be extracted. From these techniques we arc able to measure extremely high Q (of the order of 10 000), albeit only at a single frequency (or a few frequencies if we use multiple modes). Open cavity techniques are very widely used, since samples can be conveniently fabricated, and are generally small in size with respect to the wavelength. This is of particular benefit at low frequencies, for example at I GHz where the wavelength in free space is 30 cm. The classical geometry for this technique is the dielectric cylinder, as demonstrated by Hakki and Coleman, and by Courtney.

For materials with low value of ∈" (<3), the relative permittivity ∈' can be measured by observing the change in resonant frequency of a resonant cavity when a sample is introduced, and the loss factor ∈" by the change in Qfactor (Horner et aL, 1946). Various cavity shapes and modes may be used, but the Eo10 circular cylindrical cavity is the most convenient in practice, and it is capable of analytic solution for e' and e". The test sample, in circular rod form and of small diameter compared with the cavity diameter, is inserted concentric with the cavity and occupies the full height. The cavity is operated as a transmission cavity, loosely coupled to avoid reducing the Q-factor by external loading. The NA is set to sweep a band of frequencies centered on the cavity resonant frequency, and the receiver is set to display the transmission coefficient on a decibel scale; the display is of a classic resonance curve, and a frequency marker is set at the peak of the curve. The sample is then introduced and the cavity resonant frequency decreases, a new frequency marker being set on the maximum point The change in resonant frequency Δ f gives the value of ∈' as

∈' =1 + 0.539/ (a ²/b ²) (Δ f / f 0)

where,

a = cavity diameter

 b = sample diameter

Δ f = frequency shift with sample inserted

f0 = resonant frequency of unloaded cavity

Questionnaire:

• Explain more about Resonant Cavity?