Theory, Design and Tests on a Prototype Module of a Compact ...

78 5. RADIOFREQUENCY MEASUREMENT
method gives a reliable k value with a small error. In figure 5.7 a
typical case is reported.
Figure 5.7. The result of parabola method applied to
two coupled cavities. The coupling coefficient <strong>and</strong> the
minimum frequency, which is the one of the π/2 mode,
are reported.
The method gives an high degree of reliability since it is based on
a set of measurement. This means that it is possible, using st<strong>and</strong>ard
techniques, to evaluate the correctness of the results <strong>and</strong> the reliability
of the procedure. The method can not be applied to cavities whose
frequencies are very different since too large perturbations could be
necessary to reach the minimum; in this case the behaviour of fields in
the perturbed cavity could be too much modified.
3.2. Measurements on three coupled cells. In the case of
three coupled cells with f0, f1 <strong>and</strong> f2 resonant frequencies respectively,
the theory of the coupled resonators gives for the resonant frequencies
of the coupled structure the following solutions (valid in the particular
case of f0 = f2, for the bridge coupler case, these are the coupling
cavities frequencies):
f0 ˜f =
1 + k2/2
f 2 ± = [f 2 0 + f 2
1 (1 − k2/2)] ± [f 2 0 − f 2 1 (1 − k2/2)] 2 + 2f 2 0 f 2 1 k2 1
1 − k2/2 − k2 1/2
(5.7)
(5.8)
where f± <strong>and</strong> ˜ f are the measured frequencies, k1 <strong>and</strong> k2 are the coupling
of first <strong>and</strong> second order <strong>and</strong> f1 is the resonant frequency of the bridge
coupler central cavity.