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

5. COUPLING BETWEEN WAVEGUIDE AND BRIDGE COUPLER 41
L
C1
Figure 3.16. The final equivalent circuit for a cavity
seen from the waveguide through the iris.
Here is a first disadvantage: if the resonant frequency of the simulated
structure is different from the working frequency, the procedure
with MAFIA should be repeated until the correct frequency <strong>and</strong> matching
are reached. Once one has the correct frequency <strong>and</strong>, of course, the
right dimension for the iris, one can calculate the right dimension d2
for the short-circuited waveguide that makes the reactance null.
The latter point can be satisfied if one defines Zi = Ri + jXi as the
impedance of the circuit in figure 3.16, then
Yi =
Ri
R 2 i + X2 i
next, one finds the frequency satisfying
R 2 i + X 2 i
Ri
C
R
− j Xi
R2 i + X2 ;
i
= Z0
<strong>and</strong> last, gets the value for d2
d2 = 1
β arctan
− R2 i + X2
i
XiZ0
(3.3)
It is worth noting that from this procedure a perfect matching frequency
is always given, but it could happen that the correspondent
frequency is not the designed π/2 mode frequency. Note that the value
of d2 given from the formula (3.3) is always negative, but it is sufficient
to sum to it one half of waveguide wavelength.
5.1. The procedure for the whole module. With a 3D numerical
code as MAFIA it is impossible to simulate the whole module
with more than one hundred cavities. It is necessary to introduce some
equivalences in order to use the simulation with a single cavity. We substitute
the equivalent lumped circuit for one cavity with a circuit which
represents the whole module considering only the cavities charged with
electromagnetic energy (N = 52 accelerating cells plus N = 3 bridge