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

7. MEASUREMENT OF THE WAVEGUIDE-MODULE COUPLING 95
Figure 5.26. Coupling through an iris. The cavity is
referred to the primary.
For cavities with high quality factor ω ≈ ω0 <strong>and</strong> then, equation (5.22)
can be written as
Zaa ′
= j
Z0
X1 β1
ω − ω0
+ , δ = , (5.23)
Z0 1 + j2Q0δ ω0
<strong>and</strong> the quantity δ is called the frequency tuning parameter. The second
term of equation (5.23) corresponds to a circle on the complex
impedance plane, where the first term expresses the effect of the selfreactance
of the coupling system.
We can choose the reference planes along the transmission line at
which the first term disappears <strong>and</strong> this series of positions are called
the detuned short positions. Let the terminals b − b ′ be selected at a
distance l away from the terminals a − a ′ . The impedance Zaa ′ can be
transformed in
Zbb ′
Z0
= Zaa ′ + jZ0 tan αl
Z0 + jZaa ′ tan αl,
(5.24)
where α is the propagation number. The location of terminals b − b ′
can be chosen so that the impedance at terminals b − b ′ becomes zero
when the cavity is detuned. This means that the impedance locus is
symmetric respect to the real axis on the complex impedance plane,
since the far points out of resonance are near the point where R = ∞.
7.4. RF procedure. In this section we derive a RF measurement
recipe that implies only the use of a Network Analyzer. The used
functions are so general that each specific model should have them.
• First, we assumed that the source of our cavity had an internal
impedance Z0 equal to the characteristic one of the transmission
line used to feed the cavity in the previous relations. This
implies that the network analyzer cables <strong>and</strong> the other tools
used to feed the cavity right on to the coupling mechanism
should be perfectly matched too.
• Then, we consider the measurement of reflection coefficient S11
<strong>and</strong> we use the Smith chart visualization of it. If the frequency