X-couplings or non adjacent couplings are couplings between resonators, which are not placed just next to each other in the signal main-path. The reason to include x-couplings in a filter is most often that they create notches or transmission zeroes in the filter characteristic. With x-couplings it is therefore possible to improve stop-band performance without increasing the order of the filter.
To explain why x-couplings do generate notches the most common approach is to use lumped element representations of resonators and couplings. Though correct - this approach does not explain what really happens in the filter. To get a hunch about this one has to look at the electromagnetic fields in the filter so lets do that.
We will take a look at the folded waveguide filter shown in figure 1.
The filter is of 5th order, with a x-coupling between resonator 2 and 4. The arrows show entry and exit ports of the filter. The resonators are coupled by irises going from top to bottom in the filter. Full-height irises are known to be inductive (positive) by nature and hence all couplings in figure 1 are inductive. The corresponding coupling diagram is shown in figure 2.
the filter topology in figure 2 generates a notch above the pass-band, but
for the waveguide filter in figure 1 the notch will appear below
order to explain exactly how this works we have to look at the magnetic
field patterns in the cavities.
only resonators 2, 3 and 4 are involved we will limit ourselves only to
look at these three cavities.
Above fc (figure 3)
At frequencies above the
filter center frequency the field patterns are as shown in Figure 3. The
x-coupled fields are here in phase with the original fields in cavities 2
and 4, which means that in the upper stop band signal energy takes a
shortcut from input to output via the x-coupling aperture. A x-coupling as
above therefore has the effect of decreasing the stop band attenuation above
the pass band. This is also seen in practice.
Below fc (figure 4)
At frequencies below the
filter center frequency, the field patterns are as shown in Figure 4. The
blue horizontal H-field line is the x-coupled field originating from cavity
If the x-coupling
aperture is opened up the x-coupled field will be stronger and extinction of
a stronger existing field is then possible, i.e. the notch will move closer
to the pass band.
This means that at
frequencies below the notch frequency the signal on the output of the filter
is predominantly x-coupled field. Since the x-coupled signal below the
pass-band is in opposite phase of the main-line signal, one should expect
that the phase of the signal changes 180 deg at the notch frequency. This is
also observed in practice.
The explained features are summarized in the figure below:
|Having realized what the x-coupling does from the above example, other configurations can be explained by similar observations.|