It is sometimes desirable to include couplings between non-adjacent resonators to obtain more optimum filter transfer functions. An example of a fourth order dielectric resonator design incorporating a single capacitive cross coupling is shown in Fig. 1.

The single cross-coupling in this even order circuit (4th order) provides
a pair of transmission zeros which emphasize the attenuation close to the
passband. Inclusion of both capacitive and inductive couplings
are possible, with respective effects on stopband attenuation or on passband
group delay and amplitude flatness. The technique can also be applied
to dual mode filters, bandstop filters or most kinds of TEM, quasi-TEM
or evanescent mode filters.