Quadruplet Coupled Resonator Band Pass Filters

Full cross coupled filters have the disadvantage in that it may not always be realizable for all desired technologies. It is sometimes convenient to remove some resonator couplings so that only series quadruplet couplings remain. selecting, "Half Band Ripple" stop band in the main control panel. removes transmission zeros from the stop band, partly to enable the construction of he filter with series quadruplet couplings. Selecting "Single Point Ripple" in the stop band results in the symmetric construction of the filter. Deselecting, "Single Point Ripple" in the stop band results in a flat stop band, but requires an asymmetrical construction of the filter.

FilterQuick

In the FilterQuick interface, options exist for "Cross Coupled" and "Quadruplet Coupled" selections, with the option of a "Single Point Ripple" feature. Half Band Ripple is already selected for you when using the FilterQuick interface.

Coupling Matrix Differences

An 8 pole Elliptic is shown below in both standard form and in quadruple coupled form in the Tables 1 and 2 ad Figures 1 and 2 below:

Cross Coupled:

0	0.08216	0	0	0	0	0	-0.0009074
0.08216	0	0.05891	0	0	0	0.007371	0
0	0.05891	0	0.04518	0	-0.03506	0	0
0	0	0.04518	0	0.08148	0	0	0
0	0	0	0.08148	0	0.04518	0	0
0	0	-0.03506	0	0.04518	0	0.05891	0
0	0.007371	0	0.04986	0	0.05891	0	0.08216
-0.0009074	0	0	0	0	0	0.08216	0

Table 1: 8 Pole Elliptic Coupling Matrix in Standard Cross Coupled Form

Figure 1: 8 Pole Elliptic Coupling Matrix Implementation in Standard Cross Coupled Form

Quadruplet Coupled with Single Point Ripple Stop Band:

0	0.08023	0	-0.01828	0	0	0	0
0.08023	0	0.07112	0	0	0	0	0
0	0.07112	0	0.05004	0	0	0	0
-0.01828	0	0.05004	0	0.05364	0	0	0
0	0	0	0.05364	0	0.05004	0	-0.01828
0	0	0	0	0.05004	0	0.07112	0
0	0	0	0.04986	0	0.07112	0	0.08023
0	0	0	0	-0.01828	0	0.08023	0

Table 2: 8 Pole Elliptic Coupling Matrix in Series Quadruplet Coupled Form

Figure 2: 8 Pole Elliptic Coupling Matrix Implementation in Series Quadruplet Coupled Form