One of the more interesting techniques of recent years is the coupled-triplet schematic. There is also a coupled quadruplet schematic, which will be treated in another example. To describe it briefly, a ladder circuit is developed, consisting of a string of one-end grounded parallel-resonant circuits, top-coupled as is conventional, with L's and C's, but coupled additionally across the top, skipping one node [1].

The result is to introduce an f-infinity (trap) at a real frequency, above or below the passband. Looked at in reverse, a conventional schematic, perhaps a zig-zag circuit, is synthesized to meet certain specifications, and it is then converted by S/FILSYN to include coupled triplets as described.

Suppose the specification is for a parametric bandpass, from 890 MHz to 910 MHz, with peaks at 865, 870, and 930 MHz. In S/FILSYN this is designed easily, and with manipulation to make all inductors equal and practical, the following design evolves. It could conceivably be built in this form, but a comparison with the new coupled-triplet equivalent is in order.

1 |---R---| 50.000000 ohm 3 |---C---| 1.857904 pF 4 | C 530.796022 fF 5 |---C---| 2.645568 pF 6 | L 13.283803 nH 7 |---C---| 8.464018 pF 8 | C 1.086293 pF 9 |---C---| 14.764986 pF 10 | L 13.283803 nH 11 |---C---| 2.697535 pF 12 | C 71.221411 fF 13 |---C---| 4.646262 pF 14 | L 13.283803 nH 15 |---C---| 4.380044 pF 16 | C 340.722476 fF 17 |--L-C--| 97.560137 nH res. frequency | | 343.027831 fF 870.000000 MHz 19 |---C---| 4.246027 pF 20 | C 843.896231 fF 21 |---C---| 2.643782 pF |-L-, | 13.283803 nH 23 | |-C-| 899.548406 fF res. frequency |-C-' | 1.648957 pF 1.075361 GHz | ,-', 24 | L C 13.283803 nH res.frequency | `-,' 2.204712 pF 930.000000 MHz 25 |---C---| 135.823784 fF 26 | C 6.842486 fF 27 |---C---| 59.619540 fF 28 | L 470.633925 nH 29 |---R---| 50.000000 ohm

This same circuit is first synthesized by S/FILSYN, automatically, in a different form, suitable for conversion to coupled triplets. Again, it could conceivably be built in this form, as shown below, but S/FILSYN will convert it to coupled triplets (automatically of course).

1 |---R---| 50.000000 ohm 3 |---C---| 188.253570 pF 5 |---L---| 169.197495 pH 6 | L 9.013291 nH 7 |---L---| 169.197495 pH 9 |---C---| 186.281721 pF | ,-', 10 | L C 876.274195 pH res.frequency | `-,' 38.633853 pF 865.000000 MHz 11 |---C---| 185.440909 pF 13 |---L---| 169.197495 pH 14 | L 11.487583 nH 15 |---L---| 169.197495 pH 17 |---C---| 189.615248 pF | ,-', 18 | L C 614.839560 pH res.frequency | `-,' 47.633508 pF 930.000000 MHz 19 |---C---| 184.641369 pF 23 |---L---| 169.197495 pH | ,-', 24 | L C 648.903372 pH res.frequency | `-,' 51.572921 pF 870.000000 MHz 25 |---C---| 186.159576 pF 27 |---L---| 169.197495 pH 28 | L 8.816057 nH 29 |---L---| 169.197495 pH 31 |---C---| 188.331174 pF 33 |---R---| 49.979397 ohm

The coupled-triplet is now shown. It should be pointed out that, in all of the processes referred to, only exact equivalences and exact transformations have been invoked, no approximations. All of the parallel-resonant circuits to ground have been made to have identical inductors, as an added convenience.

1 |---R---| 50.000000 ohm 3 |---C---| 188.253567 pF 5 |---L---| 169.399964 pH | |-, | L | 9.843839 nH 8 |---L---| | 169.399964 pH transm. zero | | L 60.883402 nH 865.001000 MHz |---C---| | 186.183601 pF | C | 2.380079 pF | |-' 9 |---C---| 185.354484 pF 15 |---L---| 169.399963 pH | |-, | L | 13.882334 nH 18 |---L---| | 169.399963 pH transm. zero | | L 72.893510 nH 930.001000 MHz |---C---| | 188.190210 pF | L | 13.874547 nH | |-' 19 |---C---| 185.453017 pF 29 |---L---| 169.399963 pH | |-, | C | 2.365622 pF 30 |---L---| | 169.399964 pH transm. zero | | L 51.221413 nH 870.001000 MHz |---C---| | 186.326065 pF | L | 9.895548 nH | |-' 31 |---L---| 169.399964 pH 37 |---C---| 188.333837 pF 39 |---R---| 49.978689 ohm

This is, of course, essentially a lumped-parameter design, based on discrete L-C circuit elements. At microwave frequencies, it is feasible to design and build the filter with microwave elements, and S/FILSYN comes with all the tools for performing this same design using microwave elements. See this equivalent, for example:

1 |---R---| 50.000000 ohm 3 |---C---| 1.148430 ohm 5 |---L---| 1.618746 ohm | |-, | L | 65.198495 ohm 7 |---L---| | 1.618746 ohm transm. zero | | L 403.848150 ohm 865.000000 MHz |---C---| | 1.166596 ohm | C | 63.413783 ohm | |-' 9 |---C---| 1.174192 ohm 11 |---L---| 1.618746 ohm | |-, | L | 91.869368 ohm 13 |---L---| | 1.618746 ohm transm. zero | | L 496.052381 ohm 930.000000 MHz |---C---| | 1.148752 ohm | L | 91.808849 ohm | |-' 15 |---C---| 1.173302 ohm 17 |---L---| 1.618746 ohm | |-, | C | 63.774688 ohm 19 |---L---| | 1.618746 ohm transm. zero | | L 339.585421 ohm 870.000000 MHz |---C---| | 1.165319 ohm | L | 65.535801 ohm | |-' 21 |---L---| 1.618746 ohm 23 |---C---| 1.147726 ohm 25 |---R---| 49.969365 ohm

Without going into details of what one enters and what intermediate steps look like, we first show a bandpass from 1.0 GHz to 1.5 GHz, with 2 finite zeros in the lower stopband, three at zero and one at infinite frequencies. That this design will perform as mentioned, can be verified using any conventional analysis program.

1 |---R---| 50.000000 ohm 3 |---L---| 3.05198550 nH 5 |---C---| 4.69664240 pF | ,-', 6 | L C 8.22789600 nH res.frequency | '-,' 4.94819660 pF .7887734 GHz 7 |---C---| 2.38308660 pF 9 |---L---| 3.05198550 nH 10 | C 1.80125040 pF 11 |---C---| 2.37212160 pF 13 |---L---| 3.05198550 nH | ,-', 14 | L C 15.81022 nH res.frequency | '-,' 3.48038960 pF .6784804 GHz 15 |---C---| 4.42762200 pF 17 |---L---| 3.05198550 nH 19 |---R---| 54.680850 ohm

Its equivalent, in Coupled Quadruplet form, transformed so that all shunt inductors are equal, is produced by S/FILSYN as follows:

1 |---R---| 50.000000 ohm 3 |---L---| 2.40206212 nH 5 |---C---| 4.66552 pF | ,-|---, | C | | 2.384818 pF | | | | |--L--|-|-, | 2.40206212 nH | | | | | |--C--| | | | 3.996204 pF | | C | | 502.7488 fF transm. zeros 7 | C | | | 1.7895224 pF .7887734 GHz | | | | C 82.466 fF .6784804 GHz |--L--|-' | | 2.40206212 nH | | | | |--C--| | | 3.439166 pF | | C | 293.4188 fF | C | | 2.4195496 pF | '-,-'-' 9 |---L---| 2.40206212 nH 11 |---C---| 4.8403184 pF 13 |---R---| 50.000000 ohm

[1] IEEE Trans. Circ. & Systems-I, Vol. 47, No.9, Sept. 2000, pp.1431-1437