The other day I mentioned that it should be possible to design the perfect input matching circuit for passive L-C Butterworth ladder filters. In fact that's a limiting case and an easy one too. It's enough to add another ladder in parallel, replacing each component by the dual of the corresponding filter element.
The simple dual trick only works for Butterworth filters for zero source impedance, but it's possible to find a solution for all filters that have re(Zin)>=Z0 over all frequencies. Seems self evident. So all filters designed for zero source impedance and 'tamer' than Butterworth, such as Bessel, Gaussian and various flat delay variants, can be perfectly matched.
Just for fun, below is an LTspice file of a normalized O(3) Bessel with perfect matching. The stuff around E1 is a return loss bridge, the LTspice equivalent of a network analyzer. It works in the time domain too, showing just the reflected signal. (Not the superposition of incident and reflected, like a TDR!)
I got the component values for the matching network by working out the continued fraction expansion of the expression for the desired matching network admittance. (No, not by hand, I'm too sloppy for that...)
Of course, this is more complicated than what I did in and, in practice, no better.
Jeroen Belleman
====================================== Version 4 SHEET 1 880 680 WIRE 80 -112 -16 -112 WIRE 176 -112 80 -112 WIRE 304 -112 256 -112 WIRE 480 -112 384 -112 WIRE 560 -112 480 -112 WIRE 80 -96 80 -112 WIRE -16 -80 -16 -112 WIRE 560 -80 560 -112 WIRE 480 -64 480 -112 WIRE 80 16 80 -16 WIRE 480 32 480 0 WIRE 560 32 560 0 WIRE -176 112 -480 112 WIRE -128 112 -176 112 WIRE -16 112 -16 -16 WIRE -16 112 -48 112 WIRE 48 112 -16 112 WIRE 192 112 48 112 WIRE 352 112 272 112 WIRE 416 112 352 112 WIRE 544 112 496 112 WIRE 560 112 544 112 WIRE -176 144 -176 112 WIRE 352 144 352 112 WIRE 560 144 560 112 WIRE 96 160 32 160 WIRE 112 160 96 160 WIRE -480 176 -480 112 WIRE 32 176 32 160 WIRE -16 192 -16 112 WIRE 112 224 112 160 WIRE 352 224 352 208 WIRE -176 240 -176 224 WIRE -16 240 -176 240 WIRE 560 240 560 224 WIRE -176 256 -176 240 WIRE -480 272 -480 256 WIRE -176 352 -176 336 WIRE 32 352 32 256 WIRE 112 352 112 304 FLAG 352 224 0 FLAG 560 240 0 FLAG -176 352 0 FLAG 112 352 0 FLAG 32 352 0 FLAG -480 272 0 FLAG 96 160 S11 FLAG 560 32 0 FLAG 480 32 0 FLAG 80 16 0 FLAG 544 112 out FLAG 48 112 matched SYMBOL ind 176 128 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 5 56 VBottom 2 SYMATTR InstName L1 SYMATTR Value 1.4631 SYMATTR SpiceLine Rser=0 SYMBOL ind 400 128 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 5 56 VBottom 2 SYMATTR InstName L2 SYMATTR Value .2926 SYMATTR SpiceLine Rser=0 SYMBOL cap 336 144 R0 SYMATTR InstName C1 SYMATTR Value .8427 SYMBOL res 544 128 R0 SYMATTR InstName R1 SYMATTR Value 1 SYMBOL voltage -480 160 R0 WINDOW 123 24 124 Left 2 WINDOW 39 0 0 Left 2 SYMATTR InstName V1 SYMATTR Value PULSE(0 1 1 1m 1m 10) SYMATTR Value2 AC 2 SYMBOL res -192 128 R0 SYMATTR InstName R2 SYMATTR Value 1 SYMBOL res -192 240 R0 SYMATTR InstName R3 SYMATTR Value 1 SYMBOL res -32 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R4 SYMATTR Value 1 SYMBOL e 32 160 R0 SYMATTR InstName E1 SYMATTR Value 1 SYMBOL res 96 208 R0 SYMATTR InstName R5 SYMATTR Value 1 SYMBOL res 64 -112 R0 SYMATTR InstName R6 SYMATTR Value 1 SYMBOL cap -32 -80 R0 SYMATTR InstName C2 SYMATTR Value .913 SYMBOL ind 160 -96 R270 WINDOW 0 32 56 VTop 2 WINDOW 3 5 56 VBottom 2 SYMATTR InstName L3 SYMATTR Value 2.4283 SYMATTR SpiceLine Rser=0 SYMBOL res 400 -128 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R7 SYMATTR Value 1.7546 SYMBOL res 544 -96 R0 SYMATTR InstName R8 SYMATTR Value 1.087 SYMBOL cap 464 -64 R0 SYMATTR InstName C3 SYMATTR Value .5752 TEXT -320 -40 Left 2 !;ac dec 100 10m 10 TEXT -312 -80 Left 2 !.tran 20