It is sometimes useful to have passive LC ladder filters that absorb, rather than reflect, energy in the stop band. The usual way to obtain this is by the use of diplexers, i.e., by connecting two complementary filters in parallel at their inputs. One filter accepts the band of frequencies that the other rejects. Except for Butterworth filters, there is no solution for the perfect complementary filter.
If there is no need
to present all out-of-band signal power on a separate output, there is a
much simpler way to obtain good input matching. The parallel combination
of a series RC circuit and a series RLC resonator can efficiently absorb
virtually all stop band energy. Even though this method yields only
an approximation of constant resistance, it is good enough for most
practical applications. For most filters treated below, the theoretical
reflection coefficient is below -50dB over all frequencies.[2]
The starting point for the design of a filter with constant input resistance is the normalized lowpass prototype for zero source impedance. This is the filter that produces the correct response with a constant input level, which is evidently the case for any constant source connected to a load that is constant as a function of frequency.
Any such filter starts with a large series inductance. Therefore, its input impedance will tend to rise with frequency above cutoff. A series RC circuit across the filter input can restore the input impedance to unity for very high frequencies, and a series RLC resonator can be positioned over the transition region to minimize the impedance ripple.
The next links reproduce the classical filter tables taken from Zverev [1], complemented with the element values for the input matching network as described. Included are plots of the reflection coefficient S11 over frequency. There are tables for Bessel, Gaussian and Linear phase with equiripple error filters of orders 3 to 10.
To reduce this to practice, I built a 6th order 50 Ohm low-pass Bessel with a 40MHz cut-off frequency. The coils were wound by hand, and the capacitors are 5% ceramic chips. The filter has a reflection coefficient better than -35dB at least up to 500MHz. (See details.) This result is compatible (slightly better than expected, in fact) with the use of 5% tolerance components.