Passive low-pass ladder filters with constant input resistance

The design concerns a 50 Ohm, 6th order Bessel lowpass filter with a 40MHz cut-off frequency. The values for the inductances, taken from the appropriate table, are denormalized by multiplying with:

(1)

Similarly, the capacitor values are obtained by multiplying with:

(2)

The resistor values are simply multiplied by 50. This yields the detailed schematic diagram shown below:

The following plot shows the practically achieved S11 (upper curve), as well as the theoretically optimum values. These results are compatible with the expected performance for 5% tolerance components, as a Monte Carlo simulation using a circuit simulator will readily show.

The practical realization (jpg, 43kB) of the filter uses hand wound coils, positioned to minimize mutual coupling, but without shielding between the filter sections.