I am trying to develop a low-pass constant output impedance filter. The output impedance must be within ±10% of 5Ω from DC up to 1GHz. The filter is driving an open load (>10M) and must filter current noise above 1kHz.
To build such a circuit, I would normally use a transimpedance amplifier with a low pass feedback. Unfortunately, the filter must only be composed of passive (RLC) elements.
Typical low pass filters have the problem that their output impedance changes after the cut-off frequency.
My current solution requires that I must add a resistor (R2) to a LC filter (L1-C1) to prevent the capacitor from shunting my output impedance. By doing so, the frequency roll-off corresponds to a filter with half the order. i.e. in this case, -20db per decade instead of -40db per decade.
Is there a way to achieve -40dB per decade without cascading other elements? There seems to be a lack of literature on constant output impedance passive filters.
EDIT: Parasitics were omitted to keep the question about the topology of the filter. In practice, I have the ESL of C1 and the parallel capacitance of L1. These parasitics are compensated by a second LC+R stage with smaller values, which have smaller parasitics.