# Topology for ideal cutband response (-20dB per decade per order) for passive, low pass, constant output impedance filter

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.

simulate this circuit – Schematic created using CircuitLab

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.

• from where to 1 GHz do you need constant impedance? In perfection, I'm almost certain constant impedance passive networks cannot exist (aside from all-pass filters, maybe), but maybe something close enough for your application? Jun 5, 2019 at 21:56
• It's also not clear how that would help you – you want to cut off anything above 1 kHz, so: if there's no frequencies leaving your circuit >> 1 kHz, why (and how) would you even want to define an impedance? Jun 5, 2019 at 21:57
• no specs for attenuation vs f or Zin vs f? or DC source Z(f) or why no active parts? so no solution Jun 5, 2019 at 21:58
• These specs are not realizable, as written without tolerances Jun 5, 2019 at 22:06
• Do you know about SRF in 1mH inductors? Maybe you can define the real requirements instead. Jun 5, 2019 at 22:12