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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.

schematic

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.

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  • \$\begingroup\$ 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? \$\endgroup\$ – Marcus Müller Jun 5 '19 at 21:56
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    \$\begingroup\$ 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? \$\endgroup\$ – Marcus Müller Jun 5 '19 at 21:57
  • \$\begingroup\$ no specs for attenuation vs f or Zin vs f? or DC source Z(f) or why no active parts? so no solution \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Jun 5 '19 at 21:58
  • \$\begingroup\$ These specs are not realizable, as written without tolerances \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Jun 5 '19 at 22:06
  • \$\begingroup\$ Do you know about SRF in 1mH inductors? Maybe you can define the real requirements instead. \$\endgroup\$ – Tony Stewart Sunnyskyguy EE75 Jun 5 '19 at 22:12
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The only way to get a higher rolloff is to insert additional poles.

Shown below:

  • Vout (green) your filter
  • Vout1 (blue) additional pole with 40dB rolloff
  • Vout2 (red) your filter with parasitics (ESR and ESL on cap and ESR and capacitance on inductor)

enter image description here

You'll probably need to get X2Y caps an parallel them with normal caps to get the rolloff to continue at high frequencies.

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