# Building a distributed low-pass filter with cutoff frequency of 1hz but the highest frequency of 10^13 hz

How does one build a distributed low-pass filter with cutoff frequency of 1hz and highest frequency of 10^13hz (or arbitrarily high)? In case of lumped circuits, this is easy to do, but in case of distributed elements circuits, I am not sure if one can build such a low-pass filter.

Any type of low-pass filter is fine, including Butterworth.

By "highest" frequency, I mean that an input signal is known to have a certain highest frequency part, and that above $1$hz all high frequency parts are low-pass filtered properly up to the highest frequency, as expected in lumped low-pass filter analysis (ex. 1/(s+1) transfer function)

• Lumped elements work fine up to much higher frequencies than 10^6Hz - distributed elements are typically not used below 10^9 Hz. A distributed 1Hz lowpass filter could probably be wound round a convenient planet... – Brian Drummond Aug 24 '15 at 10:58
• Study transmission line theory and extrapolate from that; also see second part of comment above. – Brian Drummond Aug 24 '15 at 11:06
• -1 for altering the goalposts in the question and wasting my time. – Andy aka Aug 24 '15 at 11:07
• 10^13 Hz is up in the far-infrared range. Good luck! – Peter Aug 24 '15 at 19:24

You need to consider a 2-stage filter.

First, use distributed elements to limit the spectrum to something in the region of 1 GHz. Then feed its output into a conventional lumped-element filter which is, as you say, easy to design, and is now working within parameters where you can accurately predict its performance.

You are forced into this path by the sheer physical size of the distributed structure you would otherwise need, which would be some multiple of the wavelength of a 1Hz signal in your chosen medium.

• But still how can one guarantee that frequencies above 1 GHz are decently blocked? Transmission line impedance is based on tan Bd, and that leads to periodic response, as far as I know. Am I misunderstanding something? – filt Aug 24 '15 at 11:42
This answer was given before the OP changed the maximum operating frequency to 10^13 Hz.


Why not use a resistor and capacitor based low pass filter. It's a first order type and you can set the cut-off to be as follows: -

$f = \dfrac{1}{2\pi RC}$

With the appropriate use of several capacitors of different characteristics, a low pass filter that works up to and beyond 1GHz is easily made.

As for lumping filters together, your question doesn't appear to promote any reason for doing so.

• I do not know if I understand correctly, but what I am talking of is distributed circuits, not lumped circuits. I am ruling out lumped element circuits because I heard that one has to switch to distributed element circuits (transmission lines) if signals contain high frequency parts. Is this not true, and that appropriate capacitors and inductors can easily be made? – filt Aug 24 '15 at 10:52
• @filt take a step back and maybe forget what you may have heard and ask yourself what you are trying to achieve or solve. Why must it be a distributed circuit? – Andy aka Aug 24 '15 at 10:57
• Because at high frequency, lumped circuit analysis are inaccuarate... – filt Aug 24 '15 at 11:02
• At 1MHz there will be no problem in designing an RC filter that works effectively. A few extra things need to be considered at frequencies up to 1GHz and above that it can be problematic. You want 1MHz so it isn't a problem. – Andy aka Aug 24 '15 at 11:05
• There are sources on the web for this I'm sure. I'm not going to keep answering this question as you keep altering the goalposts. – Andy aka Aug 24 '15 at 11:07