# Is it possible to create a 0.001Hz bandwidth low pass filter?

#### richiechen

Joined Jan 1, 2012
93
Hi ALL

I am trying to build a phase lock loop. And at the end of the PLL will be a low-pass filter, which only allows DC to pass. The DC voltage will be measured by an ADC.

Because the narrower the filter, the less the noise will be measured by ADC.

So here is my question, is it possible to create a 0.001Hz low pass filter, which only allows DC to pass??

Thank you very much.

Regards
Richie

#### Audioguru

Joined Dec 20, 2007
11,248
It will take a very long time (13.3 minutes) to charge or discharge.

#### bertus

Joined Apr 5, 2008
22,233
Hello,

The lower you make the loop filter frequency, the longer it takes to react on changes in frequencies.
The reaction time is 5 * Tau.
A 0.001 Hz has a delay of 5 * 1/0.001 = 5000 seconds.

Bertus

#### Papabravo

Joined Feb 24, 2006
20,617
It is theoretically possible, but probably impractical. For example a passive 8-pole Butterworth for that frequency would require inductors and capacitors with impractical values.

You might be able to get there with a Sallen-Key opamp based one, but as has already been pointed out there are tradeoffs.

#### MrChips

Joined Oct 2, 2009
29,861
Imagine an RC filter with 1MΩ series resistor and 1000μF capacitor to ground!

This would take 1000s to reach 67% of the input voltage, about 1 hour to settle to within 2% of the input voltage.

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#### #12

Joined Nov 30, 2010
18,224
It seems you have talked yourself into focusing on a method that is not practical. Go with the recommendation from Bertus and educate yourself until you realize a different method will work.

#### Jaguarjoe

Joined Apr 7, 2010
767
About 25 years ago I worked with a guy named Vern Siegel. He made a filter with a two week time constant. It had to do with earth tremors and the like. Vern is still out there, if you google his name it should be trivial to get in contact with him and go from there. Beware- he is incredibly smart.

#### ifixit

Joined Nov 20, 2008
652
Hi richiechen,

Digitize your signals and implement as many of the PLL functions in software as you can. It is not practical to implement a 1 millihertz low pass filter in hardware, but very easy in software.

What is the purpose of this PLL anyway?

Good Luck,
Ifixit

#### richiechen

Joined Jan 1, 2012
93
Hi richiechen,

Digitize your signals and implement as many of the PLL functions in software as you can. It is not practical to implement a 1 millihertz low pass filter in hardware, but very easy in software.

What is the purpose of this PLL anyway?

Good Luck,
Ifixit
Thanks Ifixit!!
Your advice is quite practical. But in current version I am trying to build a PLL in hardware.

The purpose of the PLL is to measure a sine wave of tens of nano volt amplitude.

Best regards
Richie CHEN

#### richiechen

Joined Jan 1, 2012
93
Thank you all for the useful information.

The sine wave I am trying to lock in is 1kHz actually. The reason for me to use a very low band LP filter is because I want to suppress the nosies. I am trying to detect a sine wave of tens of nano volt amplitude. So I guess the noise is a quite critical problem.

Any idea of suppressing the noises?

Thank you all very much.