1mHz LPF

Hi Mircea,

Constructing a practical 1 mHz  filter of any kind will be challenging, but an active filter may be the only reasonable option.

I checked with one of my applications colleagues about the largest capacitance SMD capacitors. The C0G capacitors, the preferred performance choice, tops out at 100 nF for the 1206 size. 100 nF is too low of capacitance for a 1 mHz filter. He did say that for X7R capacitors the maximum is about 10 uF for the 1206 size. The X7R is usable, but one can expect much higher dielectric-induced distortion than would be obtained from a C0G capacitor. An X7R capacitor is the practical choice to keep the resistors doable.

Below you will find the schematic of a Sallen-Key, 1 mHz low-pass, having a Butterworth response. The C1 value is 10 uF, and C2 is 18 uF. If you can't find an 18 uF surface mount capacitor it may be realized by paralleling two capacitors. In fact if you wish to drive down the high resistor values to something lower that will generate less noise, placing capacitors in parallel on the board would be a good way to accomplish this.

Since the 1/f noise of standard operational amplifiers will be very high at 1 mHz, it is recommended that a chopper operational amplifier such as the OPA333 be employed. Choppers don't exhibit 1/f noise and that is important in this very low frequency application. You can find more about chopper and 1/f in Bruce Trump's EDN blog:

http://www.edn.com/electronics-blogs/the-signal/4413341/Chopper-op-amps-and-noise

The resistors used in the filter are very high in value and their thermal noise √(4kTRB) will be high. A TINA-TI analysis of the output noise will show you how the noise changes as the resistors are scaled.

I have attached my TINA simulation filer the filter.

Regards, Thomas

PA - Linear Applications Engineering