Low pass filter: What are these components doing?

[wayland]

Hi all! 

I have some questions about the circuit pictured in the image attached to this post.  The circuit is part of the Low-Pass Filter stage of the Hollis OmniDrive at http://www.geofex.com/PCB_layouts/Layouts/omnidrv.pdf, but with some blue boxes indicating my analysis (component values as specified in the URL).  I think I've correctly identified:

• An RC Low-pass filter section
• A non-inverting unity opamp section

My basic questions are:

• Is my analysis correct, or should some of the other components belong in the low-pass filter box? (or other problems)
• What are R6 and C3 doing?

Thanks for any help anyone can provide! 

[Rob Strand]

There's simple RC filters which only use passive components and there are more complex RC filters which use an opamp, called active filters.   A common active filter is the Sallen and Key filter.

The main advantage of an active filter is more filtering above the cut-off frequency.   The simple RC filters only have -6dB/octave (-20db/decade) filtering whereas the active filters can produce -12dB/octave (-40dB/decade), or more.  You can have higher slope RC filters without opamps but the slope near the cut-off is very slow whereas the active filters allow the transition to be sharper.   Basically you use active filters to get more filtering.

The Sallen and Key circuit can be designed with a buffer or with a gain stage.

    An RC Low-pass filter section
    A non-inverting unity opamp section


My basic questions are:

    Is my analysis correct, or should some of the other components belong in the low-pass filter box? (or other problems)
    What are R6 and C3 doing?

So the gain stage is the part you have outline.   It's not unity gain.

R6 and C3 are part of the filter as well.   The Sallen and Key filter needs two R's and two C's; the C's are usually different values and the R's may or may not be different values.   You can't separate R6 and C3 from the C4 and R7 as both are part of the active filter.

In a normal Sallen and Key filter C3 would connect to the output of the opamp.   The slight quirk of the Hollis filter is that it connects C3 to the opamp -in input.   Connecting C3 like this means the R and C values for the filter are more like a Sallen and Key filter with a buffer.    The gain stage then only boosts the level.     While you can design a Sallen and Key filter with gain it often turns out the filter's behaviour becomes sensitive to parts tolerance so the Hollis design tries to avoid that with a different connection.   The result isn't *exactly* like an ideal low-pass filter as the feedback resistors affect the filter.

[wayland]

Great!  That's a pretty good explanation! 

The one thing I think I still don't get is why the gain isn't unity.  I would've thought that R8 and R9 being equal would have made it so.  Is it because the resistors in the filter affect the gain as well?  Specifically R6? 

Thanks!

[antonis]

The one thing I think I still don't get is why the gain isn't unity.  I would've thought that R8 and R9 being equal would have made it so.

Taking your word for op-amp non-inverting configuration, gain is always more than unity due to resistors existence inside NFB loop..
(Gain is 1 + R9/R8 so, for unity gain you need R9 = zero (short) or R8 = infinite (open)..)

[wayland]

Haha, can't believe I missed that one!  Thanks!  So it's x2 gain then?