[sdiy] Designing 4-pole filters with identical 2-pole stages - why not?

[Tom Wiltshire]

Hi All,

I've been designing 4-pole Butterworth filters using 2-pole Sallen-Key sections.

The usual way to do this is to set the Q of the first stage to 0.541, and the Q of the second to 1.307. Multiplying one by the other gives an overall Q of 0.707, which is our Butterworth response.

In the interests of simpler circuits, I wondered if it would be possible to design a 4-pole filter with two identical sections (less individual component values). Such a circuit would need each stage to have a Q of sqrt(0.707) = 0.841. So I tried it in LTspice.

The circuit, identical-stages filter above, typical 4-pole butter worth below:

http://www.tomwiltshire.co.uk/Butterworth.png

And the responses:

http://www.tomwiltshire.co.uk/ButterworthResponse.png

Now, my question is "What am I missing?" or "Why is my simulation lying to me again?" since I find it difficult to believe that people have been building unnecessarily complicated filters since 1930 without spotting that they could make life much simpler.
Is it that the identical-stages version would be very sensitive, or does it have some other flaw?

Thanks,
Tom