# Why is there a lower limit on amplification for this filter design method?

I'm designing an active low-pass filter for a differential input. The input is on a ±100V scale and needs to be scaled down to the standard ±10V scale.

I found this application note which describes how to design a 2nd order multiple feedback filter and convert it to differential inputs:

http://www.cirrus.com/en/pubs/appNote/AN048Rev2.pdf

However, they state in their first step that the magnitude of the amplification factor H0 needs to be at least one, without giving a reason (in our case H_0 = -0.1).

I don't see a reason for such a restriction, so I ignored it and designed such a filter (Bessel, with about 9kHz corner frequency) and it seems to work as expected, both when simulated with LT-Spice and in hardware.

Does anybody know where this condition originates? Is it a real restriction, or is it just arbitrary, maybe copied from somewhere without understanding the math behind it? Is it maybe because you would tend to use a different topology for gain less than one, though there is nothing really wrong in using multiple feedback?

Curiously, TI's Filter Pro also didn't let me enter anything less than 1 for the amplification.

• It would help if you posted your circuit with the attenuation of 10 built in. I'm not sure how you could have implemented it from the circuit you linked. – Andy aka Nov 7 '13 at 20:31
• The values are R1=100kΩ, R4=10kΩ (hence the attenuation of 10), R3=1.5kΩ, C5=2.2nF. Instead of two C2=6.6nF there is a single 3.3nF resulting from putting them in series and removing the connection to ground. I think that single C gives better common mode rejection. It is also done like that in a document by TI: ti.com/general/docs/lit/… (page 37). – starblue Nov 7 '13 at 21:20
• OK I get it now. Seems very reasonable what you've done but does the filter shape still look decent with the 10:1 attenuation? I mean, it doesn't turn into a very sloppy low pass with boring old gradual roll off from dc or something like that? – Andy aka Nov 7 '13 at 22:31
• @Ansy aka Good question. The second-order certainly shows, above ca 36kHz it is better than the ca 3kHz single-order low-pass we currently have. How it compares to two 9 kHz low-passes in series is difficult to see. – starblue Nov 8 '13 at 7:43