# Designing a filter: does the order i which we cascade the sections matter?

So I am designing a 4th order lowpass filter using two biquadratic sections. I decided to split the gain evenly between both sections. After some calculations, one of the sections has a quality factor of 0.9 and the poles frequency is 1.65 kHz, the other has a quality factor of 4.6 and the poles frequency is 3.4 kHz. My question is, in terms of design, is there any difference the order in which I cascade the sections? Their quality factor is so different, I wonder if I should put first the lowest or the highest quality factor? What should be the criteria here?

• Also define your Passband ripple and error tolerances Oct 12, 2020 at 20:13
• @TonyStewartSunnyskyguyEE75 The filter is fairly well made. All filters with passband ripple have low Q for low poles, and high Q for higher poles. If you'll plot OP's transfer function, you'll see a classic 2 dB ripple Chebyshev, even if the ripple is not quite stable (probably because of the one digit roundings). Oct 12, 2020 at 21:59
• @aconcernedcitizen TY for your correct reply. Chebychev has higher Q latter stage ( and horrible GD distortion) Here 0.2dB ripple i.stack.imgur.com/f0KwT.png Oct 12, 2020 at 23:01

Yes it does matter.

Your two sections are rather oddly matched, as Tony says. I presume you know you'll have quite a bit of passband ripple, and it's the right decision for your application.

If the high Q section is first, then high amplitude signals around the pole frequency will be amplified by the Q, and cause the amplifier to clip, i.e. become very non-linear.

The harmonic distortion caused by the clipping may be difficult to measure as it will be attenuated by both filter sections, but the intermodulation distortion will not. That is, tones at (say 3.3 and 3.5 kHz), both clipped, will produce a 200Hz component which will NOT be attenuated.

Put the low Q low frequency section first, and these tones will be attenuated by 12dB/octave, and they are 1 octave above its passband. That reduces their amplitude to about 1/4 before the second stage (Q = 4.6) would increase them about 4x.

So the low Q section first prevents the high Q section clipping.

• Yes the ripple in the passband is intentional, I'm implementing a Chebyshev filter.This was exactly the explanation I was looking for, i did suspect it might influence the "tendency" for the Opamps to saturate (or clip as you mentioned). Thank you! Oct 12, 2020 at 21:00
• @GrangerObliviate Mathematically, it doesn't matter whether you have H1(s)*H2(s), or H2(s)*H1(s). In practice, this answer does it. (+1) Oct 12, 2020 at 21:51

For what it's worth, not an answer but more detail than a comment.,

If there is a signal where Q is highest, and any chance of saturation, it would be better last, as stage 1 attenuates at Qmax(f). But in linear use , they are interchangeable as there are no loading effects between stages.

These Biquad filter sections are linear so it should not matter ?! .Most of the time it will not matter ,the overall transfer function is the same .This linearity only applies when the opamps are within their voltage swing ranges .When clipping starts you will not get your classical transfer function .Is overload a problem ? where and how big are your unwanted signals ? think this stuff through for your application .I would put the low Q section first .