Hi,
I am wanting to achieve something similar, a “9th order” (or similar) low pass filter with 600hz cutoff.

is the advice in this thread still relevant?
Is a 9th order filter still impossible for a beginner?
Or are the components now more accessible and cheaper?

Mod: link to old Thread.
https://forum.allaboutcircuits.com/threads/9th-order-low-pass-butterworth-filter.149173/post-1274711

 

Hi,
I am wanting to achieve something similar, a “9th order” (or similar) low pass filter with 600hz cutoff.

is the advice in this thread still relevant?
Is a 9th order filter still impossible for a beginner?
Or are the components now more accessible and cheaper?

The components you will need for a 9th order filter are unlikely to be cheaper than they were 5 years ago. To get some idea of the difficulties involved it might be helpful to simulate possible implementations to see what results you might expect. There are many capable simulators that will aid in your understanding of doing a design and evaluating the results.

Do you understand the methodology for coming up with the appropriate normalized transfer function and then scaling it to your particular application?

 

Here is an example of an ideal 5th order filter. You get the 9th order filter by adding two more 2nd order sections with the appropriate corner frequency and Q. This is where things get tricky with real components.

 

Linear Technologies, now Analog Devices, provide sampled-capacitor filter ICs and very important, the software to calculate the component values.
Sampled capacitor filters have two major advantages:
—The cutoff frequency is only dependent of the external clock source. It is relatively straightforward to build a high precision clock.
—Only precision resistors and the IC itself are required for the filter circuit. This is a *very* important consideration as precision, low-tempco, oddball value capacitors are going to be very bulky and very, very expensive.

I am out of the office and don’t remember the exact part number I have used previously, but the ADI FilterCAD tool will suggest some suitable devices.

 

Why do you need such a sharp cutoff? A 3rd-order lowpass filter cuts high frequencies fairly well.

 

It took a minute or two and some hand calculations to arrive at the following:


I've never seen a Bode plot go to -900 dB -- that's pretty insane! the rolloff is indeed 180 dB/decade as you would expect from a 9th order ideal filter. That is certainly a smaller voltage than you could EVER measure; it is down below the noise floor.

 

-60dB is one-thousandth of a voltage.
-120dB is one-millionth which is extremely small.
-180dB is one billionth.
-240dB is one-trillionth.
-300dB is one-quadrillionth.
-360dB is one-quintillionth.
One-zillionth is etc?

 

I am wanting to achieve something similar, a “9th order” (or similar) low pass filter with 600hz cutoff.

The need for such a high order rolloff is rare.
What is your application?

 

How much stop-band attenuation do you require?

 

….

Do you understand the methodology for coming up with the appropriate normalized transfer function and then scaling it to your particular application?

I don’t understand the methodology, I’m quite new to this.
I am picking things up as it applies to what I’m trying to make though, and I also find it very interesting, so what you share with me won’t be falling on deaf ears.
Additionally, I have an electrical engineer friend who I’m leaning on to help me when it comes to the execution.

I mainly wanted to check in with this group to see what the state of the art was with commoditization of this high level of filter.
So thank you for that.

 

The need for such a high order rolloff is rare.
What is your application?

i am just working through this study on DML panels and the combined optimized subwoofer (page 10).
The model they use has a 9th order low pass filter with a cutoff at 600hz.

I wanted to test this with my panels to see what the frequency response was like.

https://www.researchgate.net/profil...and-enhancement.pdf?origin=publication_detail

 

How much stop-band attenuation do you require?

it’s likely I would not need a 9th order!
I have a premade low pass filter that is 12dec/octave cutoff at 500hz on its way (for cheap) which was what I was going to test with.

 

-60dB is one-thousandth of a voltage.
-120dB is one-millionth which is extremely small.
-180dB is one billionth.
-240dB is one-trillionth.
-300dB is one-quadrillionth.
-360dB is one-quintillionth.
One-zillionth is etc?

I see. I didn’t know this. And I’m now seeing why it’s not normal to try and reach a 9th order filter out side of math models.

 

The Butterworth filters are referred to as "maximally flat" in the passband. That means the response in the passband is monotone decreasing. This places a strict set of conditions on the transfer function. In the frequency domain this will manifest itself as a set of poles on the unit circle (or any scaled version of the unit circle) at particular locations in the left half plane. For an odd order filter there is a single pole on the negative real axis with a Q of 0.5. The remaining poles of the 9th order filter are at equally space angles from the negative real axis at:

1. ±20° ≈ 0.35 radians = 2π/18
2. ±40° ≈ 0.70 radians = 2π/9
3. ±60° ≈ 1.05 radians = 2π/6
4. ±80° ≈ 1.40 radians = 4π/9

Knowing the locations of the 9 poles will give you the transfer function for the Butterworth response, and the decomposition into one 1st order section and 4 cascaded 2nd order sections arranged in order of increasing Q, as shown in the simulation.

 

For a smooth crossover between two speakers a Linkwitz–Riley filter is used, which allows a smooth crossover with no peaks or dips in the combined speaker response.
A 9-pole filter will not do that.

 

Your 12dB per octave lowpass filter produces a voltage signal above the cutoff frequency of only 0.25 per octave.
All even-order filters produce a notch in signal level at the cutoff frequency unless one of the transducers has its polarity reversed, which causes a +3dB peak at the crossover frequency. Odd-order filters produce a flat frequency response at the crossover frequency.

 

For a smooth crossover between two speakers a Linkwitz–Riley filter is used, which allows a smooth crossover with no peaks or dips in the combined speaker response.
A 9-pole filter will not do that.

something like this?
https://www.daytonaudio.com/product/1476/600-lpf-4-low-pass-speaker-crossover-600-hz-12-db-octave

 

something like this?
https://www.daytonaudio.com/product/1476/600-lpf-4-low-pass-speaker-crossover-600-hz-12-db-octave

No. That’s not a crossover, it’s just a filter. It takes 2 filters to make a crossover.
Nor is it a 600Hz Linkwitz-Riley, because Linkwitz-Riley filters are 6dB down at the crossover frequency, not 3dB.

 

something like this?

That is one-half of a Linkwitz-Riley, filter.
You need a similar high-pass filter to complete the crossover.

Nor is it a 600Hz Linkwitz-Riley, because Linkwitz-Riley filters are 6dB down at the crossover frequency, not 3dB.

But it is 1/2 of one.
The filters are usually designed by cascading two Butterworth filters, each of which has −3 dB gain at the cut-off frequency.
The high-pass and low-pass together give -6dB at the crossover.