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June 10, 2018 / consort3

4th order, single op-amp low/high pass filter + xover

4pole

This combines Conrad Hoffmans 4 pole single op filter idea with my tracking idea and was inspired by a thread on the EEVblog.

Conrads idea here (8th item down):

http://conradhoffman.com/chsw.htm

Vary the components in the table to get the -3dB point indicated. The damping is sensitive to the value of R7. If the filter is AC coupled at the input you would need a high value bias resistor to ground.

E24 table

Frequency Hz R1 R2,R3 R4
9.07k 2.7k 10k 680
8.24k 3k 11k 750
7.51k 3.3k 12k 820
6.85k 3.6k 13k 910
6.21k 3.9k 15k 1k
5.71k 4.3k 16k 1.1k
5.16k 4.7k 18k 1.2k
4.72k 5.1k 20k 1.3k
4.23k 5.6k 22k 1.5k
3.89k 6.2k 24k 1.6k
3.49k 6.8k 27k 1.8k
3.15k 7.5k 30k 2k
2.88k 8.2k 33k 2.2k

E96 table (fragment)

Frequency R1 R2,3 R4
7.5k 3.32k 12.1k 825
7.34k 3.4k 12.4k 845
7.13k 3.48k 12.7k 866
6.96k 3.57k 13k 887
6.83k 3.65k 13.3k 909

Response as R7 is varied from 0 through 500R to 1k.  The frequencies in the tables have been revised  and R7 should be 360 ohm to make  the 180 degree phase change the same as the -3db point. The ease of tweaking the damping with a single resistor is a blessing and a curse.

4pole1

I made a high pass filter by swapping resistances for reactances and vice versa. I emulated the well known LR 4th order crossover by tweaking the damping and paying attention to the phase tracking.

4polelinkfin

4polelinkfinA

For a flatter combined response (as shown in grey) I made R5 and R12 10.05k by putting 51 ohms in series with a 10k. The curse is that the 10k resistor pairs R5/6 and R12/13 have to be matched to 0.1%. This makes the individual responses more Bessel than Butterworth. Note how linear the phase is at the crossover point.Vary the components in the table to get the crossover frequency indicated.

Frequency Hz R1 R2,R3 R4 R8-11
2.94k 5.6k 22k 1.5k 11k
2.67k 6.2k 24k 1.6k 12k
2.43k 6.8k 27k 1.8k 13k
2.2k 7.5k 30k 2k 15k
2.0k 8.2k 33k 2.2k 16k

In developing the filter for crossover use, I appear to have been on the same journey as Rane who describe it more eloquently than I could here:

https://www.ranecommercial.com/legacy/note147.html

Incidentally the use of E24 series resistors for the tracking idea gives a change in frequency value of roughly 9%. If you use the E96 series you get a change of roughly 2.25%, so you can get more precision. The Yageo MFR range from Digikey will give you precision at reasonable cost. The 2.25% does not quite match the precision of the change on the DCX2496 which is roughly 2%. The component tolerances have to be tight to get good results. The idea being that you tweak your prototype using the DCX then implement the crossover in analogue hardware.  This would compensate for driver phase and amplitude. I tweak for the deepest null with the tweeter reversed. Use the LR4 filter setting on the DCX even though this implementation is more Bessel than LR.

It is annoying that the E24 and E96 series do not track. There are good explanations here:

https://electronics.stackexchange.com/questions/381446/why-are-the-e-series-numbers-different-from-the-powers-of-10?noredirect=1

http://mathscinotes.com/2016/05/standard-resistor-values/

This article from TI shows that you sometimes have to offset the filter frequency to compensate for the driver response.

http://www.ti.com/lit/ug/tidu035/tidu035.pdf

To get the same results  in the above article for the low and high pass filters try these values in my scheme. Note that you get 6dB of gain with my scheme.

R1 5.36k R2,3 21k R4 1.43k C1-4 10n R5 10.1k R6 10k C5 12n C6,7 3.3n C8 47n R8-13 10k

Application to design six different types of passive 4th order crossover filters, namely LR, Bessel, Butterworth, Legendre, Gaussian and Linear phase.

https://www.diyaudioandvideo.com/Calculator/SpeakerCrossover/4th 

The app. was probably derived from equations in Vance Dickasons Loudspeaker design cookbook which is well worth reading on crossovers. Vance dismisses the last three types as of academic interest only.

I have been reading some of JLH’s work since I am a disciple of his, but he could not get this 4th order circuit to work properly. I suspect he was not aware of the Wong and Ott article in Function circuits, Design and applications (1976) which Conrad Hoffman used. Not a  lot of people know that JLH’s nickname was Robin after the British tradition, Dusty Miller, Nobby Clark, Jack Frost, Chalky White, Drawers Chester, Foxy Reynolds, Sticker Leach, Nosey Parker, Spud Murphy, Snip or Stitch Taylor,  Dickie Bird, Errol Flynn, Robin Hood

Update 8/5/21 I got a simpler design, better reverse null and lower component value sensitivity with this 2.64kHz crossover

4thlrvarXX

4thlrvarXY

FrequencyR1R18R16R17R2R3R5R4
1.81k13k8.2k13k8.2k7.5k9.1k2.2k110k
1.98k12k7.5k12k7.5k6.8k8.2k2k100k
2.18k11k6.8k11k6.8k6.2k7.5k1.8k91k
2.4k10k6.2k10k6.2k5.6k6.8k1.6k82k
2.64k9.1k5.6k9.1k5.6k5.1k6.2k1.5k75k
2.91k8.2k5.1k8.2k5.1k4.7k5.6k1.3k68k
3.18k7.5k4.7k7.5k4.7k4.3k5.1k1.2k62k

E96 table to give more precision (as PDF)

96tabx

The weird values on the E96 series can sometimes be made by putting E24 values in series, for example 12.7k is 2.7k and 10k in series, likewise 2.4k and 10k to give 12.4k, 5.6k and 6.2k to give 11.8k. A program called Rescalc will work it out for you. Alternate rows fit the E48 series. Components should be 1% tolerance. Resistors are no problem but close tolerance capacitors are. See my page Active elliptical crossover filter for a discussion on this.

Update 5/6/21

I got even better phase tracking with the following circuit

phtrkc

phtrk

Frequency (k)R1,16,17,18(k)R2,5(k)R3(k)R4(k)
1.9485.1121062
2.1364.7119.156
2.3424.3108.251
2.5623.99.17.547
2.7933.68.26.843
3.0603.37.56.239

E96 table to give more precision (as PDF)

phtrkr

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