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October 5, 2019 / consort3

Bootstrap filters

I unearthed an article by the great guru JLH on bootstrap filters which tend to be Chebyshev types and hence give a fast cut-off. Here are the circuits for 3rd order types with low pass on the left and high pass on the right.

bootstrap2

Here are the responses

bootstrap1

bootstrap

for the low pass case

eqn1

R1/R2=x

C2/C1=y

√(xy)/(1+y)=Q

For the high pass case

EQN2

C6/C4=x

R5/R4=y

Above Q eqn. applies

For the LP filter shown f0=590Hz Q=2.2 and for the HP one f0=33.3Hz Q=2.42

There is a useful article here which mentions them (part 2)

http://www.industrial-electronics.com/aole_8.html

If you make the filters  with a higher Q and then cascade them you get the tuned response filter or a reasonably high Q bandpass filter

tunedresponse

tunedresponse1

16 db of gain from 2 unity gain op-amps? What kind of sorcery is this? Welcome to the dark arts! Actually it is positive feedback.

Responses as R1 and R2 are tracked down and C3 and C4 are simultaneously tracked up in the E24 series

tunedresp

OUT2 OUT3 OUT4 OUT5
C3 3.3N 3.6N 3.9N 4.3N
C4 68N 75N 82N 91N
R1 43K 39K 36K 33K
R2 2.2K 2K 1.8K 1.6K

See the 1970 postscript in this article for more (JLH calls it a H filter)

https://sound-au.com/tcaas/jlhmodpre.htm

I created the variable slope filter controlled by R4 in this diagram

varslope1

Response as R4 is varied from 0 through 390 to 1Kohms, green blue red traces respectively:

varslope

See the rumble and scratch filters on this page for more:

http://paul-kemble.tripod.com/sound3.html

This rumble filter has a more subtle action than your usual bass tone control. R6 can be a 5.1k resistor in series with a 10k pot.

varumble1

varumble

Readers of the blog may remember that I came up with a suggestion for matching a woofer to an enclosure by using  a negative resistance amplifier. Another way of doing this is with a high pass filter (as above). If you find when you model the system on Unibox that there is say a 6dB peak at 50Hz, then using a filter with a 6dB loss at 50 Hz will make the response level. Unibox will import an external filter in FRD form so you could convert the response given here and tweak the value of R6 to give a level overall response. Here is more on the subject of matching woofers and enclosures:

https://sound-au.com/articles/cscaling.htm

I did not think that the bootstrap filter would make a good crossover filter but it gave surprisingly good results. It is a  third order reverse tweeter design. There are pros and cons however. The pro is that the crossover can be tweaked by R6. The con is that the slope reverts to second order out of band.

bootxo1

bootxo

Freq kHz 1.9 2.08 2.3 2.55 2.8 3.06
R1 24k 22k 20k 18k 16k 15k
R2 2.4k 2.2k 2k 1.8k 1.6k 1.5k
R3 11k 10k 9.1k 8.2k 7.5k 6.8k
R4 16k 15k 13k 12k 11k 10k
R5 3.3k 3k 2.7k 2.4k 2.2k 2k
R6 6.2k 5.6k 5.1k 4.7k 4.3k 3.9k

 

Original article by JLH

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