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Analog Filter Design from Data Points?

Hello again, SEDers.

(I hate to "expose my ignorance" like this, but...)

I have a very-occasional need to design an analog filter, given a small set of data points (e.g. ratio of input and output voltages for a half-dozen frequencies).

I am looking for design-methods or procedures, and/or software tool(s), that will facilitate or automate the design process.

I am not really even sure what the "standard" design procedure might be, in this case. Currently, I use what I can remember from my basic EE courses and try to roughly approximate in my mind what combination of lowpass and highpass RC sections might be able to be combined in series and/or parallel, to come close to the desired transfer function, and then calculate very-approximate cutoff frequencies and amplitude combinations, and then draw a schematic in LTSPice and tweak the component values and architecture until the response matches the data points. That last step can be quite tedious, which is mostly what has driven me to make this request for help.

For example, below are the data points for a filter that I am currently working on (which is for a filter that will help produce the correct current levels (1 mA to 0.125 mA) versus frequency, for a current-controlled resistance that will cause an audio-frequency ramp generator to give a contant output-amplitude versus frequency):

60 Hz: 1.00v, 200 Hz: 1.20v, 750 Hz: 0.660v, 4.5kHz: 0.297v, 12 kHz: 0.178v, 22kHz: 0.125v.

I need to have the response at the data points above be accurate within

1%, but don't care what the response is like in between and outside the data points' frequencies. [So, I realize that, for the six data points above, I could just use six separate bandpass filters and sum their outputs. But I think it "should" usually be able to be made more parts-count-efficient (And board space is limited.). For the example dataset above, for example, I came up with two parallel/summed sections, each with three cascaded simple RC sections, i.e. a total of six caps and six resistors, plus four opamps (for i/o buffering of each parallel cascade), and one opamp and four resistors for summing, and a couple of resistors for a voltage divider for the output of one of the cascades (which could all change, somewhat, if I convert it to an active-filter architecture), which is not yet optimized for component count or performance, etc, etc.]

Actually, I can usually come up with the "rough approximation" for the filter architecture and component values fairly quickly/easily. The tedium usually lies in tweaking the component values, and possibly the architecture, to get the response down from, say, 5% or 10% accuracy, to 1% or less at every data point.

Since I currently use LTSpice for that "tweaking", I'm also looking into being able to use LTSpice's features to automate that portion of the process. I'm hoping that there is some good way to have it vary the component values and stop when the response matches at the given data points. (Anyone here know about that? I'm also posting a question about that to the LT-Spice discussion group at

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If anyone cares to offer any ideas, methods, procedures, advice, software titles, websites, references, et al, I will truly appreciate it.

Regards,

Tom Gootee

Reply to
tomg
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[snip]

No simple answers, but I find "Synthesis of Filters", Herrero and Willoner, Prentice-Hall, 1966, very useful for the math necessary to fit arbitrary shapes.

...Jim Thompson

--
|  James E.Thompson, P.E.                           |    mens     |
|  Analog Innovations, Inc.                         |     et      |
|  Analog/Mixed-Signal ASIC\'s and Discrete Systems  |    manus    |
|  Phoenix, Arizona            Voice:(480)460-2350  |             |
|  E-mail Address at Website     Fax:(480)460-2142  |  Brass Rat  |
|       http://www.analog-innovations.com           |    1962     |
             
I love to cook with wine.      Sometimes I even put it in the food.
Reply to
Jim Thompson

Do it digitally, of course.

Analog filters normally have shape factors. For any particular choice of order and implementation, all points are predetermined.

Further, rude surprises involving phasing and group delay can be expected with analog filter designs.

Linear phase digital filters are normally specified by selecting the amplitude at a number of given points. The number of points determines the number of taps needed.

Digital filters, of course, are smaller and cheaper than analog.

Tutorials at

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and
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Since the 24kHz response is more than twice the 12 kHz response, parallel channels involving allpass or highpass summing will be required with an analog route.

If you must use traditional analog, use my Active Filter Cookbook

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--
Many thanks,

Don Lancaster                          voice phone: (928)428-4073
Synergetics   3860 West First Street   Box 809 Thatcher, AZ 85552
rss: http://www.tinaja.com/whtnu.xml   email: don@tinaja.com

Please visit my GURU\'s LAIR web site at http://www.tinaja.com
Reply to
Don Lancaster

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Oops. Shoulda been

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not 106.

Determinent stuff in 106 has been superceeded by later Gauss Jordan tutorials as well.

--
Many thanks,

Don Lancaster                          voice phone: (928)428-4073
Synergetics   3860 West First Street   Box 809 Thatcher, AZ 85552
rss: http://www.tinaja.com/whtnu.xml   email: don@tinaja.com

Please visit my GURU\'s LAIR web site at http://www.tinaja.com
Reply to
Don Lancaster

Jim,

Thanks for the reference. I'll see if I can find a copy. Sounds like it would be good to have around.

Tom

Reply to
tomg

Don,

Gee, I wasn't expecting such well-known heavyweights to comment on my little question. (Many thanks to you and Jim Thompson and the others, for taking the time.)

Thanks for the pointers! I wasn't going to consider using digital, on this board. But you just had to go and say the magic words, "smaller and cheaper". So, my next stop will be at

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, to check out your muses 105 and 107. Thanks again.

Regards,

Tom Gootee tomgATfullnet.com

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Reply to
tomg

Don,

Gee, I wasn't expecting such well-known heavyweights to comment on my little question. (Many thanks to you and Jim Thompson and the others, for taking the time.)

Thanks for the pointers! I wasn't going to consider using digital, on this board. But you just had to go and say the magic words, "smaller and cheaper". So, my next stop will be at

formatting link
, to check out your muses 105 and 107. Thanks again.

Regards,

Tom Gootee tomgATfullnet.com

formatting link

Reply to
tomg

Jim,

The servo loop is an excellent suggestion. Thanks! To be honest, I had already thought of doing that. And it is attractive, in my case, since I already know HOW do do that, and recently designed a similar one, for a different purpose, that used the output of a peak detector and a feedback control loop to set and maintain the output amplitude of a power amplifier that pushes a test signal into a device under test (for the same unit for which I was thinking about the filter design being discussed in this thread). Works perfectly. I may just do the same thing, here, rather than spending any more time trying to get a good-enough "pre-determined" filter designed. It might perform better, overall, too, since it should be able to automatically correct for certain types of circuit variations, etc.

Thanks again.

Regards,

Tom Gootee

Reply to
tomg

Joerg,

Thanks for responding. I have read many of your posts, in the past, and have learned a lot from them.

I did mention, in the next sentence after the one you quoted, that I realized that I could just use six separate bandpass filters and sum their outputs. And at least that's mathematically possible to do, with the required accuracy.

If I don't decide to just use a servo loop, instead, or maybe a digital filter, as Don Lancaster mentioned, then I will probably just use the six separate bandpass filters, instead of spending any more time trying to tweak a smaller-component-count filter architecture, to try to coax it to within the required 1% response accuracy at the six frequencies.

Thanks again.

Regards,

Tom Gootee

Reply to
tomg

On 1 Oct 2005 13:19:04 -0700, snipped-for-privacy@fullnet.com wroth:

For this problem, I would be tempted to use a circuit measure the amplitude at *any* frequency as it is being generated and use that information to supply a current to the attenuator that would adjust the amplitude so that it becomes constant. That's a type of negative feedback also called a "servo". The advantage would be that you wouldn't have to figure out anything in advance and if the frequency ramp generator's output changed for any reason, the output would remain constant.

Another way to do it, this time without feedback, would be to take the ramp that controls the frequency and pass it through a piecewise-linear function generator that would output the correct current for each desired data point. The function generator could be as simple as a string of diodes and resistors. The advantage here would be that you could use a variable resistor, pot, for each frequency of interest and twidle it to get exactly the amplitude you wanted.

Jim

Reply to
jmeyer

Hello Tom,

In that case, why not build six simple bandpasses and run their outputs into a summing node? The resistors into that summing node would be set so you get exactly the desired amplitude for each.

A regular filter would not likely yield 1% accuracy. Except for very elaborate digital ones.

Regards, Joerg

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Reply to
Joerg

Hello Tom,

Sorry, didn't see that. I responded in a break while moving an upright piano, to lay tile where it was. Whew, you get pretty tired doing that kind of stuff.

I think the separate filters may be the easiest solution. You really don't want anything but resistors in the equations since caps under 5% are rare and expensive.

For an active filter solution you would only need a few quad opamps of the 10 Cent class. LM324 or something like that. Since you said space is a concern many opamps come in TSSOP. Of course, if it is likely that the frequencies and ratios might change a lot in the future then a digital solution would be easier in the long run.

Switched-capacitor filters are another option. However, they never really made a big splash in the market place so other than a few chips from LTC and National there ain't much available. They are great though. I have used them a lot in the early 90's.

If you are at liberty to say what this is all intended for there may be other solutions, who knows.

Regards, Joerg

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Reply to
Joerg

Tom, if you want to make "inverse" filters, also the phase response is necessary to design an appropriate compensation filter. The final response will only be OK, if the dynamic behaviour is compensated for as well. If you make bandpass filters, their Q-factor will cause a delayed overshoot since the input is not static. When you want 1% accuracy the only approach is via digital. The appropriate software tools can be found on the net. I use Adobe Audition with the Aurora plugins

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for this purpose, but you can also do it with Matlab or similar. These progs will output an appropriate FIR-filter, which can be implemented easily. You can do it in realtime on a PC, so there is no need to make hardware to test it.

--
ciao Ban
Bordighera, Italy
Reply to
Ban

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