splitting a filter

There is no zeroes in the Bessel filter. All you have to do is factorize the denominator of H(s) then split it into sections. How to split depends on the application; good rule of thumb is put the lower Q section first. If that is a problem, I can do that for you.

Vladimir Vassilevsky DSP and Mixed Signal Design Consultant

My favorite filter book is "Synthesis of Filters", Herrero & Willoner, Prentice-Hall, 1966.

I like it because it covers transforms that get you from response to pole-zeroes. Also ways to split transfer functions... I used it years ago to make cascaded active filter stages. ...Jim Thompson

--
| James E.Thompson, CTO                            |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC's and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon at http://www.analog-innovations.com |    1962     |

               I can see November from my house :-)

Sure, I can get the pole locations and split them up and shuffle them around. That's easy. I could run some standard active filter design program for that.

Of course, I'd get three 2nd order stages, when what I'd prefer is two

2nd order guys and two 1st order, so I can cascade two 3-pole filters. But I could cascade two 4-pole filters just to sidestep that little math problem... a 8 pole Bessel would be fine.

The hard part, at least for me, at least this week, is to turn the pole locations into L and C values. Hmmm, there are many permutations of shuffling around the pole groups, which adds potential complications.

We could also have one pole be active on each end, an RC and an opamp. Even more fun.

This is still being considered, but I may well wind up expressing this as a formal problem and asking you to quote us on working up the design. We could do two separate 3-pole or 4-pole LC filters, but we need a Bessel or similar lowpass response with, say, 100 MHz cutoff and impulse-response tails below, say, 0.1% after 10 or 12 ns. With parts we can buy! Our existing 5-pole LC filter is doing this pretty well.

John

They're passive filters. There's a section of transmission line in the middle that's going to interact with the two filters. Have you done this, to back up the "all you have to do" claim? It seems like it'd be a good start, but I suspect you'll have to do more than that, particularly if you want to preserve time domain behavior.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

How long is the cable between the sections? Seems like reflections be a problem, right? It shouldn't take too much to split a filter into two sections, but you might have to modify at least one side (with an appropriate network) to make it look more like the connecting cable's characteristic impedance.

Actually, why can't the whole thing be in the main box, if you're trying to reduce the bulk of the remote box? Would flattening the input impedance of the filter fix the problem so that this would work?

I suspect that anything you do with a transmission line in the middle is going to have reflection artifacts from the transmission line, unless you insert either an attenuator or an isolation amplifier in there. If you're looking to see tiny reflections 10ns later, you don't want your electronics donating them.

I assume that you want to hold down the number of components in the remote box, for space considerations?

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

Of course, buffer amp is the simplest. Just for the sake of argument, there are many ways to do lossless or nearly lossless passive matching circuit from/to a complex impedance.

VLV

There would be opamps, line drivers and receivers, too. So the filter halves are truly isolated. I certainly wouldn't throw a few feet of coax into the middle of an LC filter... even if I could guarantee that the length would always be the same.

John

You could easily split the filter into 2 and 3, or 2 and 4. 3 and 3 won't work because a 6-pole bessel has all complex poles, and that's kind of hard to get with a pair of two isolated three-pole filters.

Someone else asked this, but I have to reiterate: why filter in the measurement head at all? Why not just let the pulse remain unfiltered until it hits your big box?

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

e e

el

ize

the

d text -

Just a question re the filter spec:

You say, 100 MHz cutoff and impulse-response tails below, say, 0.1% after 10 or 12 ns.

Is that =963dB at 100MHz and 10ns from the pulse starting edge? =9660dB at 150MHz? Just trying to sort out the time domain and freq domain spec.

If my assumptions are correct you=92ll be using some controlled impedance line for the interconnect. So at some point you'll have to match accordingly. Regardless if it's a buffer or the filter to line. It's smart to use a buffer for isolation.

Re placement of the filter, Tim has a valid question.

For LC filters I tend to dodge the maths and use this online utility:

though it does not optimise the values to ones which are common, so there is some iteration involved, more for more poles.

Coilcraft seem to do some nice 5% shielded 1812 filters for the frequencies I deal with (100's of kHz) though the footprints are problematic. I think there are second sources of such devices around, which is convenient.

I was looking at Bessel characteristics recently with the thought of improving a 3 pole LC to 7, and realised that a Bessel's rolloff is about the same for a 3 and 7 pole filter, until you get beyond 3x cutoff I think. Are you sure you want the hassle of a 7 pole?

Nemo

l

ze

e

Is absolute phase dly an issue? If it's a good quality cable group dly won't be an issue. A bigger problem might be match, i.e., return loss at the cable interfaces. This could affect ripple and loss in band.

text -

Actually I realized after I posted that if you're trying to reduce the amplitude of the pulse to make for easier amplification, and if you're trying to impedance match to a cable, filtering in the measurement head may be inevitable.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

You can not create a 6 pole filter from two 3 pole filters. The reason is that a 6 pole filter hase no real poles. All (realizeable) odd order filters have at least one real pole.

Jon

The photodiode pulses are too fast to economically process with opamps, especially preserving linearity. So it's nice to filter them down to 100 MHz, 3 ns glitches maybe. Then we go over a cable to the main board, in a bad EMI environment, so it's good to filter there again. Thus the desire to make a split filter. As I mentioned, we have the radar problem, the need to resolve small signals 10 or so ns after the big pulse, so the filter has to recover fast and clean. A 5-pole Bessel is pretty good;

But I've run into this gneral problem before, splitting an LC filter into sections. It's common to have an opamp section that, intentionally or otherwise, add a single pole, and it would be nice to use that, or compensate for that, in a successive LC filter design. I don't think I've seen that discussed anywhere.

Do you know of any software that will design the L and C values for some arbitrary transfer function? That would sort of do the job.

John

I wish people made more packaged filters, either silicon ICs or ceramic multilayer things. If you do a DDS synthesizer or arb, the filters are bigger than the FPGA and DACs combined, not to mention a huge pain to design. Mini-Circuits has some ceramic filters, but nothing below 80 MHz and sort of ugly responses.

Low-order Bessel filters have lopsided impulse response and long decay tails, which smears our big main pulse into the smaller reflections. 5 poles and up look pretty good.

John

When I've needed to do that I've just used Maxima, Maple or that ilk, at least for the sort of low component count filter you're talking about.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

Then we'd have to go 4 poles on each end, or else do something that's not quite a Bessel but behaves about like one. Still messy.

I want a filter that will take a very narrow impulse and shape it into a sorta Gaussian blip, maybe 3 ns wide, and be totally recovered (to

0.1% or less) in 10 or 12 ns after the response peak.

What I need is software that accepts a time-domain response mask and finds the parts values. That has nothing to do with classic filter responses.

John

le

he

sel

s

rize

the

John,

Go download the eval copy of Eagleware. Eagleware was bought by Agilent sometime back. Make sure you download the vers with the Filter and Active Filter package. You should be able to goggle Eagleware and get the link. At least 6 months ago that was the case.

Makes doing what you're talking about very easy. I use to do all this stuff by hand and tables. I've use the uwave filter program with good results. Certainly helps in trying to solve difficult probs.

good luck.