filter-design with identical part-values in multiple/sub-multiple numbers

Leapfrog design will let you do that. You need to use topologies that use one op amp or more per pole. To get the flexibility in the component values, you need to break the filter down to basic integrator stages and summing nodes. Then the problem is a simple signal flow graph.

There is an odd configuration (one of the Friend topologies I think) that can do this as a cascade of biquads if you can't do leapfrog design. I don't have it handy since I don't cascade biquads.

miso schrieb:

I asked for passive filters. Sorry for didn't clarify that.

- Henry

Restricting the variety of parts has some minor advantages, but on the face of it this doesnt strike me as a good match to such an approach. But you've not said what sort of filter youre looking for, in terms of its frequency characteristics etc.

NT

Coffee? Electronic? Digital? Child-friendly?

RF? Audio? Microwaves? Highpass? Lowpass? Bandpass? Band-stop?

In amateur radio practice it's not uncommon to see "half wave" and "quarter wave" filters -- the quarter wave filter is just a PI-section LC filter with component values selected so the reactance is 50 ohms at the design frequency (this for feeding a 50 ohm transmission line). A half- wave filter is just two quarter-wave sections concatinated (so the middle cap is 2C.

Circuit analysis is up to you: it works fine for hobby radio construction, but I have absolutely no clue how it works for more critical applications, nor do I know how well it would extend to more sections.

I am pretty sure that the quarter-wave filter, when terminated at the characteristic impedance at both ends, makes a 3rd-order lowpass filter with a Q of 1 -- but don't count on even that much.

L L Vin ___ ___ Vout o-----o----UUU---o---UUU----o-----o | | | | | | --- --- --- --- C --- 2C --- C | | | L=Zo/(2*pi*f) | | | C=1/(Zo * 2*pi*f) | | | Zo = charact. impedance === === === GND GND GND (created by AACircuit v1.28.6 beta 04/19/05

Tim Wescott schrieb:

Nice question. I will answer Bessel, Gauss, Tscheby... etc. So I'm looking for the filter-class mathematical model.

I made a sim with LTspice for the Hagerworth-Filter and it looks good. He even shows the coefficient calculation but no theory. Maybe it is just found by playing around?

- Henry

My experience with tweaking passive filters by fiddling around has been dismal. I soon get into divergencies, lost in solution space.

The Nuhertz filter design software is great. It will design all sorts of LC filters, including ones most people have never heard of, using standard-value finite-Q parts.

John

"John Larkin" wrote in message news: snipped-for-privacy@4ax.com...

It's not that hard. Ok, if you're doing a high order (>10 poles??) filter, sucks to be you, but small filters are pretty easy.

Nice thing about SPICE is you can create a metric from standard components -- e.g., if you're interested in step response, then you can drive it with a step, and calculate the RMS error from an idealized response. And you could generate that response from a Laplace domain transfer function, or from a stepwise approximation. And you can weight the error increasingly with time (i.e., you don't want a solution that keeps on ringing!). Then set up some sweeps for each component value you want to change and simply select the lowest final voltage on the error summation node.

Unfortunately, this process does fall victim to traditional "compute what I thought was the best" solution errors, i.e., if you want a smooth pulse response, but weight the error in such a way that it doesn't matter if the error is above or below the desired response, then it will gladly oscillate above and below, at least for most regions of the solution space.

As for filter types with similar component values, you'll have the hardest time with Bessel filters. Typical designs have a really high pole out front (e.g., f_0 of L1 + C1 is 5-10 times the cutoff frequency of a lowpass) so you will always see much smaller values there. Butterworth seems to have reasonable values, at least for a couple orders; to get proper Cheby response you'll probably have to go with more critical values. And as always, rounding becomes very important in high order filters.

Tim

Tuning high order filters starts with working in reflection, which makes the bumps much more obvious. The next thing to do is to get the right number of bumps (n-1 extrema usually), spread out over the right bandwidth, and only then tuning for the detailed response.

It's normally really easy to get a nice-looking response that's a bit too narrow, but it's very difficult to get from there to the desired bandwidth--you need to change the section resonant frequencies, but the adjustments change L and C. Grid-dipping the individual sections helps a lot, and for high-Q filters, you can always use the Dishal method, which allows you to tune each section resonance in the circuit, looking only at the return loss.

I was taught this art about 30 years ago when I worked for the phone company,(*) by a crusty old technician who was probably 28 at the time. His name was Brian Murray, and he unfortunately died a couple of years ago. He was a dedicated motorcyclist--he even came to my wedding in leathers.

Cheers

Phil Hobbs

(*) Microtel Pacific Research in Burnaby BC, part of AEL Microtel, formerly GTE Lenkurt of Canada (also now defunct).

Grid dipping sections, sounds like something you'd do with one of these beasts:

Tim

-- Deep Friar: a very philosophical monk. Website:

Tuning loosely-coupled bandpass filters for frequency response isn't hard. Tuning higher-order lowpass filters for both frequency response and settling time is, at least for me, very hard. I'm talking about anti-aliasing LC filters for ADCs and DACs, where fast settling to a fraction of a per cent, and proper image rejection, are both important. These tend to be "transitional" filters, nearly gaussian in the passband but dropping fast at higher frequencies. The Nuhertz software can do in minutes what a week of fiddling can't, namely make the filter you want from parts you can buy.

(Even then, we sometimes do a Nuhertz design and then hack in an unauthorized notch or two, and check that in Spice.)

John

I've actually never tuned a filter for settling to high accuracy. I can believe that that's a harder problem.

Cheers

Phil Hobbs