Can anyone answer my hypothetical question about filters?

[zxcvb]

As I understand it, the ideal frequency response for a filter is that we want maximum gain in pass band, a vertical or instant cutoff and 0 in the stop band, however this is ideal and can never be achieved in real life.

Along came Butterworth and found a relationship / formula for choosing the right combination of inductors and capacitors to be able to create filters that matched a certain spec and resembled the frequency response that we want - but not ideal.

With the exact same filter structure along came Chebyshev and he worked out an even better formula to get an even tighter / more tuned relationship to give us a filter that was closer to idea than Butterworths relationship, for example a much more steeper transition band than the same design using Butterworths.

Then again, along came Cauer with his own method of calculating the relationships and values needed to get an even better and closer approximation to an idea filter. With the steepest transition yet.

With all these, they haven't discovered a new "structure" or found that by making a different connection you get a better filter, but instead each one devised a better and more accurate formula for choosing the values of your components to get your filter close and closer to ideal.

So my question is this.

Lets say we are dealing with a 5 order low pass filter. (The type doesn't really matter). With Butterworth we have a good filter, then still using a 5th order and same structure Chebyshev was able to "tune" it even more to create and even better response, and then the same with Cauer.

Now if I was to take my 5th order structure and was able to simulate for every possible inductor value and capacitor value would I find a combination that would give me the best possible / closest model to ideal, that beats all previously known filter types?

And then when someone is able to devise or work out a relationship linking all these values together and with the spec thats required it would then be a classified its own filter type such as Butterworth etc?

My second question is then,

Do mathematicians / engineers know of a "best" filter response that is physically possible for a given order but so far do not know how to create it.

Similar to saying, if NP = P was proven it would mean we know for sure that there are solution to the problems but we haven't worked out yet how to get there / havnt worked out an algorithm for it. (Sorry if thats a bad example or its wrong but its the best analogy I can think of for now)

PS: the filters I got was bought from http://www.kynix.com/Parts/2686543/5487BP15C675.html.

 

[ruffrecords]

All low pass filters of this sort have a time delay. A perfect brick wall filter has an infinite time delay so although it is the 'best' solution you never get to hear how good it is.

Cheers

Ian

 

[gyraf]

spam?

 

[abbey road d enfer]

Now if I was to take my 5th order structure and was able to simulate for every possible inductor value and capacitor value would I find a combination that would give me the best possible / closest model to ideal, that beats all previously known filter types?

Butterworth, Chebychev, Legendre, Bessel are all variations of the same type of filter.
They are all optimised for different things. For example, Butterworth is the flattest in the passband when Chebyched has some ripple, Bessel is optimized for lowest overshoot...
You can't say one is better than another; it all depends on what you expect.

Do mathematicians / engineers know of a "best" filter response that is physically possible for a given order but so far do not know how to create it.

The "best" filter is the one that ticks all the cases. If you want minimal overshoot, it is the Bessel, although it has the gentlest slope.
The Cauer (elliptic) filter has the steepest slope, but a very poor transient response and does not attenuate enough the out-of-band signals.

 

[JohnRoberts]

spam?

good chances.... not sure to what end...

perhaps to accumulate posts.

JR

 

[abbey road d enfer]

good chances.... not sure to what end...

perhaps to accumulate posts.

JR

I think it's a pretty fastidious way of doing that. At least the guy seems to be dedicated...

 

[Newmarket]

Haslet ?

 

[gyraf]

whaddyamean haslet?

 

[Bo Deadly]

spam?

Yes.

They're disguising an advertisement as a legitimate post. Just like any banner ad, there's an image of the product and a link to it. In this case the image is of electronic components and the link is to an electronics distributor in HK called "Kynix".

Basically they just scrape some vaguely relevant content off of some other page and then add a little PS at the end with the link. You can probably find the source content by searching google for a somewhat unique phrase in quotes to assert an exact match. I used "along came Cauer with his own" and found the source site on the first try (itectec.com).

Clues to watch for are discontinuity between the content and what the link points to and advertisement-style images. In this case, there is a well formed and intelligent description of filters but with a nonsensical image and much less well formed "PS: the filters I got was bought from <link>".

Another tactic would be to post scraped content to a few posts and then come back later and change the signature to a link.

Note that normally the moderator might just delete an account like this and all of it's posts with it. But strangely the first post from this user, which did not contain images or links but the content was scraped from this page, triggered the whole "current through a capacitor" discussion which you may not wish to delete (although I personally I wouldn't miss it).