Tricky (posablly) RC Filter Question

[Johnny G]

OK, with a simple lowpass RC filter. the equation to work out the breakpoint where the level is -3db is 1/(2 * pi * Resistance * Capacitance). im im not mistaken thats %70 of the origional signal voltage level

how could you go about finding the frequency at which it would be %95 or %80. is there a realativly simple way of doing it or are we talking heavy integration etc here?

cheers in advance guys

[Satch12879]

Yes you can fairly easily but you wouldn't use that equation to do it.  That expression only gives you the so-called corner frequency.

I'm at work and don't have my textbooks in front of me but you need to compute the reactance of the capacitor and then compute the impedance of the entire filter which you can express as a percent attenuation of the input signal voltage.  I've made up a little Excel spreadsheet that does it, but again, it's at home.

Hopefully someone on the board can fill this in...

[stm]

The answer is simple (after you do some Laplace and complex number algebra):

Code Select Expand


                               2
                    sqrt( 1 - a )
                f = -------------
                     2·pi·a·R·C


Where:

'f' is the frequency at which an RC lowpass filter has an attenuation of 'a' in volts/volts.  In other words, 80% means a=0.8

Regards,

STM

[Satch12879]

Very nice.  Didn't think Laplace was involved...

[Johnny G]

beilliant. thats exactlly what i wanted.

satch thinking about it thats a really good point and if id thought about it more then i should have realised that.

stm, cheers a bunch thats exactlly what i was looking for. very helpful.

[Satch12879]

:mrgreen:

I'm glad, now you're starting to think like an engineer!

[Johnny G]

lol now theres an undeserved compliment. god forbid anybody think i actually know what im doing

[Transmogrifox]

Jonnny (and others in this forum) :  I give you a lot of credit for not being scared of this stuff and thinking, "That's way over my head".  With enough questions, trial and error, you will get to where you can legitimately engineer pedals--then you can do mods more purposefully.

Often times multiple order filters are used to keep the pass band flat up to near the corner frequency, then drop off fast afterward.  A 6th order butterworth filter truly makes a nice ideal filter approximation, but doesn't sound good in the audio realm because it rejects harmonics too much.

[Johnny G]

lol thanks man. i dont really think theres much with regards to FX im scared of. generally its not as if the maths is hard, unless we're talking phase calculations with filters where you have to do some natty integration tho even that i should be ok with.

ive found that the majority of stuff in the FX world seems to revolve around building blocks and biasing. eg pedals can be made of different sections like the geofex FX Bus idea, or different sounds come from biasing things in different ways to generally create different clipping and distortion. atm im very loosley thinking of making a DIY resource website based around the idea.

as for the multiple filters i can see that it would be a great way to keep things relativly flat up untill the breakpoint tho i didnt realise that about the harmonics.

and talking of butterworth filters etc. do you know of a website that actually gives detailed descriptions of what exactly makes a filter a butterworth or chebyshev or bassel etc. i have a book entitled "Practical Electronic Filters" by babani electronics books and it gives the differences between those three types but doesnt explain what makes each what it is. as well as that i havent been able to find anything on the web.
cheers if you know of anything. i may start a new thread on this so i can get a few more people reading it

[Transmogrifox]

I'm not sure I can recall any web sites I've seen recently that describe it.   Lancasters Active Filter Cookbook gives a fair deal of useful information about the practical aspect of generating these responses.  Otherwise, I have seen discussion of it in a couple of my circuits and I think my RF analog electronics text has something about it.  If you're interested enough in it to buy a book, I can look up the title and author of my texts that have that info.

These filters are generally classified by a particular pattern of pole locations in the complex plane--IE, elliptical filters form an ellipse around 0,0---and I believe off the top of my head, if the magnitude of the distance from the origin is greater than 1, it's not a filter, but an oscillator.  I have dealt with the discrete version in DSP in a little more depth (in the e^(jw) plane) in terms of digital filtering, but the two phenomena are very similar and can be mish-mashed interchangeably as long as one is aware of the important discrepancies and assumptions about digital vs. analog signal processing.

All the same, a Chebychev I believe is in the elliptical filter family.

Here's a real brief run-down of the strengths of filters:

Butterworth:   Flat pass-band and stop band response

Chebychev:   Good stop-band rejection, better approximation to ideal filter in terms of magnitude being near unity up to stop band, however, pass band ripples are the downfall of the idealized approximation.  I conjecture that a wide-bandwidth 4rth or 6th order cheby filter with greater than 6 dB ripples would begin to sound similar to a phasor.  One would have to design so that the stop bands don't sweep far into the audio range on a 6th or greater order filter.

Bessel:  Linear phase filter, accomplished by transmission zeros.  Not particularly flat, generally not as easy to accomplish good rejection in the stop band, however I think these would make a very interesting audio filter effect.  It would take some careful design to modulate a Bessel filter precisely enough to keep the filter parameters in the "bessel" category.



I have made my envelope filter in a modular manner so that I can easily remove the filter board and put others in it, so I intend to experiment with different filters when I complete the project.

I hope you (whoever reads this post) have found the information interesting, and if I stated anything incorrectly (for those of you who are well-versed in analog filters) please correct me.

[Johnny G]

wow, a chance to actually use imaginary numbers lol. never thought thatd happen. i understand what you mean about being an eliptical filter and how if the distance from the origin (i take it it would still be the modulus here ye?) is greater than 1 then you get an oscilator. i assume that the distance is proportional to the effective impedance at certain frequencies going between infinite at the origin and zero at a distance of one away (hence the oscillator with negative impedance)

if you could come up with the name of a book that goes into it fairlly indepth then id be highlly tempted to get it. i dont mind going into the whole imaginary numbers thing. was one of the few parts of doing double maths A level i was pretty good at

cheers for the info man. inever thought maths would actually be useful

[Transmogrifox]

The reason this math is seldom useful in analog circuit design is that somebody has already done it and condensed their results into an algebraic "design equation" form, so we don't need to re-derive the elliptical filter math and theory every time we want to design one.

The theory is interesting all the same, and it certainly helps one understand the "design equations" much better.

[Johnny G]

aahhhh i see. so thats why we already have the nice simple RC filter equations and not hulking great behemoths that would scare anybody but a hardened electrical engineer. yeah thats sensible if a little boring