The two or four pole filter?

[guitarhacknoise]

hello!
Been looking at state variable filters and the like,
So I've gotten to  wondering what makes a filter Two pole and what makes it Four pole?
Is it that a Two pole would have two LP stages set at two differant Q's?
I have no clue, but would like to know!
Any knowledge shared is MUCH appreciated.
-matthias

[loscha]

two pole has a cuttoff slope of 12 db/octave
four pole is 24 db/octave

the different pole counts also make them sound different when you have the resonance higher, because in a 24db/oct filter, the resonant notch is tighter, giving a sharper spike in the spectrum.

[Mark Hammer]

The Q is given by the way the corner frequencies are situated and any gain built into active circuits.  The number of poles is simply the number of sections.  For example, if you had four consecutive sections with a 10k resistor in the signal path followed by a .001uf cap resistor to ground, that would be a 4-pole filter.

Of course, it is not always easy to identify when a particular component constitutes a filter section/pole.  For example, one often sees filters constructed around single transistors in choruses, flangers, and anything else using a BBD chip.  A common configuration is an RC combination (as described above) at the input, an RC combination at the base of the transistor, and a capacitor that could be described as "returning" from the emitter back to the input side of the base resistor.  That is a 3-pole lowpass filter.  The signal "returning" to the base provides another pole/section of lowpass filtering, dictated by the cap value.

Filtering can also be distributed across multiple devices.  For example, I like to use cascaded clipping stages that each have 1-pole lowpass filtering in them, provided by a simple cap in the feedback path of the op-amp.  Gather 1 pole here, another pole there, and another pole elsewhere, and you have 3 and sometimes even 4 stages iof lopwass filtering, even though no more than one stage/pole resides with any single semiconductor.

[SeanCostello]

One interesting tidbit: In a four-pole filter such as the Moog ladder, when the negative feedback is increased, two of the poles head towards the imaginary axis in the s-plane, while the other two head AWAY. In other words, the actual "resonant" part of the Moog filter has pretty much identical characteristics to the resonant part of a 2-pole filter such as a state variable.  The other two poles in the Moog filter contribute to the steeper cutoff away from the resonant peak.

So, it would be possible to simulate a Moog filter by two second-order sections in series, with different Q (and possibly frequency) characteristics. The nonlinear characteristics would probably be different, though.

Sean Costello

[guitarhacknoise]

Thanks guys,
Still A little lost, Not your fault.
Mr. Hammer said:
"The Q is given by the way the corner frequencies are situated and any gain built into active circuits. The number of poles is simply the number of sections. For example, if you had four consecutive sections with a 10k resistor in the signal path followed by a .001uf cap resistor to ground, that would be a 4-pole filter.
Of course, it is not always easy to identify when a particular component constitutes a filter section/pole."

So I guess I'm on the right track.
I obviously need to do a lot more reading!

Loscha say:
"two pole has a cuttoff slope of 12 db/octave
four pole is 24 db/octave. the different pole counts also make them sound different when you have the resonance higher, because in a 24db/oct filter, the resonant notch is tighter, giving a sharper spike in the spectrum."

Does this mean that the desired cutoff is around 6 db/pole?
db is definetely on my reading list.

Sean :
"So, it would be possible to simulate a Moog filter by two second-order sections in series, with different Q (and possibly frequency) characteristics. The nonlinear characteristics would probably be different, though."

I think I'm confused with the differance of Q and Freq.

I'll be back with more questions. (Hopefully)

-matthias

[Johnny Guitar]

I think I'm confused with the differance of Q and Freq.

A very simple explanation (all I'm capable of) is that frequency is the ....er,... eh, frequency of the cutoff of the filter  :oops: (not sure that helped). Q is sometimes called resonance. It is where the output is run back into the input of the filter. On many synths, when the Q is raised a high enough level, the filter will start to oscillate (produce it's own tone at the cutoff freqency).

I can't think of an example from a song/instrumental but I think we have all heard a flter slowly sweep over a a very rich signal (like white noise) and as the filter sweeps a real pitch or pitch range is easily discernible as a "cheesy" wind sound. This is possible due to having a high reaonance on the filter.

While many fiters we encounter have variable frequency (parametrics, the treadle of a wa wa pedal both do) many don't (the tone control on a guitar or amp, a fixed high cut control on a mixer, each band of a graphic EQ).

The resonance control is somewhat rarer (the bandwidth control -- is that right? -- on a parametric, and many VCFs on synths).

Hope that helped a bit.
J

[space_ryerson]

I'm not sure if this helps much; but the manual for the access virus b explains filters (and all of a synth's functions) in layman's terms well enough for me to understand.

You can download the pdf of the manual at their website here.

edit: link doesn't work quite right. Instead, click on the link, and go to Support:Virus KB; scroll to the bottom of the page; and the file is called Manual Virus B Series (english).

[puretube]

6dB per cap...
(LP & HP)

[Mark Hammer]

When it comes to filters, corner frequency or centre frequency describes what does and doesn't "get through".

Filter slope (e.g., 1-pole, 2-pole, 6db/oct, 18db/oct, etc) describes how abruptly the filter rejects content beyond the corner frequency.  For example, if you have a passive crossover for your speakers, a 6db/oct highpass filter for your tweeter will still let a lot of mids and bass through, which could blow your tweeter.  In such cases the corner frequency is set higher, so that even with a 6db/oct slope, there won't be enough in the way of mid and bass energy to blow your tweeters during kick drum hits with the volume up.  If the slope is made steeper, you can afford to move the corner frequency downwards a bit because the filter is more selective (i.e., rejects more of the bass, relative to highs).

The filter Q, on the other hand, describes the relative emphasis within the passband.  That is, among the frequencies that are passed without any attenuation, is there any difference in amplitude.  Since we are talking here about *additional* amplitude, rather than relative *attenuation*, it is no small surprise that Q/res and gain are interrelated.  When you look at an op-amp-based bandpass or lowpass filter, you will see that the Q is determined by exactly those resistors that set the gain of an op-amp stage.  Take a look at the simple bandpass filter of a Dr. Q or Baseballs, and you'll see a 470k feedback resistor in the bandpass section.  Increase it and the Q will go up as will the gain/level.

One of the cool things (or rather, musically convenient things) about lowpass filters is that when the Q/resonance is cranked, they acquire the sonic properties of both lowpass AND bandpass filters.  Wahs and other bandpass filters sweep where the sound is emphasized, but they do so at a cost of the "mass" of the note.  Things tend to thin out at the high end because you lose the bass.  However, when you increase the Q of a lowpass filter, you get a pronounced emphasis at the corner frequency that sounds very much like a bandpass filter to most ears, BUT, you do not lose the bass below that corner frequency.  Personally, I think this was one of the factors that made the Mutron III such a mainstay amongst bass players in the 1970's and afterwards.  Most of the envelope-controlled filter pedals made by E-H were bandpass in design, and while they sounded funky for guitar and were more than adequate for rhythm work, they sucked for bass BECAUSE they were bandpass.  A pedal like the Mutron made it possible to emulate the sorts of things guitars could do (i.e., bandpass-like sounds created with high Q) without losing the bottom and foundation of the rhythm section.  I suspect this is one of the reasons why E-H teamed up with Mike Beigel to re-release the basic Mutron design (plus changes) as the Q-Tron - it simply appeals to a much broader market (guitar AND bass) than most of their other filter pedals did.....Tube Zipper notwithstanding.

[puretube]

http://focus.ti.com/lit/an/sloa093/sloa093.pdf
(filter design in 30 seconds...)

[zachary vex]

as puretube stated, each time you throw a frequency-filtering cap into a stage of a circuit you've added another 6dB/octave "pole".  if you've chosen these caps at the different stages of the circuit to focus on the same frequency, you end up with another 6dB/octave for each pole... if there's 2 of them, you get 12dB/octave, 3 gets you 18 dB/octave... and keep in mind that the idea is to have each of the poles focused on the same frequency so the cutoff point sounds more and more dramatic as you add poles.

basically, if you use a single-pole (6dB/octave) filter you get the same kind of filtering you get from a tone control on your guitar, which consists of a variable resistor from the pickup connected to a cap to ground.  if you built a second tone control into a box with a little buffer in it, you could set it to the same setting as your tone control on the guitar. it would then give you 12dB/octave filtering at the selected frequency, which is a 2-pole circuit (one in the guitar, another in the box).  the sound of the filtering would be "steeper" and therefore more dramatic than the one tone control in your guitar.

steep filters (brick wall, as they are often called) are used to completely elminate frequencies you don't want to hear... you'll notice that your rather wimpy 1-pole 6dB/octave filter in your guitar does still let some of the higher frequencies leak by.  every time you add a pole, you're shutting out more of the stuff you're trying to get rid of.

[puretube]

http://focus.ti.com/lit/an/sloa058/sloa058.pdf

http://focus.ti.com/lit/an/sloa062/sloa062.pdf

http://focus.ti.com/lit/an/sbfa001a/sbfa001a.pdf

[puretube]

watchit ! 3.6MB...
http://focus.ti.com/lit/an/sboa093a/sboa093a.pdf

[guitarhacknoise]

AWESOME!
HUGE THANKS!
I really appreciate all the explanations and guidence.
Puretube:
man, you wer'nt kidding.
That last link turns out to be over 80 pages!
My boss would kill me!
I might have to print that out at home on the crappy inkjet!
-matthias

[puretube]

one more:

http://www.microchip.com/stellent/idcplg?IdcService=SS_GET_PAGE&nodeId=1406&dDocName=en010007

(dunno if it has already been posted before... just stumbled across...)

[RedHouse]

There is also an old book by Don Lancaster called "Active Filter Cookbook" which is quite good on this.

[davebungo]

One of the cool things (or rather, musically convenient things) about lowpass filters is that when the Q/resonance is cranked, they acquire the sonic properties of both lowpass AND bandpass filters.

It's worth pointing out that this doesn't apply to first order low pass filters as Q/bandwidth doesn't really exist.

[bwanasonic]

basically, if you use a single-pole (6dB/octave) filter you get the same kind of filtering you get from a tone control on your guitar, which consists of a variable resistor from the pickup connected to a cap to ground.  if you built a second tone control into a box with a little buffer in it, you could set it to the same setting as your tone control on the guitar. it would then give you 12dB/octave filtering at the selected frequency, which is a 2-pole circuit (one in the guitar, another in the box).  the sound of the filtering would be "steeper" and therefore more dramatic than the one tone control in your guitar.

This sounds like it accounts for the *sweetspot* effect that I try to exploit when using wahs/envelope filters. By slightly rolling back the guitar tone knob, it seems like you get a steeper filter effect.

Kerry M

[aron]

Great thread. Archive material. Thanks guys!

[puretube]

 for filters, see section 5...
http://www.analog.com/library/analogDialogue/archives/39-05/op_amp_applications_handbook.html

watchit: huge downloads/#pages...