Filter pole question
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Filter pole question
What does the "pole" of a filter mean?
Such as when a filter is referred to as having a two pole or a four pole.
I understand what dB roll off means but I'm a little unclear on what a pole represents.
Such as when a filter is referred to as having a two pole or a four pole.
I understand what dB roll off means but I'm a little unclear on what a pole represents.
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Here´s what I learned so far:Stab Frenzy wrote:1 pole = 6dB/oct rolloff
ie 2 pole = 12dB/oct etc.
I don't know where the term originates, maybe someone will enlighten us. I have a hunch it might be related to the number of inductors used in passive filter design, but that might be wildly wrong.
I think the term has a specific origin much like the term "bug" originates from a real bug that got trapped inside a relay back when computers were mostly electro-mechanical.
But yes, the term "pole" refers to one filter section. For a low-pass either one resistor in series to the signal path plus a capacitor to ground or an inductor in series plus resistor to ground are used to attenuate the signal by 6 dB/oct. This is one pole (for high-pass the components positions in the path are reversed). A second pole in series, identical to the first one, will take on the previous rolloff and attenuate the remaining signal by another 6 dB/oct and so on. For a Moog-type 24 dB/oct attenuation, 4 poles in series are needed.
BTW...
To constantly alter the cuttoff frequency one of the components must be variable, and the easiest is the resistance as potentiometers are more available than variable capacitors or inductors of adequate value.
So, since in a four-pole filter there are four resistors, a four-gang potentiometer is required. Add a buffer to the output to compensate for the changes in impedance and there you have a manually controllable four-pole filter.
To make it controllable by several external sources you use voltage-control. Oberheim, Roland and the SSM2040 filters all use the same configuration of operational transconductance amplifiers (OTAs) acting as variable resistors.
These weren´t available in 1966 so Bob Moog used the well-known transistor base-to-emitter inherent resistance. Nobody had thought of it before since this particularity in transistors was regarded as something to avoid rather than an active part in a design. This technique added some distortion to the audio signal so it was impractical in hi-fi terms but in the end it was responsible for the filter´s and the instrument´s musical character. Today it´s known as "Phatness"...
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That sounds right - pole from complex analysis - not that I know a whole lot about filter implementation, but if you write the transfer function of a filter down, it's of the form p(z)/q(z), (p,q polynomials taking complex arguments z) and the 'poles' are the zeros of the q function - the higher order q is, the more zeros or poles it has.
That said, if you showed me a circuit diagram I would have *no* idea :)
That said, if you showed me a circuit diagram I would have *no* idea :)
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I'd half-agree with this. You could use a 4-gang pot, but they're not commonly available in more than 2-gang. It's easy to make a 2-pole filter this way, but as good a reason as any for voltage control is to get not just external control, but higher order than 2-pole operation.Mooger5 wrote:since in a four-pole filter there are four resistors, a four-gang potentiometer is required. Add a buffer to the output to compensate for the changes in impedance and there you have a manually controllable four-pole filter.
To make it controllable by several external sources you use voltage-control.
Loads of synths use OTAs, they're common and cheap. Transistor ladders are the classic Moog-style ones, diode ladders are around but less common, and Steiner's multi-input filter is also an occasional one. What I like about the modern modulars (and some other synths) is the availability of different filter types. Lowpass gets a bit samey after a while. Nice to have some HP/BP/Notch floating around.
http://electronotes.netfirms.com/free.html
The best info around concerning poles ( and zeroes ) and synths!
The best info around concerning poles ( and zeroes ) and synths!
I'd half-agree with this. You could use a 4-gang pot, but they're not commonly available in more than 2-gang. It's easy to make a 2-pole filter this way, but as good a reason as any for voltage control is to get not just external control, but higher order than 2-pole operation.
Alps make 4 and 6-gang potentiometers. They´re used in high-quality Home-Theatre preamps. You can get them easily from Ebay and they´re not so expensive as one might think.
http://cgi.ebay.ie/ALPS-Quad-Potentiome ... m153.l1262
The motorized models even mean they´re voltage-controlled, but the motor wouldn´t be fast enough for synthesizer use.
I think there were full-range filters available in the early days (just not sure about the steepness of the curve), and the difficulty was precisely in making them voltage-controlled. See Till Kopper´s comments about the Moog filter patent here: http://www.till.com/articles/moog/patents.html
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I was looking for the Electronotes link for ages. Thanks!solderguy wrote:http://electronotes.netfirms.com/free.html
The best info around concerning poles ( and zeroes ) and synths!
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Don't forget the MF-101 and Voyager filters have 2 pole options. I find it gives a more aggressive character. Interesting summary Mooger5. I wonder how it is that the component reversal for multi-mode filters is done without any extra circuits, just alternate wiring and some switching.
I am no longer in pursuit of vintage synths. The generally absurd inflation from demand versus practical use and maintenance costs is no longer viable. The internet has suffocated and vanquished yet another wonderful hobby. Too bad.
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--Solderman no more.
Yes, 2-pole filters sound buzzier as higher harmonics are less rolled-off per octave.Solderman wrote:Don't forget the MF-101 and Voyager filters have 2 pole options. I find it gives a more aggressive character. Interesting summary Mooger5. I wonder how it is that the component reversal for multi-mode filters is done without any extra circuits, just alternate wiring and some switching.
I only knew about this pole stuff until very recently, since I started researching for an alternative to the 80017A filters in my Juno 106.
The Moog filter requires more discrete components, but it´s not impossible to implement a Memorymoog clone.
An OTA-based 2-pole (LM13700) requires few adjacent components but I think wouldn´t be appropriate to the already thin sound of the Juno´s oscillators...
The SSM2044 plus CA3080 VCA combination is perfect. I made a prototype and it sounds very moogish, only requiring a little more tweaking. When I have the time I´ll finish this project.
The multi-mode operation in the Oberheim filter (and the Steiner-Parker) is still out of my understanding, but for now I find it ingenious since it appears so deceptively simple. Instead of a switch I think a linear pot could be used to continuously select the mode. The wiper would go for the BP tap and the other two pins for LP and HP taps...
I´ve read in the Moog Music forum that a multi-mode 4-pole filter is immensely difficult to create, hence the 2-pole in the Obie.
After I read Kevin Lightner´s "Why a Moog Sounds Like a Moog" article I modded my Rogue to run on 10 Volts like the Mini, and yes it sounds a little more fatter. But curiously (or predictably) I must have miscalculated some resistor values as the filter now has a limited upper-bandwith. My Rogue must be the only Moog synthesizer in the world whose filter has the ARP error. I´ll have to revise the circuit .

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You can read lots about the filter theory, why 1 pole equals 3dB and rolloff curves around the net.
soundonsound.com has a series of articles called Synth Secrets. One chapter goes deeply into filter theory.
Here's a good wikipedia article:
http://en.wikipedia.org/wiki/Low-pass_filter
soundonsound.com has a series of articles called Synth Secrets. One chapter goes deeply into filter theory.
Here's a good wikipedia article:
http://en.wikipedia.org/wiki/Low-pass_filter
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You're somewhat on the right track, however, your equation is in the z domain which is for discreet time systems and we're discussing analog systems. You need to be in the s-domain young grasshoppa'.GeneralBigbag wrote:That sounds right - pole from complex analysis - not that I know a whole lot about filter implementation, but if you write the transfer function of a filter down, it's of the form p(z)/q(z), (p,q polynomials taking complex arguments z) and the 'poles' are the zeros of the q function - the higher order q is, the more zeros or poles it has.
That said, if you showed me a circuit diagram I would have *no* idea

As an example here is the simplification process for a fifth order transfer equation in the s (analog complex frequency) domain:

Nasty isn't it?
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