What's this notch filter called that I just "invented"?

[Fancy Lime]

Hi there,

I've been tinkering with a high gain distortion type of thing and was looking for a better mid control. Several iterations of various bootstrapped and non-bootstrapped Twin-T and Bridged-T topologies brought me to this:



I have never seen that done like that and have no idea what it is called. Semi-bootstrapped bridged Pi? The result of a Sallen-Key filter crashing into a bridged-T? Does anyone know? You sometimes see the non-bootstrapped version of it but I don't even know what that is called. Bridged-Pi? Dual bridged-T? Most generally, it is a kind of ladder filter, but I'm sure someone must hae used it in the past and given it a name.

To the filter itself: I really like it. It is one of the few ways I know to get a pronounced asymmetric notch from a single filter stage. With the Mids at full, there is a -3db notch at 230Hz, which can be eliminated by using a 250k pot. With the Mids pot at 10k (the middle position assuming audio taper), the notch has deepened to -24db and shifted slightly up to 300Hz. At the same time, a resonant hump of 3db appears at 100Hz. With the Mids all the way down, the notch shifts to 700Hz and deepens to 36db, while the boost hump rises to 5db at 150Hz. With all this interaction between frequency, depth, and Q, the range of scenarios where this thing is really useful is certainly limited. But for a Muff or Rat type circuit, where one wants a kind of mud control without loosing all the bite, I can see this being useful. One may want to increase R2 to 4.7k or something, though, for a more useful range. And I would definitely add a treble control. That combination is much more useful to me than most of the usual 2-band EQ schemes employed on high gain drive pedals.

Cheers,
Andy

[Rob Strand]

I've read zillions of filter papers and I've never see it with a name.

The result of a Sallen-Key filter crashing into a bridged-T?

Pretty much.

There *is* a more formal way to view it though.  If you make the input ground and then make the ground the input, what you get is a first order low-pass in cascade with a second-order high-pass.   There is a circuit theorem called the complimentary transformation (?) which lets you get new transfer functions with such a trick.

For example take a first order RC high-pass followed by an RC low-pass.  That is a crude RC band-pass filter.    Now do the input and ground-flip transformation and you end-up with a bridge-T circuit which is a notch.

In your case you start with asymmetrical band-pass then that becomes an asymmetrical notch.

I believe the electronics book by Sedra and Smith has some stuff on the complimentary transformation.   It's very much an example of the high-level circuit theory tricks you see in academic papers.   There's no magic it's all provable with maths.  If the original circuit is transfer function is H(s) then the flipped one is 1-H(s) ; something like that.

When I did research work on new filters I used that trick a lot to come-up with "new" configurations.
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Just as a simple example,

If you have a divider input ---> R1  then R2 to ground you get Vout/Vin = R2/(R1+R2).
If you apply the input & ground flip trick you expect to  1 - R2/(R1+R2) = R1 / (R1 + R2)
which is exactly  the result you get directly from a divider with  input --> R2 then R1 to ground.

[swamphorn]

The RC portion resembles the Hall Network notch filter (a single-pot tunable notch filter¹) but I have never seen a bootstrapped version, nor am I sure if it would work if you bootstrapped both grounded resistors.

¹ http://www.kennethkuhn.com/electronics/hall_network.pdf

[Fancy Lime]

Hi Rob,
the input-ground-flip trick is neat! Never heard of it before but I can think of a lot of situations where that may come in handy. Thanks!

Hi swamphorn,
that does indeed look similar. Interesting topology as well.


Cheers,
Andy

[edvard]

The RC portion resembles the Hall Network notch filter (a single-pot tunable notch filter¹) but I have never seen a bootstrapped version, nor am I sure if it would work if you bootstrapped both grounded resistors.

¹ http://www.kennethkuhn.com/electronics/hall_network.pdf

Configure that circuit with R1 as a common-value potentiometer and use the wiper as output, and you now have a "depth" control on top of that tunable notch.  See circuit #14 here:
http://chasingtone.com/yourguitaramp/guide-to-single-knob-tone-controls/

Nice.  I'm stealing it... 

[marcelomd]

The RC portion resembles the Hall Network notch filter (a single-pot tunable notch filter¹) but I have never seen a bootstrapped version, nor am I sure if it would work if you bootstrapped both grounded resistors.

¹ http://www.kennethkuhn.com/electronics/hall_network.pdf

Looks like the contour control in the Marshall Shredmaster.

[swamphorn]

...

Configure that circuit with R1 as a common-value potentiometer and use the wiper as output, and you now have a "depth" control on top of that tunable notch.  See circuit #14 here:
http://chasingtone.com/yourguitaramp/guide-to-single-knob-tone-controls/

Nice.  I'm stealing it... 

I don't believe the Hall Network and Circuit #14 are the same. Circuit 14# is a standard bridged T notch filter with the potentiometer forming the bridge; simultaneously, the pot fades between the dry and wet signals.

[Rob Strand]

I don't believe the Hall Network and Circuit #14 are the same. Circuit 14# is a standard bridged T notch filter with the potentiometer forming the bridge; simultaneously, the pot fades between the dry and wet signals.

They can't be the same because you can't transform one into the other.   The Hall network has three terminals but in Andy's circuit the network has 4 terminals ; the resistors to ground in the Hall circuit are stuck together.   If you started with  the transfer function*s* of Andy's *network* (not the transfer overall function) you could get the Hall transfer function by setting one of the inputs to zero.

There's some circuit theorems which state that the same network has the same poles and if the circuit looks the same with inputs set to zero.   Driving the network at different points either with parallel current sources or voltage sources inserted in series with any component preserves the poles but it does change the zeros.

When you have feedback that doesn't mean the circuit preserves the actual poles, since with feedback it creates different zeros and poles depending what that input port is and what the feedback port is, then for the feedback port the poles and zeros get mixed together.
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FWIW, it's possible to show that the bootstrapped Hall network results in a notch, 
1) Start with the Hall network an assume a transfer function H(s) = N(s) / D(s);   N(s) has a zero since it's a notch.
  The transfer function is from Vin to Vx, where Vx is just before the opamp.
2) Assume a gain of k for the opamp; otherwise simple bootstrapping doesn't work
3) Use the input-flip trick to get 1-H(s).   That gives you the transfer function when driving the two
  resistors to Vx.    The input however is Vout due to the boostrapped connection.
4) Using super position we can add the the results of the two Vx's  then remove
     Vx using Vout = Vx/k
5) From all that you can get a new transfer function for the bootstrapped ckt in terms of the
     N(s) and D(s) for the hall network.   What you will see is N(s) ends up in the numerator
    so that means the boostrapped ckt is still a notch.   It's doesn't say if it's a good/stable notch.

Basically the input flip trick lets you analyse the new configuration without having to solve the
big mess of circuit equations.

[edvard]

I don't believe the Hall Network and Circuit #14 are the same. Circuit 14# is a standard bridged T notch filter with the potentiometer forming the bridge; simultaneously, the pot fades between the dry and wet signals.

I didn't say they were the same, and I'm well aware of what Circuit 14 is and how it works.  I'm just saying that making R1 a potentiometer and taking output off the wiper would do much the same thing for the Hall Network that it does for a Bridged T; make a depth control. 

I just did a quick & dirty workup in LTSpice, and it works more or less.
C1, C3 = 33nf
C2 = 3.3nf
R1 =250k pot
R2 = 10k log pot
R3 = 500 Ω from R2 CCW to C1/C2 junction
R4 = 10k from R2 CW to C2/C3 junction.

That gets you a sweep from ~450Hz up to 1500Hz.

[bool]

Cool!

Call it a "LimeTone deContouRator". It needs a fancy name, heh.

[swamphorn]

My apologies, edvard; I misinterpreted your post.

[edvard]

My apologies, edvard; I misinterpreted your post.

No harm, no foul.  I figured I probably didn't explain myself the first time around.  We're cool, bro. 

[Rob Strand]

I didn't say they were the same, and I'm well aware of what Circuit 14 is and how it works.  I'm just saying that making R1 a potentiometer and taking output off the wiper would do much the same thing for the Hall Network that it does for a Bridged T; make a depth control.

Sorry, I wasn't criticising what you said I was agreeing with you.  All I was just saying it there's a strong reason why they aren't 100% same (ie. Andy's ckt is more general because it has an extra connection).

You can spend hours working out the best way to tweaking these things.

[edvard]

Sorry, I wasn't criticising what you said I was agreeing with you.  All I was just saying it there's a strong reason why they aren't 100% same (ie. Andy's ckt is more general because it has an extra connection).

You can spend hours working out the best way to tweaking these things.

Yep, I got that; no worries.  And yep, you can take any circuit and tweak it until it doesn't resemble the original anymore, and wonder how you got from point A to point B and whether the trip was worth it (ask me how I know  ).  Andy's circuit is interesting, and I may try it.  I'm on the hunt for the perfect tone control to put into an SS amp design, but like the potato chip ads say, you can't stop at just one.  Looking at it again, I'm seeing more possibilities simply due to it's resemblance to the Hall Network filter.  I'll be checking it out in LTSpice tomorrow.  Bedtime here. 

[Fancy Lime]

Notch controls are fun, aren't they? BTW, if you flip the caps and resistors (meaning: put a cap where a resistor is in the schematic and a resistor where a cap is), you get the asymmetry the other way round with the resonant hump above the notch. I have yet to spice the twin variant, which I think may be interesting as well.

If it really does not have a name, I propose "Fancy Pi Filter". Because it's like a regular bridged-Pi filter but more fancy.  How does the naming of electronic topologies work anyway. Biology rules, meaning no rules as long as it sounds Latin? Or chemistry rules, meaning you have to strictly adhere to a giant rule book, which is edited by an international cabal of superscientists in their lair below a volcano on a secret island, lest lightning striketh thee? Or physics rules, meaning someone has predicted it a hundred years ago and you have to name it after them?

Andy