Unveiling Bridged-T Notch design

[stm]

Hi all!  I've seen interest in the bridged-T notch circuit and I decided to study it to come down with an easy-to-follow design procedure.  In addition, I am including some hints on how to tweak and adjust the circuit for your particular needs (some of them have already been mentioned).  

Code Select Expand


-------------------------
0) Definitions & Circuit
-------------------------

  fn    : notch frequency in Hz
  depth : notch depth or attenuation in dB

  Bridged Tee circuit:
                         C1
                         ||
                 .-------||--------.
                 |       ||        |
                 |                 |
                 |   ___     ___   |
            In o-+--|___|-+-|___|--+-o Out
                      R1  |   R2
                          |
                         ---
                         --- C2
                          |
                          |
                         ===
                         GND

  (created by Andy´s ASCII-Circuit v1.27 beta www.tech-chat.de)

----------------
1) General Case
----------------
                 1
  fn = ----------------------   [Hz]
       2·PI·sqrt(C1·C2·R1·R2)
       
                (    C1·(R1+R2)      )
  depth = 20·Log(--------------------)  [dB]
                ( C1·(R1+R2) + C2·R1 )
             
----------------------------
2) Simplified Case: R1=R2=R
----------------------------
               1
  fn = ------------------   [Hz]
       2·PI·R·sqrt(C1·C2)
 
                (    2·C1   )
  depth = 20·Log(-----------)  [dB]
                ( 2·C1 + C2 )

---------------------------------
3) Step-by-Step Design Procedure
---------------------------------

  a. Choose C1 to your liking (1nF to 10nF are good starting values)
 
  b. Choose C2 for the desired notch depth according to the following table:

        C2     depth [dB]
     ---------------------
       1 x C1      3.5
     1.5 x C1      4.9
     2.2 x C1      6.4
     3.3 x C1      8.5
     4.7 x C1     10.5
     6.8 x C1     12.9
      10 x C1     15.6
      15 x C1     18.6
      22 x C1     21.6
      33 x C1     24.9
      47 x C1     27.8
      68 x C1     30.9
     100 x C1     34.2
 
  c. Calculate both resistors as:

                       1
     R1 = R2 = ------------------   [ohms]
               2·PI·fn·sqrt(C1·C2)

     where fn is the desired notch frequency in Hz

-----------------
4) Mods & Tweaks
-----------------

  a. Frequency tuning

     If you move both resistors equally you change notch frequency
     without altering the notch depth. A dual ganged pot can be used
     for this purpose. Don't forget to add a series resistor on each
     pot to limit minimum value.

     My recommendation here would be: a dual ganged 100k LOG taper +
     1kohm in series with each pot, allowing a frequency tuning range
     of 100:1.

  b. Notch depth adjustment

     You can change the notch depth WITHOUT altering the notch frequency
     if you change the C1/C2 ratio without altering its product (i.e. C1·C2).

     In plain english, choose a constant K and then divide C1 by K and
     multiply C2 by K.  This effectively changes the notch depth keeping
     its frequency intact.  K values greater than one increase original
     notch depth, while values smaller than one reduce its depth.

     There is no easy way to accomplish the above with tunable elements,
     so the best you can do in this respect is have a two or three position
     switch to select from some preset depth values.  A six position rotary
     switch would be ideal.  By the way, to implement zero dB notch depth
     or all-pass response you just have to leave C2 open.

  c. Use of two independent pots for R1 and R2

     This offers an interesting option to control both frequency and depth
     but in an unusual manner.  Assuming identical valued pots and series
     resistors the situation is as follows:

     * Whenever both pots track each other (on the same value), you will
       be changing frequency maintaining the original notch depth.
            ___        ___
           / | \      / | \
          |  '  |    |  '  |
          | R 1 |    | R 2 |
           \___/      \___/

     * If R1 pot is greater than R2 pot you will increase notch depth with
       respect to the original desing value.
            ___        ___
           /  /\      /\  \
          |  '  |    |  '  |
          | R 1 |    | R 2 |
           \___/      \___/

     * If R1 pot is less than R2 you will reduce notch depth with respect
       to the original design value.
            ___        ___
           /\  \      /  /\
          |  '  |    |  '  |
          | R 1 |    | R 2 |
           \___/      \___/


Hope this is useful for somebody...  

Best Regards,

STM

[WGTP]

Great work.  I'm thinking a concentric dual pot would be cool for this application.  Here is the post that describes how to modify the James version at Duncan Amp Tonestack simulator to see what is going on, (after you do the math of course).

http://diystompboxes.com/sboxforum/viewtopic.php?t=22908&highlight=&sid=08d2e9978150f92e12666b77ff354f17

[stm]

The idea of concentric pots is a clever one!

[strungout]

That's pretty cool, thnx. I was just wondering about the formula for the notch depth to make me a little list. I'll just print yours

you forgot to talk about width! Making R1 variable (while R2 remains static) allows you to expand or contract the notch width. Let's say notch Fc is 159Hz, we have two slopes coming down to 159Hz from (let's say) 165Hz (set by bridging cap) and 154Hz (set by the lowpass filter). So lowering R1 would nudge the lowpass Fc away from the 159Hz notch Fc.

Hope I got that right.

[B Tremblay]

This information is great!

One question: what is the effect of series resistance placed between C2 and ground?  Does this affect notch depth, frequency, or both?

Thanks again for your contribution.

[stm]

Glad you asked!

About a week ago I gained new understanding on this circuit, but didn't post it because interest seemed to die soon.

OK, instead of adding a series resistance with C2, there are two more tweaks taht can be added to this circuit:

1) Place a parallel resistor with C2 (let's name it Rp).  This attenuates low frequencies, producing an overall increase in the high frequency content.  The response of the filter now is identical to a typical Fender or Marshall tonestack in the sense that you have a notch and low frequencies are more attenuated than high frequencies.  There are two advantages in this:

  a. The circuit has minimum possible attenuation, since very high
      frequencies pass directly through C1 (0 dB).  On other tone stacks
      you can have an overall insertion loss in the range of 6 to 20 dB!

  b. You only need two capacitors and three resistors to implement a
      fixed-setting typical tone stack response.  On the other hand, if you
      replace values on a standard tonestack, you may need up to three
      capacitors!

2) The dual circuit consists in placing a series resistor with C1 (let's name it Rs), thus attenuating high frequencies while letting low frequencies pass without attenuation.  Perhaps this circuit is of less interest than 1)


Now to the formulas.  In case 1),  the attenuation suffered by the low frequencies is:

  AL = 20·Log[ Rp / (R1 + Rp) ]


And for case 2), the attenuation suffered by the high frequencies is:

  AH = 20·Log[ R2 / (R2 + Rs) ]

As a simple example for case 1), if Rp = R1, then attenuation of low frequencies is 6 dB, i.e. high frequencies are 6 dB above low frequencies.

Have fun!

[B Tremblay]

Excellent!  You've given me some interesting options to consider.

Thank you for the detailed response!

[stm]

Being curious as I am, I checked the effect of a series resistor with C2 and found out that it can be used to control notch depth.

At 0 ohms, you get maximum notch depth as given by the ratio of C1/C2.  As you increase the resistor you reduce notch depth.  A side effect I observed is that when notch depth has been reduced to half its initial value, the notch frequency has dropped down to 70% (i.e. if you started at 1000 Hz now you have 700 Hz).

Now this should answer your original question.  :wink:  

Regards.

[Peter Snowberg]

Very very VERY.... VERY cool stm!

[Kleber AG]

 OK, now take a look at this http://www.diystompboxes.com/pedals/schems/Marshred.GIF
and see how easy to "pan" beetwen "two" different tone stacks... a "low-pass-filter" versus "the mid-scooped-filter".

Just add that 100K pot named "contour" and connect the wiper of this pot the ground

Try a 50K pot also, I think I like 50K better...

It's very powerful, nice...

Regards
Kleber AG

[Chico]

STM:

Cool info, and exceptionally clear write up, thanks for sharing.  As an observation, simply adding a variable resistor between C2 and ground does indeed affect notch depth, but it appears to me that the notch depth may be difficult to control in this manner depending upon the max and min depth required.

One solution, presented by R.G. (to make a twin T variable) is to "bootstrap" the filter.  (see www.geofex.com) and search for parametric EQ.

This bootstrapping technique may also work for the Bridged T configuration.

Essentially,
1.  Take the output of the filter and buffer it with an op amp.  

2.  Tie a potentiometer, say 50k between the output of the buffered filter and Vref (or ground in your case)

3.  Now, connect the wiper of the potentiometer to a second opamp set up as as voltage follower, i.e., connect the wiper of the new "notch depth pot " to the (+) input and connect the (-) input to the output of the second opamp.

4.  Replace the connection at C2 to ground (or vRef) with the second opamp output.

This approach, while more costly in parts, may give better control over the range of notch depths.  

Let me know what you think.  I have never tried this (but am about to), so I would be interested in your experience using theses concepts.

Best regards

Tom

[stm]

Chico:

I tried (in the SIM) the bootstrap approach you mention and indeed it works, but also narrowed the notch a lot (high Q), which is not desirable for tone shaping, except if you want to reject just a specific frequency.

STM

[stm]

And the snow ball starts rolling downhill... again!

After my previous post about the parallel and series resistor with C2 and C1, respectively, an idea came to my mind:  if you can control highs and lows then you have a tone control or tonestack.  I mangled the circuit so as to obtain a useful tonestack suitable for guitars.  Small component count and simplicity are key in this design!



The circuit presented above has a mid frequency of 450 Hz, and behaves quite well with the interaction of the Treble and Bass controls (mid frequency remains constant)  Lowering both Treble and Bass reduces mid scoop, while raising them increases it.

I managed to use two identical 100k LOG pots and voiced the circuit for a Fenderesque  sound.  If you want to get Marshallish voicing change C1 and C2 to 4.7 nF and 100 nF, respectively, for a 700 Hz notch frequency (a DPDT can take care of this!)

These are the response curves for pot values of 1k, 10k (mid rotation) and 100k:



As a closing comment, you could also add a series pot with C2 to have additional control over the mids, but this will move somehow the notch frequency and interact with the other controls, as it happens on all three-knob passive tonestacks.  If you look carefully at the curves you will find most tonestack curves represented there, except for mid boost, which is  not present on most tonestacks anyway.  I marked in red the curve that resembles my favourite equalization  (for humbuckers):  nice and simple, Bass at the middle, Treble at max.

I checked the VOX AC-30 tonestack for a benchmark comparison.  It uses 3 caps, 2 resistors and 2 equal valued pots with their three lugs connected.  In comparison, the Bridged Tee Tone Stack (BTTS) uses one capacitor less and potentiometers are connected to two lugs only (well, even if one outer lug is shorted to the center, you just need to run 2 wires per pot out of the PCB; simpler and less room for mistakes, since cable order doesn't matter!).

Have fun!

STM

[Kleber AG]

It's so exciting!  
Thanks for posting it...
Unfortunately I'll can try it only next week, I like this kind of tone circuits...

Kleber AG

[Chico]

STM:

Your observation about the Q is right on.  In RG's article, he describes the bootstrap approach as a great way to generate a tight notch e.g., for 60 hz hum elimination.

One thought that came to mind was to mod the basic bootstrap by adding a series resistor between C2 and the bootstrap.  This would serve to limit the notch depth, and provide a little more ease of control of notch depth.

Best regards

Tom

[stm]

Chico:

On a past thread (gotta search it) we talked about a variable capacitor. The circuit used one cap, one resistor, one buffer (op-amp preferrably) and one potentiometer.  The potentiometer scaled directly the capacitance value.

Since the above circuit alowed simulation of a capacitor with one leg to ground, it was well suited for implementing a variable C2.  The drawback is that if you change C2 you not only affect notch depth but the notch freqeuncy as well.

Also, IIRC, Puretube posted a circuit suitable for implementing a floating capacitor.  It required 2 caps, 2 buffers, etc.

Even if said circuits allow implementing variable capacitors, the beauty and simplicity of the circuit is lost and perhaps other aproaches can be a better choice (like a parametric band eq).

I really liked the topology of this new tonestack and gotta try it during the weekend.  I pretend to have a Fetzer Valve -> BTTS -> CD4049 amp.  I'm pretty sure the above would be very valve-amp-like.  Will post my findings.

Regards,

STM

[stm]

Last night I was about to fall asleep when a thought hit me like a rock...

The Treble pot must be Reverse LOG (C taper) instead of LOG (A taper) if you want it to work in the conventional manner, i.e. increasing highs to the right (CW) and cutting highs to the left (CCW).  Mmmhhh.... at least Small Bear has this kind of pot, but it is less nice to need this taper.


1) Connections would be as follows if you manage to have a LOG and a REV LOG couple of pots:

* Bass Pot:  100k LOG, connected to CCW and WIPER lugs.
* Treble Pot: 100k REV LOG, connected to CW and WIPER lugs.


2) If you have two LOG pots only, it will work, but bear in mind that the Treble pot will act in the opposite direction.  Not so terrible, at least for prototyping and DIY...

* Bass Pot:  100k LOG, connected to CCW and WIPER lugs.
* Treble Pot: 100k LOG, connected to CCW and WIPER lugs.

---
A disgression here: if ZVEX has an affect with a "crackle OK" knob that scratches when you adjust it, I think we can live with something like this  :lol:  Please notice I'm not flaming on ZVEX!  Pots crackle when they have a DC voltage applied, so it is clear in this case said pot is controlling the biasing of some circuit, so DC just can't be removed, as is usually done on volume and tone controls.
---

I have to think harder to see if I cand find a workaround using something like a higher valued LIN pot with a cleverly chosen resistor, as in the article entitled "The Secret Life of Pots".

Regards,

STM

[puretube]

.......

your imagination will do the rest :wink:

[stm]

I further studied the problem of the pot taper to have a reasonable control over all the frequencies, and this is what I came up with!



As you can see, pots are different in taper and value, but anyway they are made of readily available values (instead of a 100k REV LOG).  I had to include an additional resistor, otherwise bass are fully cut at minimum Bass pot rotation.

Notch frequency is set at 400 Hz (like in a Fender).  To raise it, cut both capacitors in proportion.  For instance, using 560pF and 39nF you get a 700Hz notch frequency.  Keep in mind that a DPDT switch lets you change mid frequency easily.

These are the curves: (sampled at five positions each pot)



Both pots at minimum produce nearly flat frequency response with -20 dB attenuation. From that point, each pot adds more Bass or Treble accordingly.  Mids remain relatively fixed at that level.  If you raise both Treble and Bass controls, mid attenuation even increases, as opposed to typical three-knob stacks where Bass, Mids and Treble controls tend to "fight" each other, partially cancelling their effects.

Hope you build this little device.  I think it can be a nice building block for those small 386 amps and FET-based overdrives.  I also raised overall impedance so it can be driven by a typical FET gain stage like a Fetzer valve.

Have fun,

STM

[tomographs]

I'm bumping a really old thread here. I hope that's ok.

I'm half way through a university project, and STM's guide to Bridged T design has proven invaluable, so thank you very much for that. I was wondering whether STM, or another member would be able to explain further how the Q of the Bridged T's notch can be calculated.

I understand that I could use the first equation, with the separate values for R1 and R2, and go by trial and error, but it would be preferable to have an equation to calculate the Q value.

Also, is there a way to alter Q, without altering depth and centre frequency?

Many thanks

Tom