OK, I give up. Can someone explain this bass boost and possibly a formula for it

[bool]

....
Before this I had never seen this kind of filter before, but it seems so amazingly useful that I really want to use it in many circuits! Thats also the reason I wanted to calculate and simplify the equations, because now in the simplified form they provide a much help to the design process.

I used T's since 80's - mostly as a predistortion boost, but with varied R2 (from your schem) which would in effect boost fe. low-mids differently than upper-mids when varied by user. I simply calculated the two extremes to fit within the what was deemed to be the "right" places to boost and then finally tweaked by ear to be ... well, "musical" in context.

[stm]

definitely understand the reversal "notch" concept ... good there, thank you

I'm with you on the wiper position concept too PBE6, both with regards to gain and the frequency calculation. Thanks!

So then the center frequency here is really about 89Hz and not 150Hz as advertized?
I have a spreadsheet to make 

During the development of the Thunderbird circuit we started with the BOTTOM center frequency at 150 Hz and 15 dB of maximum boost, and so these values were propagated into the final write-up.  Nevertheless, the tone control filters were tweaked by ear afterwards until they sounded right.  We also found that going below 4.5 dB of bass boost was not necessary, so we split the 100k pot into a 50k pot and a 47k resistor so the entire BOTTOM control pot travel could be used.

Similarly, the TOP control is not centered at 3000 Hz anymore, and it does provide a bit more boost than 15 dB.  Guess it is time to update the write-up.

[Derringer]

cool

and you just answered another question for me as well, i think ...
I was wondering what would happen if I did just use a 100K pot instead of the 50K pot + 47K resistor.

The spreadsheet I made shows that it would essentially become a buffer if I used a 100K pot and rolled it down to 0R.

Is that in fact the case?

Looks like I may get a chance to finally breadboard this today.


something else too, with reference to jatalahd's equations and schematic ...
I find that if I swap the capacitor values and make C2 the larger cap, then the Q factor does not change as much as the pot is turned.
It ranges from 0.45 at minimum gain up to  0.51 at max gain.

But when C2 is the smaller cap, the Q factor ranges from 0.16 at minimum gain up to .51 at max gain

does that seem right? The center frequency seems the same. Granted though, I am using a simpler gain formula then Jatalahd is (I haven't found a nice way for Excel to compute imaginary numbers) so maybe the gains are affected when C2 is the larger cap somehow?

[jatalahd]

maybe the gains are affected when C2 is the larger cap somehow?

Yes, the gain is affected a great deal in that case, because the capacitor C1 has much larger reactance at the center frequency and cannot be neglected in the gain calculation. When C2 is the larger cap, the gain varies between 1 dB - 2 dB (min - max, pot rotation) and this also kind of explains the small variation in Q.

[stm]

cool

and you just answered another question for me as well, i think ...
I was wondering what would happen if I did just use a 100K pot instead of the 50K pot + 47K resistor.

The spreadsheet I made shows that it would essentially become a buffer if I used a 100K pot and rolled it down to 0R.

Is that in fact the case?

Exactly.  You can take a look at the Thunderbird TOP control for an example where the frequency response can vary from totally flat to a high peak around 6 kHz.

something else too, with reference to jatalahd's equations and schematic ...
I find that if I swap the capacitor values and make C2 the larger cap, then the Q factor does not change as much as the pot is turned.
It ranges from 0.45 at minimum gain up to  0.51 at max gain.

But when C2 is the smaller cap, the Q factor ranges from 0.16 at minimum gain up to .51 at max gain

does that seem right? The center frequency seems the same. Granted though, I am using a simpler gain formula then Jatalahd is (I haven't found a nice way for Excel to compute imaginary numbers) so maybe the gains are affected when C2 is the larger cap somehow?

The order of the capacitors does indeed alter the Q factor, and yes, the Q factor diminishes as the peak amplitude is reduced.  This may not be desirable for a graphic equalizer, but luckily for us it works OK for guitar purposes :-)
If you are simplifying the formulas to avoid using imaginary numbers then the results are likely to be inaccurate.  I understand Excel can handle imaginary numbers, but last time I checked (Excel 2003) this was not part of the default installation, so you had to install/enable this capability first.

[Derringer]

ok then,
and 1 to 2 dB's may not be all of that much of a problem though if the larger Q factor sounds better
simple enough to swap a pair of caps on a board to hear what's what
(edit .. unless you meant that max gain may only be about 2dB's with the caps swapped)


from what I've been able to find out in excel, I can get a cell to have the value of "i" by inputting =COMPLEX(0,1)
but then it seems I need to have a different cell, or perhaps a much more complicate formula, where for every computation with a complex number I have to input a function that specifically tells the program that it will be adding, multiplying, or divideing a complex number etc etc
That degree just doesn't seem worth the effort right now when the simple gain calculation gets me in the ballpark.

however if I get a hold of mathlab or octave ... then let the games begin !

[jatalahd]

(edit .. unless you meant that max gain may only be about 2dB's with the caps swapped)

Yes, this is what I meant, sorry for my bad English skills. First I was surprised that the gain would go that low, but I verified it by Spice simulation and indeed the max gain with caps swapped is 2 dB.

[Derringer]

No sir, your English is just fine. It's way better than my Finnish.

You did say the gain was "affected a great deal," which didn't sink into my brain until after I posted.
I just confirmed it for myself on the breadboard too.

Paljon kiitoksia

[jatalahd]

If you still want to get your spreadsheet completed, the Excel calculation is actually not that bad for the gain at the center frequency. In Excel I would suggest trying this (I tried it myself and got the correct result):

Cell D3 holds the value of the real part of the numerator:                 0
Cell E3 holds the value of the imaginary part of the numerator:       w*R1/( C2*R2*(R1 + Rx) )
Cell D4 holds the value of the real part of the denominator:             1/( C1*C2*R2*(R1+Rx) ) - w*w
Cell E4 holds the value of the imaginary part of the denominator:   w*( 1/C1 + (1/C2)*(1 + Rx/R2) )/(R1 + Rx)

In the above equations, you need to replace the component values (R1, R2, Rx, C1, C2) as references to the Excel Cells, where you have the values defined.
Also above, w = 2*PI()*f, where f is the center frequency 89 Hz. You can pre-calculate w into some other Cell and make a reference to it.

Then in Cell D6 write:   =IMDIV(COMPLEX(D3;E3);COMPLEX(D4;E4))
Then in Cell D7 write:   =20*log10(1 + IMABS(D6))

Finally, the value in D7 is the gain in dB

[Derringer]

Great! thank you.

What values were you getting then for the maximum gain of the circuit then? I'm getting about 9.4 dB's which seems low.

[jatalahd]

What values were you getting then for the maximum gain of the circuit then?

The Excel should give the same values as the Octave calculation, 14.208 dB max and 4.2955 dB min. Actually, when using the exact center angular frequency as w (instead of the very slightly rounded 89 Hz), all the real terms vanish from the quotient, and then the calculation could be done without using the complex() function. Anyway, here is a link to my "not so clear" .xls file, which should help you to get the correct values. I am still using the complex arithmetic in the Cell formulas, so it will give the correct gain value for any single frequency given as the angular frequency w.

http://www.guitarscience.net/gains.xls

You can change the value of "a" between 0.0 and 1.0 to simulate the turn-percentage of the pot. In the given spreadsheet I have now used the exact center frequency (real parts will be zero), and I also noticed I needed to make a small correction into the final formula giving the gain in dB in Cell D7. But you will notice the change from the file. I used Gnumeric in Linux to save the file in MS Excel format, hopefully it still works in Windows... I will remove the file from that download link after few weeks, since it is only there for special purpose in this case.

[PBE6]

Hey!!! I bought your book! Fantastic resource with all the nitty gritty details, thanks for putting it together!

[jatalahd]

nitty gritty details

As can be seen from this thread, I often get lost in the details

[Derringer]

I often get lost in the details

Is that like "Jazz Algebra?" 

Hey, thanks again for your help Jatalahd!
I downloaded your spreadsheet, replaced the gain calculation cell with your D7 value, then poked around and found the error in mine.
I have a separate cell where I can input R2. Then I have a cell next to it that shows the value of (R2) + (Pot resistance towards gain).
I had all the calculation cells referencing plain old R2 and not the sum of R2 and the variable pot resistance.

This spreadsheet is an awesome tool to have!