Baxandall puzzle

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ruffrecords

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Nov 10, 2006
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I don't normally do active EQ designs but the other day I was playing around with a tube based Baxandall like bass and treble EQ. The Basic schematic is pretty much as per the attached pic I found on the net except the op amp is replace by a tube.

If you simulate this using a voltage source input with zero input impedance all is fine. With the controls centred the response is flat. However, I expect it will in practice be driven by a finite source impedance. So I tried the sim again with the source impedance set to 2500 ohms. Result disaster; there's a 1dB dog leg in the middle of the response. JHowever, if I add a 2500 resistor in series with the op amp output it becomes flat again.

Is this a known property of the Baxandall EQ?

Cheers

Ian
 

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ruffrecords said:
I don't normally do active EQ designs but the other day I was playing around with a tube based Baxandall like bass and treble EQ. The Basic schematic is pretty much as per the attached pic I found on the net except the op amp is replace by a tube.

If you simulate this using a voltage source input with zero input impedance all is fine. With the controls centred the response is flat. However, I expect it will in practice be driven by a finite source impedance. So I tried the sim again with the source impedance set to 2500 ohms. Result disaster; there's a 1dB dog leg in the middle of the response. JHowever, if I add a 2500 resistor in series with the op amp output it becomes flat again.

Is this a known property of the Baxandall EQ?

Cheers

Ian
Yes. The Baxandall transfer function depends on the ratio of the NFB impedance to the input impedance, as seen by the active gain element. It should be preceded by a low impedance stage for perfect symetrical curves. Peter J. made it clear in his presentation document by taking the source impedance into account in the equations.
Check p.6 of the original document
http://www.learnabout-electronics.org/Downloads/NegativeFeedbackTone.pdf
 
abbey road d enfer said:
ruffrecords said:
I don't normally do active EQ designs but the other day I was playing around with a tube based Baxandall like bass and treble EQ. The Basic schematic is pretty much as per the attached pic I found on the net except the op amp is replace by a tube.

If you simulate this using a voltage source input with zero input impedance all is fine. With the controls centred the response is flat. However, I expect it will in practice be driven by a finite source impedance. So I tried the sim again with the source impedance set to 2500 ohms. Result disaster; there's a 1dB dog leg in the middle of the response. JHowever, if I add a 2500 resistor in series with the op amp output it becomes flat again.

Is this a known property of the Baxandall EQ?

Cheers

Ian
Yes. The Baxandall transfer function depends on the ratio of the NFB impedance to the input impedance, as seen by the active gain element. It should be preceded by a low impedance stage for perfect symetrical curves. Peter J. made it clear in his presentation document by taking the source impedance into account in the equations.
Check p.6 of the original document
http://www.learnabout-electronics.org/Downloads/NegativeFeedbackTone.pdf

That's just it, I don't see where in that article he mentions the impedance of the preceding stage in deriving his equations. The only time I see it mentioned is in his final comments - unless of course I missed it.

Cheers

Ian
 
ruffrecords said:
That's just it, I don't see where in that article he mentions the impedance of the preceding stage in deriving his equations. The only time I see it mentioned is in his final comments - unless of course I missed it.

Cheers

Ian
Equations 3, 4, 5 and 6 clearly involve Zin.
I must admit he doesn't specifically mentions if Zin is an actual component, an equivalent impedance or a combination thereof.
 
This is a well known interaction.

I have even used this sensitivity to add a HPF whose pole frequency shifts with the amount of boost/cut. Placing a cap in series with the input R of the bass leg will give a higher cut-off frequency, due to lower effective input R, when the bass control is set for maximum boost.

This can be helpful to protect the customers from themselves when they turn up the shelving bass boost all the way.  :eek:

When adding tone controls to background music systems that often feed constant voltage distribution systems with easily saturated (cheap) speaker transformers, it is nice to give them lots of bass boost without too much very low bass content. 

JR

PS: I also recall one competitors value mixer (M____)  that that used an unbuffered insert jack feeding a typical Baxandal channel tone control. When using that insert jack the output impedance of the patched in device could cause a couple dB change in the frequency response at full boost.  It was only a few hundred dollar mixer, but their advertising hyperbole made you expect better than things like that. Most people would blame the unit patched in, not the mixer design for the frequency response shift. Details matter.
 
abbey road d enfer said:
Equations 3, 4, 5 and 6 clearly involve Zin.
I must admit he doesn't specifically mentions if Zin is an actual component, an equivalent impedance or a combination thereof.

Agreed. It's pretty obvious that the driving source impedance needs to be taken into account. What surprised me was its effect. I would not have been much bothered if it had simply caused a change in the flat setting gain or the amount of boost or cut or the frequencies at which they occur. What bothers me is that when the controls are set flat, the response is no longer flat.

What I suspect is happening is that the driving source impedance cause a small bass and treble cut to occur. However, as the total resistance in the bass and treble arms is not identical, the cut that occurs is not the same and it is this that causes the dog leg in the response. I'll tweak the circuit values so they are the same and see that fixes it.

Cheers

Ian
 
It is the nature of the Baxandall EQ where it spans across the input and feedback network, that the input and output feedback networks need to be identical for perfectly flat response. I am not familiar with tube design but wasn't there a popular input/output termination of 600 ohms way back when?  A similar impedance in series with the active stage feeding the feedback network might tidy that up if the driving impedance is known and repeatable. 

Good practice in solid state design (that I am actually familiar with) is to buffer this input node. As I mentioned I saw at least one value mixer that did not use a buffer when fed from the insert jack so suffered your identified behavior, while the higher the impedance of the Baxandall EQ network, the less deviation caused by this source Z interaction.  (In that cheap mixer I noticed it with the signal generator set for 600 ohm source impedance, and then at full boost. When set flat the 600 ohm error was more modest and probably within their nominal response tolerance. IIRC it was only a few dB change at worst case (full boost). 

JR

 
ForthMonkey said:
Reading carefully. But i always wonder that what is the "spell" of Dangerous Music BAX EQ...
Please say Great Guru Baxandall's Holy name only on your knees facing Malvern.  Evil spellers who get it wrong will be de-pinnaed  :mad:
__________________

There are small variations that allow shelving EQ with 'fixed' turnover frequencies .. as opposed to the sliding turnover of the original.  PJB was a fan of sliding turnover as in his original article .. hence the centre tapped linear pot.

That's cos in da old days, tone controls were used to apply judicious bass boost to speakers and also as HF filters to reduce vinyl distortion.

For the unwashed masses today who want supa dup EQ with zillion turnover freqs, selectable turnover (by switching caps) with shelving behaviour on the pot is better.  For that, resistors in series with both sides of the pots is sensible and will (hopefully) highlight the importance of matching both sides of the twiddle network.
 
I think I may have solved, or at least understand, the puzzle. Referring to the schematic below:

baxinteractionscaled.jpeg


The top schematic shows a typical Baxandall EQ implementation. The input is at A and I have shown the signal source impedance as Ro. The outout is at C and point B is the virtual earth referred to in Baxandall's original paper. Cbass ,at the top, is the capacitor that sets the low frequency turnover points and Ctop sets the  high frequency turnovers for the treble control. The little triangle with the minus sign in it represents and inverting amplifier with a relatively large gain.

The second schematic shows what happens at low frequencies when the bass control is active. At low frequencies we can consider all the capacitors to be open circuits. As you can see, this means the treble network at the bottom is completely disconnected from the virtual earth so if has no effect on the bass control. The driving source resistance Ro is effectively in series with the input arm. When the bass pot is centred we should have unity gain but the input arm (equal to half the pot (50K) plus the 22K = 72K) has Ro in series with it which causes about 0.5dB bass cut when Ro is 2500 ohms

The third schematic shows what happens at high frequencies. Here we can consider all the capacitors to be short circuits. The 100K bass pot is therefore short circuit and has no effect so the bass network looks like a 22K in the input arm and another 22K in the feedback arm. The gain is therefore controlled by the bottom 100K pot but notice that the bass network is still connected unlike in the low frequency case. This is the basic cause of the nteraction between the bass and treble controls. If the bass is set to full boost the is an additinal 22K + 47K = 69K in parallel with the treble input arm. This means the trevble shelving resistors have to be smaller to achieve the same boost (8K2 instead of 22K). This means that when the pots are centred, the driving source resistance Ro now affects the gain of both networks. The dog leg I observed in the response occurs because Ro is a greater proportion of the 22K bass input arm than it is of the treble input input arm which is 50K + 8.2K = 58.2K. The result is that at high frequencies the gain drops by about 1.5dB when Ro is 2500 ohms.

The bottom line is that the dog leg is caused by the interaction of the bass network with the treble network which in turn is caused by Cbass shorting out the bass pot. The solution is to either remove the interaction of make the treble interact equally with the bass. The final schematic shows one possible solution to equalising the interactions. In the treble section, instead of a capacitor in series with the wiper of the pot, we place an inductor across the pot in the same way as the bass control has a capacitor across the pot. At low frequencies, the inductor now shorts out the treble pot and interacts with the bass control in exactly the same way that Cbass interacts with the treble control at high frequencies. I guess Baxandall shied away from from using an inductor in a hi-fi product. Simulation shows that the response is flat across the audio spectrum with the controls centred whatever the value of Ro. All that happens is the gain drops a dB or so below unity.

Cheers

Ian
 
ruffrecords said:
The bottom line is that the dog leg is caused by the interaction of the bass network with the treble network which in turn is caused by Cbass shorting out the bass pot.
I beg to differ.
The "dog leg" is caused by the input  impedance dropping at mid fequencies.
The only way to avoid this is to insert an identical resistance between the actual output and the NFB path. See arrached pic. 
 

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For even more fun, and more interaction, it is not unusual to add a third peaking section in the middle of the bass treble shelving.

tone-control-3-band-tlo82-opamp-circuit.jpg


Since opamps are cheap and this EQ is inverting overall I have put the the mid band EQ on it's own opamp with the two stages in series. This way a bypass switch maintains the proper polarity.  IIRC there is still some interaction due to phase shift but not as bad as attempting all three on a single gain stage.

JR
 
ruffrecords said:
Simulation shows that the response is flat across the audio spectrum with the controls centred whatever the value of Ro. All that happens is the gain drops a dB or so below unity.
My simulation doesn't show that.
Green: response with Zsource=ca. 1/100th of pot value, no output Z compensation
Red: same with Output Z compensation
 

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abbey road d enfer said:
ruffrecords said:
The bottom line is that the dog leg is caused by the interaction of the bass network with the treble network which in turn is caused by Cbass shorting out the bass pot.
I beg to differ.
The "dog leg" is caused by the input  impedance dropping at mid fequencies.
The only way to avoid this is to insert an identical resistance between the actual output and the NFB path. See attached pic.

I think we are saying the same thing. The reason the input impedance drops at mid frequencies is because of the interaction of the bass control. I had already noted that adding an equal resistance in the output restored a flat response. However, this is not the only solution. An alternative is to ensure a similar reduction occurs in the rest of the spectrum which is what the inductor achieves. The advantage of the inductor solution is that it is independent of the value of the source resistance. Having said that, and having read your post on your own sim, I will check my sim again.

Cheers

Ian
 
JohnRoberts said:
Perhaps an inductor in series with the bass control wiper, and cap in series with treble wiper could reduce source Z sensitivity some.

JR

I have checked my sims again and unfortunately abbey road d enfer is right. What has happened is that the interactions are now the same at high and low frequencies but not in the middle. So now you get a small dip at mid frequencies which is dependant on the source resistance. The only fix is to add it back in the output of the amp which is a pity.

I had tried your idea of an inductor in series with the bass wiper and a cap in series with the treble wiper with the intention they would effectively disconnect themselves from the network outside their operating range. However, so far it looks like you need impracticably high values of inductor to achieve this.

Cheers

Ian
 
JohnRoberts said:
Perhaps an inductor in series with the bass control wiper, and cap in series with treble wiper could reduce source Z sensitivity some.

JR
That would be an active "Thordarson EQ". It seems calling that this type of circuit is known only in Europe (maybe only in France). Thordarson were a mfgr of wound components, so they may have published application notes and the name would have stuck with it here; that was back in the late 50's.
Anyway, in this configuration, the inductor and cap provide LF and HF paths only, no midrange, so a resistive path must be added. In addition, due to the phase cancellation when both L and C contribute, there is a midrange dip.
 
and that's why I don't design with tubes or inductors (except for switching supplies).

I almost suggested using a gyrator but in tube land the gain stages are dear.

JR
 

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