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Ian Williams

Mar 18, 2014

audioopampportal

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Get the most out of your pot - Don’t mess up the rotation!

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“Hey!
Turn it down!”

You’ve
probably heard these words at some point, especially if you’re like me and enjoy
listening to music LOUD! If you decide to oblige and actually “turn it
down” then what must you do? Reach for the volume control, of course!

What
is a volume control? Put simply, it’s a circuit which attenuates the
amplitude of an audio signal. Usually the desired behavior is for the amount of
attenuation to vary from none, down to some high level of attenuation so that
the audio is too quiet to hear. Many audio devices are digitally controlled, but
there are still plenty of systems out there with a knob that you can rotate in
order to adjust volume.

Figure
1 - The Potentiometer

This knob
is actually an electronic component called a potentiometer, or pot, as shown in
Figure 1. Pots are a special type of resistor with a third terminal, called a
wiper. The wiper moves back and forth as you rotate the knob, changing the
amount of resistance seen at the wiper terminal. This creates a voltage divider
kind of behavior, making pots ideal for use in volume control
circuits.

However,
not all pots are created equal. The three most common types, or tapers, are the
linear taper, logarithmic (or audio) taper, and reverse logarithmic (or reverse
audio) taper. Figure 2 shows how the resistance of each taper changes versus
rotation.

Figure
2 - Typical Potentiometer Characteristics

Human
hearing spans a large dynamic range, so logarithmic units of decibels (dB) are
typically used to describe the power of audio signals. An ideal volume control
would have an attenuation characteristic which is linear in dB, since the result
is a very natural change in volume as you rotate the volume knob. For this
reason, audio taper pots are often used as volume controls. However, as you can
see from Figure 2, these pots are not actually logarithmic, but rather a
combination of two linear pots with different slopes. This does a poor job of
achieving linear-in-dB attenuation, but thankfully there’s a better
way!

Figure 3 - Baxandall
Active Volume Control

Back in
1980, Peter Baxandall presented a circuit which has become known as the
Baxandall Active Volume Control, shown in Figure 3. It’s simple, flexible, and
achieves excellent linear-in-dB attenuation performance with a linear pot
by implementing a clever type of shunt feedback.  The high input impedance
and low output impedance of this circuit ensure that its attenuation performance
is maintained no matter what kind of source and load impedance is
connected.

Figure 4 - Baxandall Active Volume Control
Analysis

The
transfer function of this circuit can easily be analyzed using Kirchoff’s
current law and Ohm’s law. I won’t go through the full analysis here, but this
is the result:

An
important note about this transfer function is that Rx represents the
percentage of pot resistance after the wiper, and
R1-x
represents
the percentage of pot resistance before the wiper. If you plot
this transfer function versus percentage of pot rotation, as shown in Figure 5,
you can see that a nearly perfect linear-in-dB attenuation characteristic is
achieved. The attenuation drops off sharply as rotation goes to zero, since the
transfer function approaches negative infinity. This is actually desirable,
since in a real circuit this would provide a very low “off” volume which is
inaudible.

Figure
5 - Calculated Volume Control Response

The
Baxandall Active Volume Control circuit is used as the basis of a TI Precision
Design: Active Volume Control for Professional Audio. In this
design, I provide a detailed analysis of the theory behind this circuit, as well
as full simulation and real-world results and all the circuit board schematic,
layout, and bill of materials files. If you have an interest in audio, I highly
recommend that you check it out!

Stephen Power

Hi Ian

That's quite an interesting circuit. I think there may be a typo in the
transfer function equation given above. I worked through the calculations in
'Active Volume Control for Professional Audio' and I believe that the R1/R2
term should be multiplied by (R_1-x + R_x). In any case you can see that the
dimensions don't add up. R1/R2 is dimensionless but is added to R_1-x?

regards

Steve

Mar 21, 2014

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Ian Williams

Hi Stephen,

Thanks for the feedback, and for taking the time to check the math! There's
a "gotcha" that I forgot to mention in this blog, which is that R_x and R_1-x
are in fact unitless as well. R_x represents the percentage of pot resistance
after the wiper, and R_1-x represents the percentage of pot resistance before
the wiper. I do specify this in the first paragraph of Section 2.2.1 in the TI
Precision Design.

I hope you enjoyed the blog post!

Best regards,

Ian Williams

Linear Applications Engineer

Precision Analog - Op Amps

Mar 21, 2014

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Ahmet Cetin

Thank you very much.

Mar 24, 2014

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Stephen Power

Hi Ian

Thanks for clarifying this for me.

regards

Steve

Mar 24, 2014

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Ian Williams

Hi Ahmet - I'm glad you enjoyed the post!

Hi Stephen - you're very welcome!

Mar 24, 2014

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George Kay

I've been in the hi end audio design business for most of my life. This is
a solution to something that ain't broke.

A good quality audio pot worked beautifully for many years and still does.
No one complains about the lack of a perfect log response in an audio pot. The
curve is not necessarily cast in stone as 2 linear tapers. There are pots
available that have a log response.

There is also the presumption that these op amps don't alter the quality of
the audio. They do, no matter what the specs are. My experience is that less
circuitry = more audio, 2 buffers and 2 amplifiers in series with the audio
will eat up low level information - reverb tails, ambience, room tone, all
part of the realism of a good recording. This is subjective evaluation.

This is essentially a variable negative feedback amplifier and the amount
nfb changes the gain bandwidth product. While differences may measure outside
of the audio band, to good ears it changes the quality of the
presentation.

As for the quality of the pot itself, these vary widely and the contact
quality and the resistance track quality determines most of the performance
quality. So unless you have a pot for this circuit that has high quality
contacts and resistive medium, then you are no better off than having the same
qualities in a standard audio pot.

So in essence we've added 9 components and additional power supply
requirements for a problem that a professional quality or audiophile quality
potentiometer doesn't have.

So if it ain't broke, don't fix it.

Apr 6, 2014

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Ian Williams

Hello George,

Thank you for taking the time to read and comment on this post, and I
appreciate your perspective as someone with years of experience in the
high-end audio industry.

You may be correct that "no one complains about the lack of a perfect log
response in an audio pot." I'm not an audio end-equipment design engineer, so
I don't hear that kind of feedback. While not every audio pot may have the
kind of two-linear-taper characteristic mentioned here, many in fact do, and
this design fully solves that problem.

I also believe that amplifiers are necessary in order to solve various
issues which are present in audio designs, such as buffering, filtering, and
power amplification. For example, a colleague of mine designed an active
crossover circuit for two-way studio monitors, detailed here: http://www.ti.com/tool/TIPD134. 10 amplifiers
are used on that board in order to achieve the desired performance, not to
mention the power amplifier in the following stage. My two-amplifier volume
control solution is also incorporated into the design before the crossover.
Despite all this silicon, these speakers sound great and have outstanding
measured performance at every stage!

Thank you again for reading! Perhaps I can run some future design ideas by
you in the future.

Best regards,

Ian Williams

Apr 7, 2014

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Wayne Bonin

Ian,

I just plotted the transfer function in Excel on a linear graph and it
looks exactly like what I want for controlling the brightness of an LED. The
non-linearilty is adjustable by changing the gain, which is an excellent
feature that was not mentioned. The only problem for me is I need a circuit
that works off a single supply. Have you looked at the effect of adding an
offset voltage at A2?

Thanks,

Wayne

Jun 20, 2014

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