Every audio system needs at least one volume control, or “attenuator.” Since most audio equipment is stereo, the most common kind is a dual gang type, which bonds two attenuators together. Since our ears respond on a logarithmic scale, most audio attenuators have a log response, also called “audio taper.” After you narrow the field of commercial attenuators to the dual-gang audio-taper type, there really aren’t that many choices available to the hobbyist. There is a great variety in the prices, though: from just a few dollars to well over $100. Which should you choose, and why? I decided to do some research to find out what separates the good from the bad.
I’m going to talk about decibels in this section without defining them or how different values relate. If you’re not up on the terminology, I recommend you read Peter Elsea’s short essay, “Decibels.”
The most important feature of a dual audio-taper attenuator (which I’ll just call a volume control from here on) is how well it tracks: that is, how closely matched the two channels are to each other. No volume control has perfect tracking: one channel will always be a little different from the other. Even well-trained ears are only sensitive enough to notice a difference of about 1 dB, though, and for the average person the minimum noticeable difference is more like 3 dB. It’s no surprise, then, that the least expensive volume controls have a 3 dB tracking specification.
With potentiometer type attenuators, the tracking spec will only be given down to a certain level. A common spec is 3 dB down to -40 dB. 40 dB is a factor of 100, so such a pot is guaranteed to have its channels within 3 dB of each other down to the point where the pot is attenuating the signal to 0.01×. Below that point, the channels can be badly mismatched and the pot will still be within spec. The reason pots are specified this way is that manufacturing errors build up over the range of the pot’s travel. It’s much harder to make a pot with good matching down to -60 dB, for instance. This spec is a good indicator of a pot’s quality, since it reflects the accuracy and repeatability of the manufacturing process.
It’s common for audio pots to be very badly mismatched in the final few degrees of their rotation. Since tracking isn’t guaranteed to any level of accuracy at such high attenuation values on any commercial pot, this is something you must plan for.
Our ears respond to sound on an exponential scale. A sound has to be 10 times as powerful for us to hear it as twice as loud. For a 4× increase in volume, it must be 100 times as powerful. This kind of increase gives a curve like this:
This is also called a log curve, since logarithms are the inverse of exponentials. You can look at the same data either way.
Obviously a volume control needs to be designed with a response like that in mind if our ears are to hear a steady change in volume as you change the setting steadily.
Oddly enough, though, commercial volume controls don’t have true log curves. (I’ve yet to see one that does, at any rate.)
The first major reason for this is that it’s harder to manufacture a pot with a varying taper than one with a linear taper. So, many of the less expensive “log” pots are made from two linear segments joined together to approximate a log curve.
The other major facet of this issue has to do with the way volume controls are typically used. Audio systems are designed so that the volume control is set near the top of their range most of the time in common use. Since you want fine control in the range you use the volume control most often, the control is designed to have fine attenuation rates at the top end of the range. But, because our ears are so sensitive to soft sounds, you wouldn’t want fine control across the entire range. People want to be able to turn the volume all the way down and have the sound practically muted, even though an attenuator is not a mute control. The solution is to increase the attenuation rate towards the end of the control range, so that the control’s total attenuation is very high.
So, enough with the theory. What kind of curves do actual volume controls use? I’ve measured the curves of several popular attenuators used by audio hobbyists and put them into an Excel spreadsheet with graphs. This spreadsheet works best in recent versions of Excel, but it does render adequately in OpenOffice.org’s Calc module, which is free and runs on most operating systems.
To acquire this data, I put a voltage across both elements of the attenuator, then measured the voltage at each wiper at various attenuator settings. Although I used 10 V as my test voltage to get good measurement resolution, I scaled the results so full scale is 1 V to make the numbers easier to manipulate. I used a Fluke 189 to do the measurements, using the millivolts scale up to the point where the volts scale gave more accurate measurements. I threw out the highest and lowest data points since they were often divergences from the smooth changes over the rest of the curve, probably due to manufacturing limitations.
In order to get reasonably accurate 15 degree adjustments for the pots, I made a scale (PDF, 7 KB) in a vector drawing program. I glued it to a square of acrylic with a hole in the center, and then I mounted the pot to the finished scale. With a well-marked knob on the pot, I was able to get decent accuracy, evidenced by the fact that the resulting data doesn’t show a large amount of jitter.
I measured both channels so I could get channel matching data. This data is plotted on two graphs for each attenuator, one with a linear Y axis, the other with a log axis. The linear version is easier to understand intuitively, but the log version shows important details that don’t show up in the linear version due to lack of graph resolution.
In addition to the measured voltage vs. rotation curve for both channels, the graphs have a third curve which is an idealized approximation of the measured data. Most of the approximations have the form of the equation at right, where x is the amount of rotation from 0 to 1, and a and b are curve fitting parameters. a is dB per step, and b is a vertical scaling factor to match the curve with the data. Since all of the tested attenuators have a varying attenuation vs. rotation curve, I have only tried to match the approximation curve with the upper part of the range.
To come up with values for a and b, I used two curve fitting programs, CurveExpert and NLREG. The latter is more powerful but harder to use and more expensive. If you just want an inexpensive tool to do basic curve fitting, CurveExpert is a great option. I ended up using CurveExpert to decide on a function family, and then I used the power of NLREG to narrow things down.
Before settling on these two programs, I tried a lot of shareware and demo software. Some of this software was quite expensive, but nothing else worked as well as these two dedicated programs for basic curve fitting. All of the other inexpensive packages were buggy or hard to use, and the expensive packages had a huge amount of unrelated features so curve fitting was harder than necessary. If you just want to fit some curves to measured data, I recommend that you look at CurveExpert and NLREG before looking at the more general packages.
If you don’t want to spend any money, recent versions of Gnuplot will also do curve fitting. This is a powerful command-line plotting package, so it isn’t very easy to learn, but it’s worth your time to learn it if money is an issue. I used it to make the exponential curve graph above.
This data set shows clearly why this pot is popular among audiophile DIYers: for the cost, it gives pretty good performance. The average channel matching is much better than the specs allow for, so that the two channel curves are almost on top of each other on the graph. It also has a reasonably smooth log-like curve.
You’ll notice that this pot uses a different type of function for the idealized curve than the other attenuators. If you look at the data in the log version of the graph, you’ll notice that it's continuously curved, while the other attenuators have a straight section that is well-modeled by the base-10 exponential function above. This data calls for a different kind of model. I settled on a variation of a simple cubic function, which matches pretty well. If you wanted to get a really accurate fit, I suppose you’d have to use a high-order polynomial instead.
This is the data for a stepped attenuator built into a clone of the RK27 enclosure. It’s not certain who actually made it, even though the label says “ALPS.” The best information seems to be that it’s a ripoff design made by a Chinese company. These were common on eBay a while back. You can find out more about them in this Head-Fi thread.
As you can see, this stepped attenuator shows the fine channel matching typical of stepped attenuators. Interestingly, while the manufacturer cloned the packaging of an ALPS RK27, they didn’t try to clone the attenuation curve.
This is one of the most popular audio pots for audio DIY use in North America. It’s inexpensive, it has great performance for the cost, and it’s readily available from DigiKey.
As you can see, it doesn’t have channel matching as good as the ALPS RK27, particularly at the very bottom of the scale. One occasionally hears reports of a unit with audible tracking error, though most of the time they perform like the sample I tested, with quite good channel matching. Since this pot is so inexpensive, those who have had this problem often just throw the pot away and get another.
You’ll notice that this is one of those pots that uses linear segments to approximate a log curve. In practice, you’re not likely to be able to hear the difference.
This pot performs quite well, considering its price. I’ve had experience with a pot from another manufacturer that costs about 3 times as much with virtually identical performance. It’s little wonder that that other pot isn’t carried by any of the major distributors.
This pot is popular mainly because it’s easy to find in North America, since it’s one of two audio pots carried by Radio Shack. Although the curve for it looks good and my sample had good channel matching, this pot has a bad record for repeatable performance. Lots of people have gotten units with either audible tracking error or scratchy sound. It’s a good pot to have in your parts bin for temporary experiments, but you’d do well to buy a better pot if you’re making something permanent.
This pot proves an important point: the ones I’ve bought are marked “ALPS,” but this is no guarantee of high performance. A lot of newbies see “ALPS pot” and think it means they’re getting an RK27. ALPS makes a very wide range of pots, from the excellent to outright junk. When in doubt, get the model number and look at the data sheet.
This is a high-end stepped attenuator. Among the features you can see in the data are a ruler-flat 2 dB per step attenuation curve down to about -33 dB, and very nice channel matching. Although even better channel matching would be possible, it would be pointless.
This pair of graphs best illustrates the reason for showing the log version of the data as well as the linear: on the linear graph, the idealized curve seems to match very nicely with the actual data, but in the log version you can see a big divergence at the bottom of the scale.
If you’re making your own stepped attenuator, the above data can serve as a guide to deciding on what kind of attenuation curve you should use. A lot of DIY attenuators use a simple log curve (constant dB drop per step), but from studying the data it appears that commercial attenuators drop the signal by 2 to 2.5 dB per 15 degrees of rotation for the first 40 dB or so of attenuation, and then they start dropping much faster. For the reasons I outlined above, I think this kind of curve is worthy of emulation.
Another thing you might consider is using a formula like the approximation I found for the ALPS RK27. This type of function accounts for both the fine-tuning and fast-drop sections of a typical audio attenuator. Instead of using the exact function I came up with, you can use y = x3, as that gives a similar curve with a much simpler function.
People have tried to come up with ways of faking a log curve using a linear pot. This idea is attractive because linear pots are cheaper, available in greater varieties, and have better tracking specs. The most common technique is the shunted linear pot, described here.
Unfortunately, this method gives pretty terrible results. Here’s a graph made by Morsel on Head-Fi that shows the problem:
This is a log-scale graph, so the straight red line is an ideal log pot, and the blue line is a linear pot. The purple and black lines show segmented linear pots, which as you can see are a fairly good approximation of a log pot. The surprise is the green and cyan lines, which are variations on a shunted linear pot. Seen on a linear-scale graph, the curves look pretty good, but on a log-scale graph the curve is seen to be a worse approximation than even a two linear segment log pot.
Another problem with this technique is that a shunted pot presents a varying impedance to the source as you turn the knob. A pot without a shunt resistor presents a constant impedance to the source, so the source’s performance doesn't change as you turn the knob.
This article is copyright © 2004-2013 by Warren Young, all rights reserved.
|Updated Mon Feb 28 2011 12:08 MST||Go back to Audiologica||Go to my home page|