Double Buffered Volume- Smooth Log Taper

[MattB]

I originally came up with this idea beacuse i was looking for a way to get a little more high end out of a set of Filtertrons. The two simplest options would be using a no-load tone control and/or higher value pots, but both of those ideas have minor disadvantages. A no-load pot doesn't give you any control over the extra treble- it's an all or nothing setting. Higher value pots have a worse taper, and the increased impedance means a higher value volume pot will suck more high end whern turned down.

Another option would be to put a buffer before the voume pot. This reduces the loading on the pickup because it sees the input impedance of the buffer, which can be as high as it needs to be, instead of the volume pot. The reduced loading makes the resonant peak taller. If the guitar has a standard tone control the pickups will still be loaded by the tone pot. That limits how much extra high end is available. Depending on how much extra high end you want, you might want to also use a higher value or no-load tone pot (or a lower value pot if you don't want the extra high end, but do want the improved taper).
A buffer also isolates the pickup from the cable capacitance. This shifts the resonant peak to a higher frequency, which also makes the guitar sound brighter. A guitar without any extra capacitance loading the pickups can sound very different, probably too different for a lot of people. You can add a small value cap in parallel with the pickup to shift the resonant peak back down, and I think it's worth experimenting with a few different values to find what you like.

The problem with putting a buffer before the voume pot is that it doesn't do a great job of buffering your guitar's output. The volume pot is the last thing in the chain, so turning down the volume still increases the guitar's output impedance.

The obvious solution here is to add a second buffer, after the volume pot.

And because the volume is safely tucked away between two buffers, this is a good opportunity to use a trick that wouldn't work as well in a passive guitar, because again the varying impedance would be a problem.

It's possible to wire a dual gang linear pot to give a smooth log taper. Like this:

The second gang is wired as a variable resistor, in series with the top half of the the voltage divider formed by the first gang. The top half of the voltage divider formed by both gangs together increases faster than the bottom half shrinks. This produces a smooth curve that gradually changes from steep to shallow. You can also make an anti-log taper by putting the variable resistor in series with the bottom half of the voltage divider.

The output level at 50% rotation depends on the ratio of resistances of the two gangs. Equal value gangs will give 1/3 output at 50% rotation. Increasing the size of the 'variable resistor' gang will give a steeper taper.

This graph shows output levels for two different combinations:

Strictly speaking, I'm not sure this is a genuine logarithmic taper. It might be some other kind of curve, but I don't think the distinction really matters. In use it feels very smooth and natural, much better than the linear approximation that other 'log' pots use.

Here are two LTSpice plots, showing the output level, in 10% steps, from 10% to 100% rotation. These plots use two 100k gangs, so have 1/3 output at 50% rotation.

 The first plot shows the pickup going straight into the buffer with no additional load. The second plot shows the pickup with a 250k resistor and a 560pF cap in parallel with a pickup, which is close to the loading the pickup would see in a normal guitar.

Schematic:

The second buffer is intended to drive loads as low as 10k, and R6 and C4 are sized to let it do that easily. The first buffer is going into a known, not very low impedance, and so doesn't need as much current. As modelled in LTSpice, the second buffer draws around 220uA and the first draws just under 50uA. So the extra current draw isn't much of a problem- battery life should still be several hundred hours.

The schematic uses a dual gang 100k pot. If you use a smaller value, you might want to decrease R3 and proprtionally increase C2 to deal with the heavier load. R3=47k and C2=1u would work fine for a 50k load.

I used cheap MLCC caps for C2, C3 and C4. Cheap MLCC caps aren't temparature stable- the capacitance value can drop by up to 80% at the far ends of the range. So C2, C3 and C4 are oversized enough that they will work fine even under less than ideal conditions. If you use film caps you could reduce the values to 220n, 22n and 2.2u with no audible change.

Layout and pictures:

The ground wire is for linking to any other parts of the circuit that need gounding- pot shells, pickup ground wires and so on.

Behind panel depth is just under 20mm, and the whole thing measures about 22mm by 22mm, so it should fit almost anywhere a full-sized pot would.

Really this isn't a very sensible layout. As you can see from the pictures, I made it far smaller than it needed to be. A 10x11 hole board fits a standard strat cavity, and could be a lot easier to build.

I used a 9mm pot. I think there should be plenty of space in most guitars for a 16mm. That would make swapping one wafer out a lot easier, if you want a steeper taper.

These are the pots I used: Aliexpress link

I should have used a 5-pin socket, and put the battery connections on the plug.  That would make fitting R8 more difficult, because the socket would sit halfway over the hole it needs to use, but it could be done (or just make the board bigger). I ended up supergluing the battery leads to the board, and that works ok, but it's not as secure as it couuld be.

I should also have left a little more material on the board, so the socket wasn't overhanging the edge. This isn't much of a problem- the socket is more than secure enough, but it could be even better.

I used a surface-mount MLCC cap for C5. There is enough space to fit a through-hole MLCC or even an electrolytic on the board, but I was trying  to make it as small as I could. It's a 1206, which is 3.2mm by 1.6mm. I haven't used SMT caps before, so I thought I might have some trouble soldering it into place, but it wasn't really difficult. 

Breathing in fibreglass dust is a bad idea. If you're cutting boards down take precautions to protect yourself.

I've never really cared much about pot tapers, but after trying out this design I don't think I would be happy going back to a regular bilineal log taper pot.

I'm not sure it's worth putting a buffer and battery in the guitar just for the improved taper, but if you were planning on putting a buffer in anyway, I think it's worth going for a double buffer instead.

[Yogi B]

Jun 4, 2022 12:48:10 GMT -5 MattB said:

The second gang is wired as a variable resistor, in series with the top half of the the voltage divider formed by the first gang. The top half of the voltage divider formed by both gangs together increases faster than the bottom half shrinks.

Just a note that equivalent results can be had by instead putting the lower half of the second gang in parallel with the lower half of the first gang. Thereby halving the lower portion of the voltage divider, as opposed to doubling the upper portion. (This keeps the voltage division ratio the same, but to be exactly equivalent one must also double the pot values.)

The output level at 50% rotation depends on the ratio of resistances of the two gangs. Equal value gangs will give 1/3 output at 50% rotation. Increasing the size of the 'variable resistor' gang will give a steeper taper.

An alternative approach to steepening the taper is to wire the gangs as two volume controls in series, i.e.:

This gives 1/5 (20%) output at 50% rotation, which is what I usually aim for.

Here's a plot comparing this series volumes method (green) to your dual 100k (red) and your 250k+50k (blue):

[MattB]

Jun 4, 2022 14:15:46 GMT -5 Yogi B said:

An alternative approach to steepening the taper is to wire the gangs as two volume controls in series, i.e.:

This gives 1/5 (20%) output at 50% rotation, which is what I usually aim for.

Here's a plot comparing this series volumes method (green) to your dual 100k (red) and your 250k+50k (blue):

Thanks for this.
After trying the 1/3 taper i found I liked the flatter slope at high volume levels, but I really wanted a bit more control over the lower settings. I was going to try the 250k/50k version next, but your approach produces a much better balance between the high and low ends of the range.

Here's an updated layout with Yogi B's version of the pot:

[Yogi B]

Also, ever curious, I wondered how these three stacked up against the formula I use for idealised log tapers. But first, as I don't think I've ever posted it, here is that formula:

R_{(1,\,2)} = R \cdot { a^{1-w} - a \over 1 - a }
where R_{(1,\,2)} is the resistance between terminals 1 & 2 of the potentiometer, R is the pot's total resistance, 0 \leqslant w \leqslant 1 is the fraction of the wiper's rotation, and a \neq 1 is given by:

a = \left({r_\text{tap} \over 1 - r_\text{tap}}\right)^2
where 0 < r_\text{tap} < 1 is the taper of the pot (e.g. r_\text{tap} = 0.1 gives the typical 10% log taper), with values greater than one half giving reverse log tapers (e.g. 0.9 gives the 10% reverse log taper, i.e. an idealised version of the "C" taper).

As the excluded value, at a = 1, r_\text{tap} = 0.5, is equal to a linear taper is not especially missed.

In the below: the dual gang circuits retain there previous colours; the idealised 1/3, 1/5 & 1/7 log tapers are coloured yellow, purple & dark red respectively. (I'll explain the additional dark green trace on right-hand graph in a moment.)

It occurred to me that instead of switching out the wafers in the 250k + 50k version, using your original "variable resistor" layout you could get an identical taper by inserting a 25k resistor across the outer lugs of the second (voltage divider) gang.

With the series volumes variation, this would be a 50k resistor in order to get the same attenuation at 50% rotation. This results in an overall a closer result to the idealised taper, and is the aforementioned dark green trace.

[Yogi B]

I've been wondering if the first buffer could be done away with.

Say, at maximum volume we want 250k of load on the pickups (excluding the tone control & buffer input impedance), that would be had with a 500k dual gang. But, as you note, the load wouldn't be constant: 250k at max volume, increasing towards 500k as the volume is reduced to zero. This would have the have the effect of somewhat increasing the relative amplitude of the resonant peak as the volume was lowered, but in practice I'm not sure that it would be all that noticeable.

Nevertheless the situation could be improved by further upping the value of the dual gang and then compensating for the lesser loading by prepending an additional resistor. A 1Meg dual gang plus 500k resistor would still equal 250k at max volume, but increase toward only 333k at zero. An increase of only 33% versus the previous 100%. Doubling the gangs' value again up to 2Meg, plus 333k resistor, further reduces the difference to 14%. Finally, 5Meg plus 277k resistor is down to an increase of only 5% — though at that point you would likely require full-size (24mm) pots, in addition to suffering from wider tolerances.

Obviously, with the higher value pots, the input impedance of the buffer becomes more significant, both in terms of steepening the apparent taper and increasing the value needed for the added loading resistor (thereby diminishing its purpose of minimizing the variance in loading). As such, the method employed to bias the JFET would need to be altered — this might be as simple as referencing the gate voltage divider via a very large (e.g. 10Meg) resistor, or could involve some form of bootstrapping.