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> Digital
Potentiometers > APP 1828

Dec 26, 2002

Keywords: digital pot, digital potentiometer,
audio volume control, MAX5407, MAX5408, MAX5409, MAX5410,
MAX5411, volume control, volume adjust, digital volume
adjustment, log pots, digital log pots, logarithmic taper,
logarithmic, potentiometers
Related
parts

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APPLICATION NOTE 1828

Audio Gain Control Using Digital Potentiometers

Abstract: Digital
potentiometers (pots) offer advantages for audio volume (gain)
control applications and can replace bulky mechanical pots,
especially in handheld portable devices such as MP3 players,
PDAs, cell phones, mobile Internet devices, or stereo AM/FM
radios. This document describes the types of digital pots
available for audio control such as logarithmic taper pots
(log pots). It examines several common designs using log taper
pots and audio amplifiers, evaluates their advantages and
disadvantages, and recommends circuit designs.

Attend
this brief webcast by Maxim on
TechOnline

A
similar version of this article appeared in the January 7,
2002 issue of EE Times magazine.

Introduction
It is now common for portable multimedia
equipment to include some sort of stereo audio playback
circuitry, perhaps for MP3 or mobile Internet applications.
Many specialized ICs are available for these circuits and many
use a mechanical potentiometer (pot). This application note
will demonstrate that widely available low-power components
can be just as effective. The article demonstrates how to
achieve a stereo volume control without a mechanical
pot.

Traditional Mechanical Pot Design
Historically, audio
volume controls used a special kind of potentiometer with a
log (or sometimes audio) taper or law (Figure 1). This
approach derives from the roughly logarithmic response of the
ear to changes in sound pressure levels.

Figure
1. Logarithmic response of the potentiometer to changes in
sound pressure levels.

In general, the midpoint of
the rotation usually gives around 20dB attenuation of the
audio signal, with attenuation rapidly increasing from the
midpoint counter-clock wise (CCW). There is finer control over
the "louder" settings from the midpoint clock wise
(CW).

While this approach works well in practice, there
are still several reasons not to use a mechanical pot in a
small portable device. The space constraints and reliability
issues of a mechanical pot are just two immediate issues.
Today a common volume-control interface for modern devices
uses up/down buttons in conjunction with some form of host
processor. This design provides an inexpensive, useable
solution without a bulky mechanical pot.

Stereo (or
ganged) rotary pots also have a mechanical tracking issue;
mechanical tolerances mean that L-R tracking suffers as the
volume is adjusted. Also, the desired transfer
function should be considered. Is full attenuation desired? Or
rather, can the application use a gain trim control offering
perhaps 30dB of adjustment range but no fully off' position?
Perhaps you should consider a digital pot?

Design Issues with Digital Pots
Over the past years
digital pots have become available and their performance has
evolved (Figure 2). These digital devices use resistive
ladders and FET
switching under digital control to effectively replace
mechanical pots in a number of areas. On the surface, using a
pair of these ICs would seem a logical solution for stereo
volume control, however, there are issues which must first be
addressed.

Figure
2. Functional block diagram of the MAX5160 digital
pot.

The most commonly available digital pots are
effectively linear
pots, i.e., their resistive increments are equally weighted. A
reasonably constant dB-per-step law is desirable in audio
volume control, so the design may have to emulate this log
behavior in some way. Recall now that we are no longer
constrained by the mechanical pot's audio
taper.

There is a follow-on issue. While the
digital pot steps are usually designed to give equal-value
resistive increments, a by-product of the process variation is
that the total end-to-end resistance
varies widely from part to part, as much as ±30% in some
types. This resistance variation must be considered when
designing a circuit that requires close matching between two
channels using separate digital pots.

Finally, the
transitions should be as glitch
free as possible, so a make-before-break
wiper arrangement should be considered mandatory.

Design Examples
Some design examples follow. There are
both gain-trim designs (where the control is applied over a
set attenuation range, but not giving full attenuation), and
more traditional full CW/off CCW volume controls. These
circuit ideas assume a VCC of between 2.7V and 5V
and a low-impedance VREF = VCC/2. The IN
input signals are from a low-impedance voltage
source.

Example 1
The circuit in Figure 3 would
seem to give adequate results. Using two MAX5160Ls
(assuming that their digital inputs are suitably controlled)
around a MAX4252
op
amp, the circuit should give evenly tracking gain or
attenuation over a nominal ±6dB range. The circuit should work
over a VCC range from 2.7V to 5V and have 32
useable gain settings. Even the power-on-reset (POR)
state of the MAX5160L gives approximately a unity gain
setting.

The drawback to this implementation is the
±25% overall resistance variation of the digital pot. This
variation could lead to a wide gain tolerance, especially on
the settings at the extremities of resistance,
channel-to-channel as well as unit-to-unit. For example,
assuming the 50kΩ resistors are ±1%, then the nominal, maximum
+6dB setting could vary between limits of:

Av1 = -(50.5kΩ + 62.5kΩ)/49.5kΩ = -2.283V/V or
7.16dB

Av2 = -(49.5kΩ + 37.5kΩ)/50.5kΩ = -1.723V/V
or 4.73dB

Figure
3. ±6db stereo gain trim control, 32 gain settings (1 channel
shown).

This amount of left-right mismatch is
easily audible. This circuit can be made to work better by
selecting or trimming the support resistors (or selecting the
digital pot!) to suit, but this is not feasible in mass
production. A design approach must be found which minimizes or
eliminates this gain
error.

Example 2
The circuit in Figure 4 uses the
MAX5160L digital pot in a divider chain. The MAX5160L uses
100kΩ and 50kΩ resistors to supply the MAX4252 with some
positive feedback in addition to the usual negative feedback .
The gain of this circuit can be shown as:

AV = (1 - KN)/(KP -
KN)
Where KN is the
negative feedback fraction and KP is the positive
feedback fractions. For the example in Figure 4, KN
= 100kΩ/(100kΩ + 50kΩ) or 2/3, and KP is
variable.

Figure
4. ±6dB stereo gain trim control, 17 gain settings in an
improved design.

When the MAX5160L wiper is
positioned at the VREF terminal, the gain of the
circuit is -0.5V/V, as there is no positive feedback
contribution. When the wiper is at midscale, KP =
0.5 and the gain is now -2V/V. Hence, by using those 17
positions between VREF and midscale, the gain can
be varied over a ±6dB range. The 15 unused positions have been
a trade-off for repeatability, because the gain value does not
depend on the digital-pot resistance tolerance, as did the
circuit of Figure 1. The gain tolerance is now only limited by
the ±1% 100kΩ/50kΩ resistors and the INL/DNL error of the
MAX5160L (±4.6%, max.).

There is an interesting point
to note. The limit for stability in this circuit is reached
when KP ≥ 2/3, i.e., when the positive feedback
fraction meets or exceeds the negative. The host processor
controlling the MAX5160L should, therefore, prevent this
situation from occurring.

Example 3
The circuit in Figure 5 uses digital
pots as an obvious alternative to a traditional approach for
volume control. All codes are valid, with settings ranging
from 0dB to full attenuation. Table 1 shows the
calculated attenuations based on the MAX5160L's 32
steps.

Table 1. Calculated results of Figure 3
circuit

Code Setting

Attenuation

Code Setting

Attenuation

0

0.00

16

-6.31

1

-0.28

17

-6.90

2

-0.58

18

-7.55

3

-0.88

19

-8.24

4

-1.20

20

-9.00

5

-1.53

21

-9.83

6

-1.87

22

-10.74

7

-2.22

23

-11.77

8

-2.59

24

-12.93

9

-2.98

25

-14.26

10

-3.38

26

-15.85

11

-3.81

27

-17.79

12

-4.25

28

-20.28

13

-4.72

29

-23.81

14

-5.22

30

-29.83

15

-5.74

31

Full
attenuation

Figure
5. Traditional volume control design (1 channel shown) has
drawbacks.

Notice how the attenuation figures are
spread. There is less than 6dB total variation over the first
15 codes and less than 1dB over the first four. This is not
particularly useful. Interestingly, even when choosing a part
with a far larger number of taps, you still only get 6dB
variation over half of the codes.

To address this
problem one approach selects a subset of the codes available
to achieve a reasonably constant dB/step figure. For example,
using only those codes highlighted in Table 1 gives roughly
3dB/step up to code 29, allowing 11 settings. This can work
well if the digital pot chosen has many tap positions (256 or
higher). However, parts with that flexibility are generally
more expensive. Given that the majority of the tap positions
will not be used (unless, perhaps, when interpolating between
volume settings), it would seem more efficient to try and
utilize more of the existing taps with a different
topology.

Resistively loading the wiper of a linear pot
to "bend" the characteristic is an old trick. The load
resistor is usually about 1/20th the value of the linear pot
resistance. There are two disadvantages of applying this
method with a linear' digital pot: the input impedance
of the pot is now dependant on gain setting (lowest at maximum
volume); and again, the wide tolerance on end-to-end
resistance means that L-R tracking suffers at any setting
apart from the extremes. Figure 6 shows the
idea.

Figure
6. This configuration with a resistive load creates an
equivalent fixed-resistor for clarity.

Example 4
The circuit of Figure 7 yields a
traditional volume-control characteristic, much like that of
Figure 5. However, this design uses a little positive feedback
to even out the step sizes to roughly 1.6dB/step over most of
its useable range.

An immediate disadvantage of this
design is that the negative feedback fraction (KN)
has to be 0.5 or higher for this approach to yield usable
results (although 0.25 would be the limit of stability). In
simple terms, we have already thrown away around half the
available codes just so the circuit can operate. However, the
remaining 17 codes are all used (no gaps as in the Figure 6
example), as indicated in Table 2 below. The third
column lists the delta in step sizes, showing how consistent
they are over the majority of the attenuation range. Figure
8 shows the linearising effect, with gain in dB on the
Y-axis plotted against tap number on the X-axis. This data
compares favorably with the circuit of Figure 6, where the
highlighted values gave roughly 3dB steps and only 11
settings.

Figure
7. This near-constant dB/step topology (1 channel shown) is an
improved design.

One side effect of this topology
with the values shown is that there will be a 6dB boost
for the midscale value of the digital pot. This can often be
accommodated in the gain structure of the full audio path,
where some gain shifting is usually
inevitable.

Table 2. Calculated results of Figure 7
circuit

Code Setting

Gain

(Delta)

Code Setting

Gain

<(Delta)/td>

16

6.88

24

-5.60

1.61

17

5.19

1.68

25

-7.32

1.71

18

3.60

1.59

26

-9.17

1.86

19

2.06

1.54

27

-11.25

2.07

20

0.56

1.50

28

-13.65

2.40

21

-0.93

1.50

29

-16.59

2.94

22

-2.44

1.51

30

-20.53

3.94

23

-3.99

1.55

31

-26.95

6.42

32

Fully off

—

Figure
8. Stereo, cascaded traditional volume control, more =
better?

Example 5
The circuit of Figure 9 uses a total
of four MAX5160L digital pots to produce a high-resolution,
stereo volume control. The number of possible valid codes per
channel is greatly increased, giving 32 x 32 or 1024
attenuation codes. Again, the end-to-end resistance tolerance
does not have any first-order effect because of the buffering
between the two digital pot stages. L-R tracking is only
limited by the tap-to-tap matching accuracy. The wiper
resistance has little loading effect, as each wiper sees a
high-impedance op amp input.

Figure
9. This design uses MAX1560L digital pots to produce
high-resolution stereo volume control.

Of the 1024
codes, some give duplicate attenuation values. For example,
the first pot is at -6dB and the second is fully up, thus
giving -6dB overall. This is the same as first pot fully up
and the second at -6dB., Moreover, if either pot is set to
full attenuation, any setting on the other pot is irrelevant,
all of which leaves something like 348 unique attenuation
settings from 0 to -60dB (actually -59.66dB).

To map
the codes to an attenuation figure, some sort of simulation or
spreadsheet approach would seem appropriate. Figure 10
shows the spread of attenuation obtained, including duplicate
values.

Figure
10. Spread of attenuation obtained from the design of Figure
9.

Figure 10 demonstrates that most of the codes
give attenuation values between 0 and -40dB. The delta, or dB
step size between each attenuation value, can be plotted in a
manner similar to that in Table 2 (Figure 11). This
gives a visual indication of the granularity of the
steps.

Figure
11. Plot shows the delta in dB of the step size between each
attenuation value for the codes generated by the Figure 9
circuit.

The granularity of the steps appears very
evenly distributed with differences in most of the steps well
under 0.5dB, only reaching 1dB at -41.6dB, and with the
penultimate 6dB step between -53.6 and -59.6. Repeated codes
appear on the graph as zero delta figures. This yields the
kind of control range and granularity required in the most
exacting audio level controls.

There are, however,
limitations to this approach too. Obviously, this circuit has
a reasonable control overhead, perhaps using lookup tables to
retrieve values and using some kind of ranging algorithm to
obtain smooth volume transitions. Unlike the circuit in Figure
4, however, there is no conditional stability situation so any
combination of codes is fine. More seriously, variations in
the tap-to-tap resistor matching between the first and second
digital pots could mean that monotonicity is NOT guaranteed.
Using a subset of the codes, hence coarser steps, would be one
way of assuring monotonic
steps, but this would come at the expense of fine
steps.

In theory, while the cascaded circuit of Figure
9 seems to give impressive results on initial investigation,
the practical implementation of the circuit can be
problematic.

Summary
The circuits of Figures 5 and 6 probably give
the best compromise between price, complexity and performance
for most situations. Controlled using a 3-wire interface,
Maxim also offers the MAX5400/MAX5401 and
MAX5402 devices.
These digital pots offer 256 taps for those applications
needing slightly higher resolution and have a 3-wire protocol
available for control.

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Download,
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APP 1828: Dec 26, 2002

AN1828, AN 1828, APP1828,
Appnote1828, Appnote 1828

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