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Circuits > APP 838
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Potentiometers > APP 838
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Engineering Topics > APP 838

Nov 01, 2001

Keywords: linear pots, digital pot, digital
potentiometer, log pots, log potentiometers, pseudolog pots,
pseudologarithmic, potentiometers, audio volume, volume
control
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parts

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APPLICATION NOTE 838

Use a Linear Potentiometer to Create a Nonlinear
Transfer Function for Audio Volume Control

Abstract: Linear
digital potentiometers (pots) can be used in nonlinear
applications, such as adjusting volume control in audio
applications. This article discusses how to create a
"pseudologarithmic" taper digital potentiometer (pot). This is
achieved by simply adding a single resistor to the end of the
digital pot when configured as a variable resistor.

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To
meet specific dynamic-range requirements, many applications
require circuits exhibiting a non-linear transfer
function. From linearizing the response of a circuit element
to providing a logarithmic output for volume control, these
circuits are useful in a variety of everyday engineering
applications. Linear-taper digital potentiometers can be used
in simple voltage
divider configurations to provide these non-linear transfer
functions. For the following examples of these types of
transfer functions, the 50KΩ version of the MAX5160 digital
potentiometer is used. The equations in the following
spreadsheets do not include the ±25% end-to-end resistance
tolerance of the MAX5160, but they can be easily adapted to
include this tolerance as well as other parameters and
potentiometers.

Typical divider configurations are
shown in Figures 1, 2, and 3. For each of
these circuits assume that Vin represents a low-impedance
voltage source
and Vout represents a high-impedance input node. Figure 1
depicts a simple voltage divider with a transfer function of
Vout = Vin(Rb/Rpot), where Rpot = Ra + Rb, and Ra and Rb
represent the resistances from Vin to the wiper and from the
wiper to ground, respectively. Stepping the wiper from the
bottom of the pot to the top with Vin at a constant 5V level
generates a linear transfer function, as shown in the graph on
the Linear Response spreadsheet.

Excel
spreadsheet for Linear Response (ZIP, 8K)
Figure 1.
Linear response circuit and spreadsheet.

Adding a
series resistor to the circuit (R1 in Figure 2) yields an
entirely different result. This circuit's transfer function
more closely resembles a logarithmic curve and is
characterized by the equation Vout = Vin(Rb/(R1 + Rb)). By
varying the value of R1, which in this case is 10KΩ, the
"pseudo-logarithmic" transfer function can be customized to
meet the actual needs of the circuit. A graph of the transfer
function is shown below in the Pseudo-Logarithmic Response
spreadsheet. One possible drawback to this circuit as compared
to a log-taper digital pot is that Vout can only approach the
full-scale value of Vin - it cannot reach it. Therefore, there
is some loss of the output's dynamic range; the magnitude of
that loss depends on the value chosen for R1. Using a
log-taper digital potentiometer, however, limits the response
to that particular potentiometer's specifications (i.e.,
1dB/step, 2dB/step, etc). There are arguments pro and con for
both topologies depending on the specifications
needed.

Excel
spreadsheet for Pseudo Logarithmic Response (ZIP, 8K)

Figure 2. Pseudo logarithmic response circuit and
spreadsheet.

Lastly, swapping the positions of R1
and the MAX5160 yields the circuit shown in Figure 3. This
configuration alters the response of the output to form more
of an inverse-logarithmic function. The transfer function for
this circuit is given as Vout = Vin(R1/(R1 + Rb)) and is shown
in the graph within the Pseudo Inverse-Log Response
spreadsheet. Again, as in the previous example, the value
chosen for R1 affects the dynamic
range of the output. This circuit's output does not extend
to the ground rail.

Excel
spreadsheet for Pseudo Inverse Log Response (ZIP, 8K)

Figure 3. Pseudo inverse-logarithmic response circuit
and spreadsheet.

For simple applications, such as
the examples given, any of the previous spreadsheets can be
adapted to cover a wide range of digital potentiometers and
circuit values by following these steps:

1. Double click
on the spreadsheet, not on the graph. You may have to close
the Chart Toolbar if it pops up.
2. Enter the value of Vin
in cell A3.
3. Enter the value of R1 in cell B3.
4.
Enter the value of the potentiometer resistance in cell C3.

5. Enter the total number of steps provided by the
potentiometer in cell D3.
6. Copy the formulas found in
row 34 of columns E, F, G, and H down their respective columns
until the number of steps in column E equals the total number
of steps provided by the potentiometer (and entered in cell
D3). In other words, for a 64-step pot copy the E34, F34, G34,
and H34 formulas down their respective columns to row 66.

7. Locate the graph within the spreadsheet. Single click
on the graph and the word "Chart" will appear in the menu
above the toolbar at the top of the screen. If a separate
Chart Toolbar pops up on the screen, close it. Click on the
word "Chart" at the top of the screen. From the pull-down menu
click on "Source Data." A separate window will appear with the
data range of cells highlighted. Now click and drag the
pointer down column H (Vout) of the spreadsheet until the
cells of interest are outlined. Then click OK in the Source
Data window. The graph now depicts the new Vout versus
tap-position data.

The examples given are fairly
generic in their scope and have not included such parameters
as wiper resistance, zero and full-scale error, end-to-end
resistance tolerance, temperature
coefficients, etc., but with some work the spreadsheets could
be modified to include these specifications.

Excel
is a registered trademark of Microsoft Corporation.

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Download,
PDF format (74kB)
APP 838: Nov 01, 2001

AN838, AN 838, APP838,
Appnote838, Appnote 838

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