 ### Network # How to "simulate" a logaritmic trimpot

H

#### Henrik 

Jan 1, 1970
0
Hello group,

I am trying to simulate a logaritmic trimpot in software on a small
microcontroller.

We have some industrial controllers where some parameters (i.e. max running
time) is set via potmeters on the front. And one of the potmeters are
logaritmic to give a finer change in the lower area and a more coarse change
in the high area.

My idea is to use a linear trimpot (which we have stocked) to replace a
logaritmic pot (which we have not stocked). The pot wiper is connected
directly to the micros internal AD converter and to GND/AVCC of the
microcontroller. By turning the pot I can now measure 0-1023 (10-bit AD) on
the micro, that is just fine.

I need to convert this 0-1023 value to a value between 10 and 54000
logaritmic. I think a mathematical function or a table lookup is the way to
go, but I actually cannot figure out how. I think mainly due to my lack of
knowledge about how such a pot actually works.

So any help is gladly appreciated.

Best regards
Henrik

J

#### Joerg

Jan 1, 1970
0
Hello Henrik,
My idea is to use a linear trimpot (which we have stocked) to replace a
logaritmic pot (which we have not stocked). The pot wiper is connected
directly to the micros internal AD converter and to GND/AVCC of the
microcontroller. By turning the pot I can now measure 0-1023 (10-bit AD) on
the micro, that is just fine.

I need to convert this 0-1023 value to a value between 10 and 54000
logaritmic. I think a mathematical function or a table lookup is the way to
go, but I actually cannot figure out how. I think mainly due to my lack of
knowledge about how such a pot actually works.

So any help is gladly appreciated.

You could include the math header before compiling and use the log
function in there. Hoping it contains one, that is.

However, many pots aren't exactly "log". If your client or the users
like how the former pot worked take one of these and ohm it out in, say,
one-degree steps. Mount a knob on it, glue a long thin stick to that and
keep going. Just don't ever reverse during that measurements series
because the shaft connection often has slack. Now look at the results
and divide it into linear sections that follow the curve as a whole
approximation" which is often done in gain control circuits.

With piecewise linear your code could be realized with staggered "if"
statements with an "else" only after the last one or if you want it to
look clean a "switch" and "case" statement. This avoids huge ROM lookup
tables for the pot function since uCs often don't have a lot of ROM.

BTW, questions like this might yield more answers in the embedded newsgroup.

A

#### Ancient_Hacker

Jan 1, 1970
0
Henrik said:
I need to convert this 0-1023 value to a value between 10 and 54000
logaritmic. I think a mathematical function or a table lookup is the way to
go, but I actually cannot figure out how. I think mainly due to my lack of
knowledge about how such a pot actually works.

Most log-taper pots have about 10% resistance at half a turn.

Actually you want the inverse function-- a log function grows more and
more slowly, you need an exp-like function.

A little doodling with Excel shows that a exponent of about 3 does the
trick:

0 0%
100 0%
200 1%
300 3%
400 6%
500 12%
600 20%
700 32%
800 48%
900 68%
1000 93%

.... about 12% at half turn, close enuf.

so one possible formula loks somethng like: (in/1024)^3.0 * 54000 + 10

J

#### Jon

Jan 1, 1970
0
Henrik said:
Hello group,

I am trying to simulate a logaritmic trimpot in software on a small
microcontroller.
Henrik,
This is not exactly what you asked for, but there are a couple of
all-analog tricks for getting a non-linear gain vs position with a
linear pot. What you describe is actually an exponential (inverse log)
function, since the slope is small for small values of R, and large for
large values of R.
..
Use the pot as a rheostat (in series with a small fixed resistor) as
the input resistor in an op amp inverting amplifier configuration.
This gives you a large slope at low resistance settings, and a small
slope at large resistance settings. This is just the opposite of what
you want; So o the following: Connect this circuit, in series with a
unity gain inverting amplifier. Connect a fixed resistor to the output.
Call this block the "feedback element". Use this "feedback element"
as the feedback resistor of another op amp inverting amplifier. This
gives you the general shape that you need. By tweaking the resistance
values, you can get a reasonable approximation to an exponential
characteristic.
..
Another method is to use a "Tee" network in the feedback path of an
op-amp inverting amplifier. Call the series Rs R1, R2. Use the
rheostat connected pot as the shunt resistor, R3 of the "tee".. The
effective feedback resistance = R1 + R2 + R1R2/R3. The gain vs
rotation has the general shape that you need. By tweaking the Ratio of
R3max to R1, you can get very close to an exponential characteristic.
Regards,
Jon

A

#### Ancient_Hacker

Jan 1, 1970
0
A simpler way is to just use a high-value pot with a considerably

For example, a 10K pot with a 680 ohm load resistor will give you about
10% voltage at half a turn, going up more steeply after that.

K

#### Ken Smith

Jan 1, 1970
0
I need to convert this 0-1023 value to a value between 10 and 54000
logaritmic. I think a mathematical function or a table lookup is the way to
go, but I actually cannot figure out how. I think mainly due to my lack of
knowledge about how such a pot actually works.

So any help is gladly appreciated.

The table method turns the curve into a bunch of straight lines. The
length of the lines is determined by the number of entries in the table.

// all integers:

Index = Input / (Entries - 1)
Fraction = Input - (Entries - 1)*Index
Slope = Table[Index+1] - Table[Index]
Output = Table[Index] + Slope*Fraction

Chances are, a lookup table with 17 entries will be good enough for your
pot purpose.

J

#### Joerg

Jan 1, 1970
0
Hello Jon,
This is not exactly what you asked for, but there are a couple of
all-analog tricks for getting a non-linear gain vs position with a
linear pot. What you describe is actually an exponential (inverse log)
function, since the slope is small for small values of R, and large for
large values of R.
.
Use the pot as a rheostat (in series with a small fixed resistor) as
the input resistor in an op amp inverting amplifier configuration.
This gives you a large slope at low resistance settings, and a small
slope at large resistance settings. This is just the opposite of what
you want; So o the following: Connect this circuit, in series with a
unity gain inverting amplifier. Connect a fixed resistor to the output.
Call this block the "feedback element". Use this "feedback element"
as the feedback resistor of another op amp inverting amplifier. This
gives you the general shape that you need. By tweaking the resistance
values, you can get a reasonable approximation to an exponential
characteristic.
.
Another method is to use a "Tee" network in the feedback path of an
op-amp inverting amplifier. Call the series Rs R1, R2. Use the
rheostat connected pot as the shunt resistor, R3 of the "tee".. The
effective feedback resistance = R1 + R2 + R1R2/R3. The gain vs
rotation has the general shape that you need. By tweaking the Ratio of
R3max to R1, you can get very close to an exponential characteristic.

It's simpler than that, just one resistor from wiper to top or to
bottom, depending on which direction you want to "bend". There used to
be a scan of an old, old magazine page with graphs that Martin Griffith
(here from s.e.d.) did but that web site is now dead.

I'll ping Martin in a separate thread, maybe he still has it.

J

#### Joerg

Jan 1, 1970
0
Hello Henrik,
I am trying to simulate a logaritmic trimpot in software on a small
microcontroller.

We have some industrial controllers where some parameters (i.e. max running
time) is set via potmeters on the front. And one of the potmeters are
logaritmic to give a finer change in the lower area and a more coarse change
in the high area.

My idea is to use a linear trimpot (which we have stocked) to replace a
logaritmic pot (which we have not stocked). The pot wiper is connected
directly to the micros internal AD converter and to GND/AVCC of the
microcontroller. By turning the pot I can now measure 0-1023 (10-bit AD) on
the micro, that is just fine.

I need to convert this 0-1023 value to a value between 10 and 54000
logaritmic. I think a mathematical function or a table lookup is the way to
go, but I actually cannot figure out how. I think mainly due to my lack of
knowledge about how such a pot actually works.

So any help is gladly appreciated.

Ok, Martin Griffith posted the old pdf copies again on how to mimick
that pretty closely without code and just one extra resistor:

K

#### Ken Smith

Jan 1, 1970
0
[....]
ooops, I went back and changed the constants to variable names to make it
clearer and as a result screwed it up

Here it is more like I started with.

J

#### Jon

Jan 1, 1970
0
Joerg said:
Hello Jon,

It's simpler than that, just one resistor from wiper to top or to
bottom, depending on which direction you want to "bend". There used to
be a scan of an old, old magazine page with graphs that Martin Griffith
(here from s.e.d.) did but that web site is now dead.

I'll ping Martin in a separate thread, maybe he still has it.

Joerg,
The method of using a "loaded pot" does indeed give you a non-linear
characteristic. However, the output/input curve is "S" shaped with
respect to a straight line drawn between the minimum and maximum
outputs. By using a load resistor that is extremely small with respect
to the pot resistance value, you can minimize the change in curvature
at one end or the other, but you can't eliminate it.
Regards,
Jon

J

#### Joerg

Jan 1, 1970
0
Hello Jon,

The method of using a "loaded pot" does indeed give you a non-linear
characteristic. However, the output/input curve is "S" shaped with
respect to a straight line drawn between the minimum and maximum
outputs. By using a load resistor that is extremely small with respect
to the pot resistance value, you can minimize the change in curvature
at one end or the other, but you can't eliminate it.

Yes, it won't be perfect. Then there is the old trick to provide a
piecewise linear scheme via diodes but this quickly becomes esoteric for
a simple potmeter application.

J

#### joseph2k

Jan 1, 1970
0
Henrik said:
Hello group,

I am trying to simulate a logaritmic trimpot in software on a small
microcontroller.

We have some industrial controllers where some parameters (i.e. max running
time) is set via potmeters on the front. And one of the potmeters are
logaritmic to give a finer change in the lower area and a more coarse change
in the high area.

My idea is to use a linear trimpot (which we have stocked) to replace a
logaritmic pot (which we have not stocked). The pot wiper is connected
directly to the micros internal AD converter and to GND/AVCC of the
microcontroller. By turning the pot I can now measure 0-1023 (10-bit AD) on
the micro, that is just fine.

I need to convert this 0-1023 value to a value between 10 and 54000
logaritmic. I think a mathematical function or a table lookup is the way to
go, but I actually cannot figure out how. I think mainly due to my lack of
knowledge about how such a pot actually works.

So any help is gladly appreciated.

Best regards
Henrik

Many posts, many solutions, here is one more:

1. It can also be understood as a exponential pot.

2. You want to solve out = a + e^bx for say 4 positions to get a good fit.

a and b are arbitrary constants (what we are solving for) and out is the
value curve desired and x is the shaft angle / percentage rotation of the
linear pot wiper.

3. Then you can trade off table space versus computational cost for the
curve fitting. The exponential curve and its relatives are self similar.

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