A linear potentiometer is defined by its linear relationship between resistance and rotation angle. We use this relationship to our advantage to “dial in” a desired voltage. For example, if we apply 10 VDC across the potentiometer, we expect an output voltage of 5 VDC with the potentiometer in its mid position. Devices such as the Schneider Electric XB4BD912R10K potentiometer shown in Figure 1 provide convenient calibration markings.
Fair enough.
However, we will be greatly disappointed to measure an output voltage of 4 VDC when the device is set to 5. To understand why, we need to expand to include the system level view with a focus on circuit loading.
This engineering brief explores the non-linear relationship between the ideal and the real-world potentiometer applications. It is focused on industrial controls, specifically a class of Programmable Logic Controllers (PLCs) with low input resistance typically associated with dual-purpose digital / analog inputs. We explore the application using fundamental circuit techniques including Thévenin’s theorem.
Be sure to follow part 2 of this series where we explore a lookup table application.
Figure 1: Picture of a Schneider Electric XB4BD912R10K potentiometer and integral indicator ring set to 8.5.
Thévenin’s model of a potentiometer
Thévenin’s theorem tells us that a circuit such as our “simple” potentiometer may be represented by an ideal voltage source with a series resistance. We apply this model knowing that each rotational position has a unique Thévenin voltage and Thévenin resistance.
An example is shown in Figure 2, where a 10 kΩ potentiometer driven by 10 VDC supply is set to its halfway position (50% rotation). The equivalent circuit is modeled as an ideal 5 VDC source in series with a 2.5 kΩ resistance. Similar models could be produced for different positions. For example, when set to 80%, the resulting circuit an ideal 8 VDC source in series with a 1.6 kΩ resistance. Recall that we calculate the circuit’s Thévenin resistance as 2 kΩ || 8 kΩ.
As we continue, we observe a linear changing Thévenin voltage and a parabolic Thévenin resistance response. It peaks at 50% and has zeros at the 0% and 100% positions.
Figure 2: Thévenin equivalent for a 10 VDC supply and a 10 kΩ potentiometer set to the midpoint position.
External loading
With Thévenin circuit simplification, we can now load the circuit with our PLC’s input resistance. For this example we will use the Crouzet Millenium Slim 88983902 PLC as shown in Figure 3. Close inspection of the datasheet reveals that this PLC has an input impedance of 11.7 kΩ. This is typical for PLCs that feature dual purpose input designed for either analog or digital. Note that PLCs with dedicated analog inputs generally have a higher input impedance. However, the error patterns described in this note hold – it’s a question of degree not of kind.
Figure 3: Image of the Crouzet PLC installed on a Phase Dock trainer. The 22 mm Schneider potentiometer is visible on the switch plate.
The circuit loading (voltage divider) problem is shown in Figure 4. In the upper section we see that our 50% positioned Thévenin circuit has been loaded down to 4.12 VDC. Likewise, our 80% positioned circuit with the ideal 8 VDC source is loaded to 7.04 VDC.
Figure 4: Calculations for the 10 kΩ potentiometer is loaded with a 11.7 kΩ PLC. Calculations include the 50% and the 80% rotational positions each showing a high deviation from expectations.
The voltage error (difference between Thévenin ideal and voltage measured by the ADC) is not linear as shown in Figure 5. Instead, we see ideal measurement when the potentiometer is set to 0% or 100%, with a peak at about 70%.
Perhaps we expected this graph to be symmetrical, given the potentiometer’s parabolic resistance curve. Yet, we forget that Thévenin voltage increases with rotation. Higher voltages are naturally associated with greater error. Consequently, our parabolic curve is shifted to the right.
Figure 5: Voltage error as a function of potentiometer rotational position.
Experimental verification
We can quickly verify these numbers by observing the potentiometer voltage when connected and disconnected from the PLC. Setting the potentiometer to 50% yields a measured voltage of 4.1 VDC. This becomes 5.0 VDC when the circuit is unloaded by disconnecting the PLC and its 11.7 kΩ resistor.
Circuit loading implications
The problem with circuit loading is a misalignment of expectations. We may have expected a 5.0 VDC output when the potentiometer was set to 50%. In reality, the PLC reads 4.12 VDC, which is significant voltage error.
The bottom line is that the voltage output from the potentiometer will not be aligned with the calibrated markings.
Solutions for circuit loading
There are several ways to mitigate this loading problem, including:
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Be pragmatic and live with the situation as not all systems require perfect internal consistency. Despite its linearity errors, the system is still responsive with reliable and repeatable user control. There may be downsides on the maintenance side. A future technician may question the linearity discrepancies. Also, the user’s numbers could shift if the potentiometer was replaced with a different value.
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Use a lower resistance potentiometer. This will reduce but not eliminate the magnitude of the error. For example, a 1 kΩ will reduce the error by an approximate margin of 10. While this is effective, we quickly run into limits as lower resistance values will dissipate higher current.
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Use a PLC with a higher input resistance. A PLC with a dedicated 100 kΩ input resistance would provide a significant improvement. However, a small error will still exist.
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Use an external amplifier interposed between the potentiometer and the PLC. This may be undesirable as it complicates the system, adds cost, and could increase the failure rate.
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Use an equation. Since the PLC’s input impedance is fixed, we could use an equation to linearize the results.
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Use a lookup table to provide similar functionality as an equation.
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The potentiometer could be eliminated in favor of a display with pushbuttons or even a rotary encoder. Unfortunately, these solutions may eliminate the desirable human factors of the rotary potentiometer.
Parting thoughts
The “simple” potentiometer is not so simple. Real-world circuits load the potentiometer resulting in a mismatch between the calibrated dial markings and the measured voltage. There are several solutions, ranging from keeping it simple and living with the non-linearity, use of floating point calculations to correct the nonlinearity, and even seek alternative options such as an HMI. Each has their advantages and disadvantages.
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APDahlen
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About this author
Aaron Dahlen, LCDR USCG (Ret.), serves as an application engineer at DigiKey. He has a unique electronics and automation foundation built over a 27-year military career as a technician and engineer which was further enhanced by 12 years of teaching (interwoven). With an MSEE degree from Minnesota State University, Mankato, Dahlen has taught in an ABET-accredited EE program, served as the program coordinator for an EET program, and taught component-level repair to military electronics technicians. Dahlen has returned to his Northern Minnesota home and thoroughly enjoys researching and writing articles such as this.