Curing Thermoelectric Voltage Effects

This section focuses on methods to minimize the effects of a given temperature gradient. They can be powerful aids in improving a design because they tend to be low cost.

## Metallurgy

Critical points that need to have the same total thermoelectric voltage should use the same conductive material. For example, the inputs to an op amp should connect to the same materials. The Printed Circuit Board (PCB) traces will match well, but components with different constructions may be a source of trouble.

It is possible to find combinations of metals and solders that have low Seebeck coefficients. While this reduces voltage errors, this can be complicated and expensive to implement in manufacturing.

## Following Contour Lines

Place critical components so that their current flow follows constant temperature contour lines; this minimizes their thermoelectric voltages. The figure below shows an inverting amplifier that will be used to illustrate this concept; RN, RG, and RF are the critical components in this circuit.

The figure below shows one implementation of this concept. Constant temperature contour lines become reasonably straight when they are far from the heat source. Placing the resistors in parallel with these lines minimizes the temperature drop across them.

The main drawback of this technique is that the contour lines change when the external thermal environment changes. For instance, picking up a PCB with your hands adds heat to the PCB, usually at locations not accounted for in the design.

## Cancellation of Thermoelectric Voltages

It is possible to cancel thermoelectric voltages when the temperature gradient is constant. Several examples will be given to make this technique easy to understand.

### Traditional Op Amp Layout Approach

The figure below shows a non-inverting amplifier that needs to have the resistors’ thermoelectric voltage effect minimized. The traditional approach is to lay out the input resistors (RN and RG) close together, at equal distances from the op amp input pins and in parallel.

The figure below shows one layout that follows the traditional approach, together with a circuit diagram that includes the resulting thermoelectric voltages (VTHx and VTHy). VTHx is positive on the right side of a horizontally oriented component (e.g., RN). VTHy is positive on the top side of a vertically oriented component (e.g., RF).

The output has a simple relationship to the inputs (VIN and the three VTHx and VTHy sources):

When the gain (GN) is high, the thermoelectric voltage contributes little to the output error. This layout may be good enough in that case. Notice that the cancellation between RN and RG is critical to good performance. When the gain is low, or the very best performance is desired, this layout needs improvement. The following sections give guidance that helps achieve this goal.

### Single Resistor Substitutions

A single resistor on a PCB will produce a thermoelectric voltage, as discussed before. Replacing that resistor with two resistors that are properly aligned will cancel the two resulting thermoelectric voltages.

The figure below shows the original resistor and its model on the top, and a two series resistor substitution and its model on the bottom. The original resistor has a thermally induced voltage VTHx that is based on the temperature gradient in the x-direction (horizontal).

The two resistors on the bottom have thermally induced voltages VTHy that are based on the temperature gradient in the y-direction (vertical); they are equal because the temperature gradient is constant and the resistor lengths are equal. Due to their parallel alignment, these voltages cancel; the net thermally induced voltage for this combination (as laid out) is zero.

The orientation of these two resistors (R1A and R1B) is critical to canceling the thermoelectric voltages.

The figure below shows the original resistor and its model on the top, and a two parallel resistor substitution and its model on the bottom.

The original resistor has a thermally induced voltage VTHx that is based on the temperature gradient in the x-direction (horizontal). The two resistors on the bottom have thermally induced voltages VTHy that are based on the temperature gradient in the y-direction (vertical); they are equal because the temperature gradient is constant and the resistor lengths are equal. Due to their orientation, and because R1A = R1B, these voltages produce currents that cancel. The net thermally induced voltage for this combination (as laid out) is zero.

### Non-Inverting Amplifier

The figure (non-inverting amplifier) below shows a non-inverting amplifier. We will start with the layout in the figure, Thermoelectric Voltage Model. The resistor RF is horizontal so that all of the thermoelectric voltages may be (hopefully) canceled. The model shows how the thermoelectric voltages modify the circuit.

The output has a simple relationship to the inputs (VIN and the three VTHx sources):

When the gain (GN) is high, the thermoelectric voltage’s contribution to the output error is relatively small. This layout may be good enough in that case. Notice that the cancellation between RN and RG is critical.

We have a better layout shown in the figure below. Recognizing that subtracting the last term in the VOUT equation (middle equation in the figure above) completely cancels the thermoelectric voltages, the resistor RF was oriented in the reverse direction.

With the reversed direction for RF, the output voltage is now:

The cancellation between RN and RG is critical to this layout. The change to RF’s position is not as important.

### Inverting Amplifier

Inverting amplifiers use the same components as noninverting amplifiers, so the resistor layout is the same; see the figure below.

### Difference Amplifier

The figure below shows a different amplifier. This topology has an inherent symmetry between the non-inverting and inverting signal paths, which lends itself to canceling the thermoelectric voltages. The figure below shows the layout and model.

The output has a simple relationship to the inputs (VIN, VREF and the four VTHx sources):

### Instrumentation Amplifier Input Stage

The figure below shows an instrumentation amplifier input stage, which is sometimes used to drive the input of a differential ADC. While this is a symmetrical circuit, achieving good thermoelectric voltage cancellation on the PCB presents difficulties. It is best to use a dual op amp, so the RF resistors have to be on both sides of the op amp, while RG connects both sides, the distances between resistors are too large to be practical (thermal gradient is not constant).

The solution to this problem is very simple—split RG into two equal series resistors so that we can use the non-inverting layout on both sides of the dual op amp. Each side of this amplifier will cancel its thermoelectric voltages independently. This is shown in the figures below.

The VTHx sources cancel, for the reasons already given, so the differential output voltage is simply:

### Modifications for Non-Constant Temperature Gradients

Temperature gradients are never exactly constant. One cause is the wide range of thermal conductivities (e.g., traces vs. FR4) on a PCB, which causes complex temperature profiles. Another cause is that many heat sources act like point sources, and the heat is mainly conducted by a two-dimensional object (the PCB) The temperature changes rapidly near the source and slower far away.

Non-constant temperature gradients will cause the temperature profile to have significant curvature, which causes all of the previous techniques to have less than perfect success. Usually, the curvature is small enough so that those techniques are still worth using. Sometimes, additional measures are needed to overcome the problems caused by the curvature.

One method is to minimize the size of critical components (e.g., resistors). If we assume that temperature has a quadratic shape, then using components that are half as long should reduce the non-linearity error to about one quarter the size.

Another method is to keep all heat sources and sinks far away from the critical components. This makes the contour lines straighter. The contour lines can be deliberately changed in shape. Using a ground plane (also power planes) to conduct heat away from the sources helps equalize the temperatures, which reduces the non-linear errors. Adding guard traces or thermal heat sinks that surround the critical components also help equalize the temperatures. We can modify the sizes of the critical components so that the cancellation becomes closer to exact. In order to match resistors, for instance, we need to make sure that the temperature change across each of the matched resistors is equal; see the figure below for an illustration.