Thermocouple Junction Behavior

While thermocouples are a common temperature sensor, it is not commonly known that every Printed Circuit Board (PCB) design includes many unintended thermocouple junctions that modify the signal voltages. This section covers the physics behind this effect and gives practical illustrations.

## Seebeck Effect

When two dissimilar conductors (or semiconductors) are joined together, and their junction is heated, a voltage results between them (Seebeck or thermoelectric voltage). This is known as the Seebeck effect. This voltage is roughly proportional to absolute temperature. The figure below shows the Seebeck voltage as a function of temperature for the standard type K thermocouple. Notice that the response is not strictly linear, but can be linearized over small temperature ranges (e.g., ±10 °C).

Figure 1

Most thermocouple junctions behave in a similar manner. The following are examples of thermocouple junctions on a PCB:

• Components soldered to a copper pad
• Wires mechanically attached to the PCB
• Jumpers
• Solder joints
• PCB vias

The linearized relationship between temperature and thermoelectric voltage, for small temperature ranges, is given in the equation below. The Seebeck coefficients for the junctions found on PCBs are typically, but not always, below ±100 μV/°C.

∆VTH ≈ kJ(TJ – TREF)
VTH = VREF + ∆VTH
Where:
∆VTH = Change in Seebeck voltage (V)
kJ = Seebeck coefficient (V/°C)
TJ = Junction Temperature (°C)
TREF = Reference Temperature (°C)
VTH = Seebeck voltage (V)
VREF = Seebeck voltage at TREF (V)

## Illustrations Using a Resistor

Three different temperature profiles will be shown that illustrate how thermocouple junctions behave on PCB designs. Obviously, many other components will also produce thermoelectric voltages (e.g., PCB edge connectors). The figure below shows a surface mount resistor with two metal (copper) traces on a PCB. The resistor is built with end caps for soldering to the PCB and a very thin conducting film that produces the desired resistance. Thus, there are three conductor types shown in this figure, with four junctions.

Figure 2

For illustrative purposes, we’ll use the arbitrary values shown in the table below. Notice that junctions 1 and 4 are the same, but the values are shown with opposite polarities. This is one way to account for the direction current flows through these junctions (the same applies
to junctions 2 and 3).

### Assumed Thermocouple Junction Parameters

Junction No. VREF(mV) kJ (μV/°C)
1 10 40
2 -4 -10
3 4 10
4 -10 -40
• VREF and kJ have polarities that assume a left-to-right horizontal direction.
• TREF = 25 °C.

## Constant Temperature

In this illustration, the temperature is constant across the PCB. This means that the junctions are at the same temperature. Let’s also assume that this temperature is +125 °C and that the voltage on the left trace is 0 V. The results are shown in the figure below. Notice that VTH is the voltage change from one conductor to the next.

Figure 3

## Temperature Change In The Normal Direction

Temperature changes vertically in Figure 3 (normal to the resistor’s axial direction) but does not change in the axial direction (horizontally). The metal areas maintain almost constant voltages in the normal direction, so this case is basically the same as the previous one.

When the temperature is constant along the direction of current flow, the net change in thermoelectric voltage between two conductors of the same material is zero.

## Temperature Change In The Axial Direction

Temperature changes horizontally in Figure 3 (along the resistor’s axial direction) but does not change in the normal direction (vertically). Let’s assume 0 V on the left copper trace, +125 °C at Junction #1, a temperature gradient of 10 °C/in (0.394 °C/mm) from left to right (0 in the vertical direction) and a 1206 SMD resistor.

The resistor is 0.12 inches long (3.05 mm) and 0.06 inches wide (1.52 mm). Assume the end caps are about 0.01 inches long (0.25 mm) and the metal film is about 0.10 inches long (2.54 mm). The results are shown in the figure below.

Figure 4

Thus, the temperature gradient of 10 °C/in (1.2 °C increase from left to right) caused a total of -38 μV to appear across this resistor. Notice that adding the same temperature change to all junction temperatures will not change this result.

Shifting all of the junction temperatures by the same amount does not change the temperature gradient. This means that the voltage drop between any two points in the circuit using the same conductive material is the same (assuming we’re within the linear region of response).

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