EE3901/EE5901 Sensor Technologies

Week 10 Notes

Self-generating sensors: thermocouples and photodiodes

Introduction to self-generating sensors

Various physics effects directly generate electricity. The most obvious example may be the photovoltaic effect, which is the mechanism behind solar power generation. In addition to power generation, the photovoltaic effect can also be used to measure light intensity. A light sensor using this mechanism is called a photodiode. Other examples of self-generating sensors include thermoelectric sensors, piezoelectric sensors, and electrochemical sensors.

In practice, even if the underlying physical effect can generate power, a sensor is not always self-powered. Sometimes additional power is injected to achieve better performance. For example, a photodiode in reverse bias can respond more quickly than a photodiode without applied bias.

Thermoelectric effects

A thermoelectric effect is the direct transformation of heat into electricity. There are various thermoelectric effects named after their discoverers: the Seebeck effect, the Peltier effect, and the Thomson effect. For sensing purposes, we will consider the Seebeck effect.

The underlying physics is as follows. Figure 1 shows a conductor with a temperature gradient.

The Seebeck effect is that a voltage is generated across this conductor. Specifically

where $\nabla V$ is the gradient of voltage, $S(T)$ is a material property called the Seebeck coefficient, and $\nabla T$ is the gradient of temperature. In a one-dimensional case this simplifies to

where $x$ is the distance along the conductor.

A rough intuitive description of the underlying physics is that the conductivity of “hot” charge carriers is different to that of “cold” charge carriers, hence they diffuse at different rates. The majority charge carrier tends to diffuse towards the cold side of the material. Consequently, P-type semiconductors typically have positive $S$ whereas N-type semiconductors typically have negative $S$. Metals can have either positive or negative $S$.

The Seebeck effect as presented above is difficult to measure directly, because the wires of the voltage meter would also have their own temperature gradient, and hence their own thermoelectric effect. Consequently the minimum configuration that can be easily measured uses two different materials with different Seebeck coefficients, as shown in Figure 2.

Even though the microscopic voltage gradient depends upon the temperature distribution, the actual voltage obtained by integrating along the entire length of the wire depends only on the choice of metals and the temperatures at each junction. The temperature gradient along each wire does not matter, only the temperature at the end points. This is a very convenient result that makes it possible to use the Seebeck effect for temperature sensing.

Note that a voltage is only generated when there is a temperature difference between the two junctions. If the temperatures are equal then there is no thermoelectric voltage.

Thermocouples

A thermocouple is a temperature sensor based on the thermoelectric effect. Thermocouples are often used to measure extreme temperatures, e.g. some types have a range exceeding 1000 °C. Their main limitation is accuracy: errors are typically in the range of at least 1-2 °C. Nevertheless they are widely used in industrial processes, ovens, kilns, engines, gas turbines, etc. where high temperatures need to be measured.

The basic idea of a thermocouple is shown in Figure 3. A voltmeter is connected using any conductor to the reference junction, whose temperature is already known. Then different metals (having different Seebeck coefficients) are used to make the connection to the sensing junction, which is at an unknown temperature.

The reference junction is held at a fixed temperature or is measured using another type of temperature sensor. Typically the reference junction would be somewhat close to room temperature. Temperatures in this range can be easily measured using an RTD, thermistor or other type of sensor. The thermocouple’s sensing junction can then be exposed to the extreme temperature.

Figure 3 shows four temperature gradients, and hence four Seebeck voltages. The thermoelectric voltages in the copper cancel out, because they have the same temperature gradient and use the same conductor for each direction. Therefore, the measured voltage only depends on the temperature difference between $T_{\text{sense}}$ and $T_{\text{ref}}$, and the choice of metals for conductors A and B.

For a given pair of metals, the thermocouple is described by a “characteristic function” $E(T)$ which gives the output voltage

The characteristic function can be given by a look-up table or mathematical function. A standard reference is the ITS-90 Thermocouple Database published by the U.S. National Institute of Standards and Technology (NIST). In this database, rows correspond to increments of 10 °C, while columns correspond to increments of 1 °C. The database tabulates the function $E(T)$ in Eq. (3).

Types of thermocouples

A wide array of metal combinations are useful to create thermocouples. Some popular pairs are given letter codes. Some of the most common are as follows:

Type K thermocouple

This is the most common general purpose type.

Materials: chromel (90% nickel and 10% chromium by weight) / alumel (95% Ni, 2% Al, 2% Mn, 1% Si).

Range: short term: -180 °C to 1370 °C; continuous: 0 °C to 1100 °C.

Typical error: $\pm2.2$ °C.

Type T thermocouple

Type T is used in low temperature applications like freezers. It is also corrosion resistant so it is suitable for high-humidity environments.

Materials: copper / constantan (55% Cu, 45% Ni).

Range: short term -250 °C to 400 °C; continuous -185 °C to 300 °C.

Typical error: $\pm1.0$ °C.

Type B thermocouple

Type B is used in high temperature environments.

Materials: platinum (30%) rhodium / platinum (6%) rhodium

Range: short term 0 to 1820 °C; continuous 0 to 1700 °C.

Other types

There are various other common types (e.g. J, E, R, etc) which are suitable for use in different situations (e.g. in vacuum, or inert atmospheres, or oxidising atmospheres, or reducing atmospheres).

Interface circuits for thermocouples

The output voltage from a thermocouple is typically in the mV range, so it needs to be amplified to interface with other circuitry. Suitable designs include op-amp based differential amplifier circuits or instrumentation amplifier circuits. The amplifier gain needs be chosen based upon the voltage range that is accepted by the downstream circuit.

Photovoltaic sensors

The photovoltaic effect is the mechanism behind solar cells. Light shining onto a semiconductor can create electron-hole pairs, if the photon wavelength lies within the absorption spectrum of the material. However, a current is only created if the electrons and holes are then conducted away from each other. One way to separate the charge carriers is with a p-n junction: the built-in field across the depletion region will drive the carriers towards their respective electrodes, and hence generate electricity.

This effect can also be used as a sensor to measure light intensity. A device optimised for sensing (as opposed to power generation) is called a photodetector or a photodiode. Its behaviour is characterised by a current-voltage curve. An idealised current-voltage curve for a photodiode is shown in Figure 4.

The main mechanism for light sensing is to measure the current at short circuit $(V=0)$ or reverse bias $(V<0)$. The advantage of using reverse bias is that the electric field is stronger, resulting in faster response times and a linear dynamic range that extends to higher light intensities. Another approach is to measure the open circuit voltage, which is the voltage developed when no current is allowed to flow.

A typical small-scale silicon photodiode has a short circuit current under illumination in the range of tens of μA, open circuit voltages in the range of hundreds of mV, and reverse bias dark current in the range of a few nA.

Photodiodes will only detect light that is absorbed and then converted into charge carriers. Different semiconductor materials have different absorption spectra, hence the wavelengths of light that are detected will depend upon the material choice.

A common electrical circuit model for a photodiode is shown in Figure 5. Here $I_{PH}$ is the photogenerated current (ideally linearly proportional to the light intensity within the operational range of the sensor), $C$ represents the capacitance of the device, $R_{SH}$ is called the shunt resistance and should be as large as possible, and $R_{s}$ is the series resistance and should be as small as possible. We adopt the sign convention that positive current is forward bias across the diode, even though the desirable photocurrent flows in the opposite direction. This same circuit model also applies to solar cells (albeit with different numbers for each element).

Interface circuits for current-generating sensors

In theory, converting a current signal into a voltage is easy: just use a resistor! Direct the current through the resistor, measure the voltage on the resistor, and calculate the current with Ohm’s law. A resistor used in this way is called a “current sense resistor” and is a common design for many circumstances.

However if the current is small, then using a current sense resistor is impractical. A small current would require a large resistance in order to produce a voltage big enough to be easily measured. However, a current-generating sensor may not be able to drive a large resistor.

A better design is the transimpedance amplifier (also called a transresistance amplifier). The prefix trans- means that the resistance is a ratio between an output voltage and an input current. Therefore it has units of ohms, but does not represent a simple resistance in the sense of Ohm’s law.

Transimpedance amplifiers

A transimpedance amplifier is a current-to-voltage converter. It is useful for sensors that produce a small current, e.g. photodiodes. The idea is to use an op-amp to create a “virtual ground”, as shown in Figure 6.

Notice that the voltage across the sensor is constant. The op-amp will drive $V_{0}$ in such a way that the voltage across the sensor is (almost) zero. Analysis of the current flow gives an expression for the output voltage $V_{0}=-R_{f}I_{s}$. Hence we can identify the gain as $R_{f}$, i.e. having units of Ω = V/A. Often it will be written as V/μA to emphasise that small input currents are amplified to produce a convenient voltage.

The design drawn in Figure 6 is a surprisingly challenging circuit for the op-amp, because the sensor will always have some capacitance across its terminals. Consider the schematic in Figure 7. The op-amp is trying to control $V_{-}$, the voltage at the inverting input. However, notice that $R_f$ and $C_s$ form a low-pass filter. Consequently, the op-amp’s feedback is hindered by the capacitance of the sensor.

In practice, the situation is even worse than is immediately obvious from the low-pass characteristics of the feedback network. The problem is that the voltage divider formed by $R_f$ and $C_s$ adds a phase shift to the voltage at $V_{-}$. Combined with the phase behaviour of the op-amp itself, this can cause the circuit to oscillate. (For details, please refer to The Art of Electronics by Horowitz and Hill, Chapter 4x.3.)

The solution is to add a capacitor in the feedback path to reduce the high frequency gain. A design rule from The Art of Electronics is to choose

where $f_{T}$ is the gain-bandwidth product of the op-amp and $C_{in}$ is the total capacitance to ground as seen by the op-amp’s inverting input. This would be something like $C_{in}=C_{s}+C_{cable}+C_{pin}$, i.e. the total parallel combination of capacitance due to the sensor, cable, and the op-amp pin itself.

Simulations of this circuit with and without $C_f$ are shown in Figures 8 and 9.

Bandwidth considerations

The bandwidth of the transimpedance amplifier is given by

Notice that the higher the gain (i.e. the higher $R_{f}$), the lower the bandwidth. Furthermore, going to a faster op-amp (with higher $f_{T}$) provides only a small benefit because of the square root. This bandwidth can easily become a problem, since realistic values can lead to circuit bandwidths in the hundreds of kHz range, whereas the actual sensors can be tens of MHz or faster. We don’t want our interface circuit to limit the bandwidth of a high speed photodiode.

A common way around this is to build a cascade of two amplifiers, as shown in Figure 10.

First use a transimpedance amplifier to turn the current into a voltage and provide some amplification. The second stage is then a voltage amplifier. The total gain is the product of the gains of each amplifier.

Of course there is a trade-off in this design. Each amplification stage introduces noise. Nevertheless a two stage design is a common and practical approach.

References

Paul Horowitz and Winfield Hill, The Art of Electronics, 3rd edition, Cambridge University Press, 2015.