# Make accurate temperature measurements using semiconductor junctions

There are numerous sensors available for temperature measurement under the name thermal sensors. Popular ones are the thermistor, thermocouple, RTD. Diodes can be used to sense temperature due to the change in their forward voltage with change in temperature. One of the advantage of using diodes is they have a nearly linear relationship between temperature and voltage applied. Diodes are being used extensively in integrated circuits to measure the die temperature but now are not limited to that.

Diodes are the most inexpensive among all the temperature sensors and are the likely candidate to be selected in low cost applications. Understanding of the characteristics of diode junction as a function of temperature is important for accurate measurement. Although diodes are not as accurate as other sensors like thermocouple, they provide reasonable accuracy, which makes them usable in lot of low precision applications. This article talks about the fundamentals of diode’s forward voltage and steps to make accurate temperature measurements using them.

**The fundamentals of operation**

First, let’s look at the fundamentals involved.

Equation 1 (known as the diode equation) gives the current flowing through the diode when it is forward biased.

Where I_{s }is the reverse saturation current, V is diode’s forward voltage drop, ?? is ideality factor (a constant which has value from 1 to 2) and V_{T} is the thermal voltage of diode which is given by equation 2.

T* *is the absolute junction temperature in Kelvin, *q *is the electron charge (1.602*10^{-19} C) and k is the Boltzmann’s constant:

Before we dive into the electronics of measuring the temperature, let us look into the mathematics to get temperature from these equations.

If two known currents (I1 and I2) related by I2 = N * I1are passed through diode, forward current will be given by the following equations respectively.

After dividing equation 4 by 3 and manipulating, it yields equation 5.

In this equation, K, ??, q are constants as discussed before. I1 and I2 are the known currents that were passed though diodes. V1 and V2 are the measured voltages across diode. Hence the temperature can be found easily.

Now, let us focus on how to implement this. Figure 1 deals with the basic analog front end needed for such an application.

As shown in figure 1, a programmable current source is used to set a particular current flowing through the diode. Voltage excitation is not used because it will add error in measurement due to wire resistance or trace resistance and due to routing resistances inside the device itself. The drop across the diode is later fed to an ADC, which then converts to digital value. In equation 5, if we substitute the value of N as 10 and ?? as 1, for 1 ^{o}C change in temperature, sensor produces the voltage about 200 uV. To achieve it, ADC should have resolution of 20 bits with an input range of approximately 2V.

Figure 1 shows the very basic implementation and does not show the different resistances coming in the path, which can add significant error to the measurement. In diode based temperature measurement system, generally diodes sit on the far end to sense the temperature at the remote location. Excitation to different sensors (connecting the sensors to current DAC’s output) is controlled using the analog MUX. The output of sensors to the ADC is controlled using analog MUX if they are taken from outside or directly to the ADC if routed internally as in case of figure 2. Today, SoCs available in market have on chip DAC, ADC and analog multiplexers to realize whole system in a single chip. But even in these devices, resistance of internal switches, which are used for routing, should not be overlooked. Figure 2 shows the various resistances, which come into routing and can result in significant source of error if ignored.