Make accurate temperature measurements using semiconductor junctions

If we look at figure 2, there are some internal routing resistances (R_switch) inside the device itself (due to the switches which come into path to route the output of an on chip peripheral to a particular pin) or external if external MUXes are used. There is another component of resistance that is introduced outside the device due to wires’ resistance used to connect measurement system to the diode. So, there are few important points, which should be taken care of:

Do not route the output of IDAC directly to the positive terminal of ADC internally in the device though device has capability to do it. Because it will measure voltage not just across the diode but across all the routing resistances as well. Wires running from sensor to the ADC should be connected very close to sensor pins.

Do a differential measurement. Single ended measurement will have issues due to ground offset as return path of excitation circuit also have significant lead resistance. Another advantage of differential measurement is, common mode noise, which gets coupled on the wires running parallel from diode to the ADC, does not affect the measurement, as differential voltage is still same.

Based upon the above-mentioned points, Figure 3 shows the 4-wire implementation of sensor interface (only one sensor is shown for the sake of reducing complexity) to deal with the wire resistance.

In the implementation shown in Figure 3, all the unwanted resistances get avoided and only the voltage across diode is measured. At first thought one may think about the resistance, which is coming in path from sensor output to the ADC. This thought is valid if ADC has low input impedance. So, it is needed to make sure that there is some buffer (source follower) introduced between the ADC and sensor if ADC has low input impedance to minimize the leakage current and hence the error in measurement due to wire and routing resistance. SoCs, for instance PSoC3 and PSoC5 devices have ADC with an embedded buffer, which prevents such issues and need for external components in the signal acquisition path.

As can be seen from before, two known currents should be fed through a diode and a ratio metric measurement is done. In such a case, DAC’s gain error will not play a vital role as long as gain error curve is linear. But it is not true for any practical DAC; actual current ratio will be different from the ideal value. This results in value of N to be N_error causes an error in calculated temperature.

Using equation 5 and substituting different instants, we can find that error as given by equation 8.

So first, DAC should be calibrated to make a valid measurement. This can be done by connecting the DAC’s output to a known value accurate resistance and measuring the voltage across it. In this application, only two points calibration is sufficient as only two values are of interest (I1 and I2). Ratio of the voltage read across resistance gives the actual value of N. Though, ADC should be calibrated first for gain and offset error before it is used to calibrate the DAC as discussed later in the article. DACs also have zero scale error (offset), which also will be taken care by two-point calibration done for gain error.

Ideality factor of the diode is the next concern when it comes to the error in measurement. If ideality factor is assumed to be 𝜂_assumed and actual ideality factor is 𝜂_actual, it will cause error in measurement. In this case, measured temperature will be given by equation 9.

So, based upon the deviation of 𝜂_actual from 𝜂_assumed error in the measurement will be as given in figure 4. As T_measured is directly proportional to T_actual, error becomes very high at high temperatures.

Ideality factor varies (from 1.2 to 1.5) in case of diodes. Diode connected transistors on the other hand have ideality factor close to 1.004. So, transistors should be used for better accuracy. The transistor is used in diode mode by connecting the base and collector together as shown in Figure 5.

While using transistors, another point to be looked at is it’s current gain (h_FE). h_FE is a function of collector current (Ic)(temperature as well but it can be ignored as ratio of two voltages will cancel out this effect). It causes the ratio of collector currents being different than the forced emitter currents and hence the error in measurement. So, to avoid/minimize this error, the transistor, which has low variation of h_FE over collector current, should be selected. Also, value of I2, I1 should be selected in such a way that ratio of their corresponding current gain is 1 or very close to it. Transistors’ datasheets provide h_FE verses collector current graph which can help in making a selection. Figure 6 shows the h_FE vs collector current graph taken from the datasheet of 2N3904 by Fairchild Semiconductor.

Next we need to look at the errors due to the digitization of the voltage signal using the ADC, which are the offset error and gain error. ADC’s input offset voltage results in a constant value added to its output. Moreover, offset of ADC has a drift over temperature. Correlated double sampling (CDS) can be used to eliminate the offset error and offset drift with temperature. In CDS, first zero-referenced offset is measured (to measure it, both inputs are shorted and grounded which can be done using analog MUX) and then voltage across the sensor is measured. Zero reference voltage is subtracted from the voltage measured across the sensor to get the actual voltage developed across the sensor. Though offset can be dealt with by following above mentioned steps as long as it comes to making accurate measurement, but it reduces the ADC’s usable input range. To avoid it, ADC in PSoC3 and PSoC5 devices have internal offset correction registers that can lower the offset to as low as 1.95uV at 20 bit avoiding the need of CDS. However, CDS still stands good to deal with offset drift and low frequency noise.

ADCs also possess gain error as in the case of DAC. To calibrate an ADC, there should be at least two accurate references in the system, which can be routed to ADC and a two-point calibration can be done. Two points calibration will assume gain error to be linear and stands good when it comes to calibration overhead (due to multipoint calibration) versus accuracy. Output of the ADC should be scaled as per the slope of the ADC output as per calibration.