TI Precision Labs - Temperature sensors: sensitivity and gain

In this video, Texas Instruments discuss the definition of sensitivity and gain and how it relates to temperature sensing. The gain or sensitivity of an analogue temperature sensor is a measure of how much the sensor output changes, dy, with respect to the change of temperature, dx-- usually, 1°C.

Because the term can be used interchangeably, we will reference gain for the rest of the video. If the output gain does not vary across temperature, it can be used to linearise the output voltage of the temperature sensor using the equation Vout is equal to mT plus b, where m is the gain of the sensor, T is the current measured temperature, and b is the voltage of the sensor at 0°C.

Solving for T gives an easy conversion from the measured Vout to temperature. When interfacing the Vout of the analogue temperature sensor with the ADC, the voltage resolution of the ADC needs to be smaller than the gain of the sensor.

The voltage resolution of the ADC can be found by using the following equation, with Vref equal to the ADC reference voltage. This parameter can be found in the ADC documentation.

For example, if the ADC reference voltage is 2.5V, and the ADC resolution is 12 bits, this will give a voltage resolution of 0.6 millivolts per LSB.

Now that we know the voltage resolution of the ADC, we can determine how the system will operate by examining the gain of the temperature sensor. Using the ADC voltage resolution from the previous example of 0.6 millivolts per LSB and a temperature sensor with a gain of 8 millivolts per degree C, the ADC can resolve each incremental step of the sensor per change in degree Celsius, as shown in the graph in the video.

In this system, the full resolution of the temperature sensor can be used by the ADC. And no modifications are needed. In another system example, the ADC has the same reference voltage of 2.5V but a resolution of only 8 bits.

This would have a voltage resolution of 9.7 millivolts per LSB. In this system, the full resolution of the temperature sensor cannot be used because the ADC is unable to detect the incremental output voltage change per degree Celsius, as shown in the graph.

This will result in the system having uncertainty of what the temperature is due to the ADC voltage resolution being higher than the gain of the sensor. Now the question is, how can this be fixed?

One method of rectifying the higher ADC voltage resolution is to use an operational amplifier. With an analogue temperature sensor, the gain of the sensor can be increased through the use of an amplifier to compensate for the lower than desired gain or the higher than desired ADC voltage resolution.

The end result of the solution should be to have the gain of the sensor be higher than the voltage resolution of the system measuring it. Other potential solutions also include using a different sensor with higher gain or using ADC with a higher resolution.