Brigadoon - An Occasional Corner on the Internet
Analysis for Ground Temperature Array
Designed by Mark Little
When the three sensors are driven from the same supply and earth lines, the voltage drops are basically tripled as there is three (3) times the current flowing through the wires. The voltage drop along the V+ wire has no effect on the output of the sensor. The voltage drop on the earth return wire does, however have the potential to affect the temperature reading measured by the Analogue to Digital Converter in the Raspberry Pi. The simplified circuit circuit shows why this might be an issue.
In the circuit above, the 0.5 ohm resistors represent the resistance of each wire between the Raspberry Pi and the Sensor Array. J1 Represents the input of the ADC channel used to measure the temperature. The temperature is represented by the voltage across the temperature sensor, but from the perspective of the ADC, the voltage drop across the earth wire is added to the voltage generated by the temperature sensor. Previously, it has been calculated that at 25°C, the total supply current is about 3.3mA, resulting in a voltage drop along the earth return of 1.7mV. As the sensor outputs the temperature as 10mV/°K, this represents an error of 0.17°K which is acceptable.

The lower the temperature, the higher the error as more current flows through the temperature sensor resistors as the the voltage across the temperature sensors is lower. Assuming a minimum temperature of -60°C for all sensors, the current flow will be approximately 4.8mA, resulting in a drop of about 2.4mV. This is equivalent to an error of about 0.24°K which is acceptable at these low ground temperatures.

Because the input impedance of the ADC is in the order of 10M, any voltage divider effect with the resistance of the sensor wire and the ADC input impedance can be ignored.