# Wheatstone bridge resistance and sensitivity tolerances

A pressure sensor datasheet gives its resistance as 5 kΩ +/- 1 kΩ or 3.5 kΩ +/-0.5 kΩ (optional version). The full-scale output is 150 mV +/- 30 mV at 100 psi, 5 V bridge voltage Vb.

The way I imagine the pressure sensor works is that when pressure changes, two resistors contract and two expand in length by a certain percentage, changing their resistances by the same percentage.

So if the initial resistance at zero pressure is 5 kΩ, the output voltage sensitivity to the excitation voltage Vb and pressure is the typical 150 mV/5 V/100 psi, then if 100 psi and Vb = 5 V are applied, this can be modelled by adding/subtracting 150 Ω to/from the 5 kΩ resistors. The 5 kΩ resistors change by 3% and the output voltage Vo is 150 mV.

However, if the initial resistance at zero pressure is now 4 kΩ and the same pressure and Vb are applied, the 4 kΩ resistors should change again by 3%. This can be modelled by adding/subtracting 120 Ω to/from the 4 kΩ resistors. The 4 kΩ resistors change by 3% and the output voltage Vo is 120 mV.

Is the initial resistance tolerance of 5 kΩ +/-20% the cause of the full-scale output variation of 150 mV +/-20%? This idea seems to work well for 5 kΩ resistors, but not for the 3.5 kΩ +/-0.5 kΩ (i.e. +/-14%) option.

Or is the full-scale output variation another independent inaccuracy caused by different production resistor batches contracting/expanding differently at the same pressure? In other words, should the datasheet full-scale output variation be modelled on top of the initial resistance tolerance?

The pressure sensor output sensitivity is often specified as mV/V FSR. In your case, the full scale is 100 psi and the typical output is 150mV/5 volts or 30 mV/V. So the total resistance spec is independent from the sensitivity.

In your case, the sensitivity and offset must be established by empirical measurement, then the pressure can be determined using these two values with a standard y = mx + b straight line. The common approach is to power the bridge with the same voltage used as a reference by the ADC, so that the result is unaffected by changes in this voltage.

The 4kΩ to 6kΩ (5kΩ nominal) is manufacturing tolerance of the total resistance of the bridge circuit.

It is not well-controlled, because you're supposed to use the part in such a way that it does not matter (constant voltage excitation). It's not atypical to see such ~+/-30% tolerance in such resistances made with semiconductor processes if they are not trimmed.

Controlling the total resistance would require trimming all 4 resistors, and might compromise other characteristics, to no benefit in a typical application.

• According to the App Note, the resistor tempco and the sensitivity tempco of the sensor subtract when driven by constant current. And then the resistance becomes relevant.
– Hyp
Feb 1 at 16:02
• The app note is from a different company than the sensor maker. In this case, the typical tempcos are +2300 and -1500, not so closely matched. The sensor diode is provided for compensation. And the output is specified with constant voltage (5V) excitation. Feb 1 at 17:43