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Pressure Sensor Bridge Output

Calculate Wheatstone bridge output voltage for piezoresistive pressure sensors from excitation, sensitivity, and applied pressure.

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Formula

V_out = V_ex × S × (P/P_FS)

S— Sensitivity (mV/V)
P_FS— Full-scale pressure (kPa)

How It Works

Piezoresistive pressure sensors contain a Wheatstone bridge of diffused or thin-film strain-sensitive resistors on a silicon or metallic diaphragm. Applied pressure deflects the diaphragm, causing resistance changes that unbalance the bridge. The bridge output voltage is V_out = V_ex × S × (P/P_FS), where V_ex is the excitation voltage, S is the bridge sensitivity in mV/V, P is the applied pressure, and P_FS is the rated full-scale pressure. The full-scale output is V_FS = V_ex × S, typically 10–100 mV for a 5–10 V excitation. Because V_out is a differential millivolt signal on top of a common-mode voltage of V_ex/2, an instrumentation amplifier is required to amplify the differential signal while rejecting the large common-mode component. Temperature affects both the zero offset (zero-pressure output shifts) and span (sensitivity changes), typically requiring analogue or digital compensation using a temperature sensor mounted near the pressure sensor.

Worked Example

Problem
A differential pressure sensor has sensitivity 20 mV/V and full scale 100 kPa. Excitation is 5 V. What is the output at 35 kPa, and what amplifier gain is needed for a 3.3 V ADC?
Solution
1. Full-scale output: V_FS = 5 V × 20 mV/V = 100 mV 2. Output at 35 kPa: V_out = 100 mV × (35/100) = 35 mV 3. Required amplifier gain: G = 3300 mV / 100 mV = 33 V/V 4. Output at 35 kPa after amplification: 35 mV × 33 = 1.155 V 5. Fractional deflection: 35/100 = 35% Result: Bridge outputs 35 mV at 35 kPa; a gain of 33 maps the 100 mV FS to 3.3 V ADC full scale.

Practical Tips

  • ✓Use ratiometric operation — connect both the ADC reference and the pressure sensor excitation to the same regulated voltage. If the supply fluctuates, both scale proportionally and the ratio V_out/V_ex remains constant.
  • ✓For absolute accuracy, perform a two-point calibration (zero pressure and known reference pressure) to correct for both offset and gain errors.
  • ✓Add a 100 nF ceramic capacitor from each excitation line to ground, close to the sensor, to filter high-frequency noise that would otherwise appear as pressure measurement noise.

Common Mistakes

  • ✗Applying excitation voltage exceeding the sensor maximum — overvoltage causes self-heating of the bridge resistors, shifting the zero and span; always check maximum rated excitation (typically 5–12 V).
  • ✗Using the sensor upside-down relative to its rated orientation — many sensors include the weight of the diaphragm in the zero calibration; orientation changes cause a zero offset equal to the diaphragm's dead-weight pressure.
  • ✗Neglecting common-mode voltage at the instrumentation amplifier input — the bridge output rides on V_ex/2 common mode; choose an INA with a common-mode input range that includes V_ex/2 on your supply.

Frequently Asked Questions

Gauge pressure sensors measure pressure relative to atmospheric pressure (output is zero at atmospheric). Absolute sensors measure relative to vacuum (zero absolute pressure). Differential sensors measure the pressure difference between two ports. For HVAC and fluid flow, differential and gauge types are most common; for altimeters and barometers, absolute pressure sensors are used.
Thermal zero offset is the shift in bridge output at zero pressure caused by temperature-induced resistance imbalance. It is specified in μV/V/°C or % FS/°C. Compensation typically uses a temperature sensor plus a lookup table or polynomial correction in firmware, or an integrated digital pressure sensor (e.g., BMP390) that performs internal temperature compensation.
Higher excitation gives larger output voltage (better SNR) but increases self-heating. Typical practice is to use 5 V DC excitation for silicon bridge sensors rated to 5–10 V. For battery-powered applications, use AC excitation at the minimum recommended voltage to reduce power consumption — but verify the sensor is rated for AC excitation.

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