A Wheatstone bridge is a four-resistor circuit used to measure an unknown electrical resistance by balancing two legs of a bridge network until the voltage difference between their midpoints is zero. In a real-world circuit or installation, it changes a microscopic resistance shift—like the physical bending of a metal beam or a slight temperature change—into a measurable differential voltage while actively rejecting power supply noise. People commonly confuse it with a simple voltage divider; while a bridge does contain two parallel voltage dividers, the critical difference is that the output is measured between the two midpoints (differential), not referenced to ground.
The Core Math and a Worked Numeric Example
In its original 19th-century form, the bridge was used in a "balanced" state to find an unknown resistor ($R_x$). You adjust a known variable resistor until a galvanometer reads 0V. The math is simple:
R_x = R_3 * (R_2 / R_1)
However, in modern electronics, we almost exclusively use the bridge in an unbalanced state. We start with four identical resistors (a balanced bridge outputting 0V). When a physical force changes the resistance of one or more legs, the bridge becomes unbalanced, producing a tiny output voltage ($V_{out}$) proportional to the resistance change.
Worked Example: Sizing a Load Cell Readout
Let us look at a standard 350-ohm strain gauge load cell used in digital scales. This is a full-bridge configuration where all four resistors are active strain gauges.
- Nominal Resistance: 350 Ω per leg
- Excitation Voltage ($V_{ex}$): 5.0V DC
- Rated Sensitivity: 2 mV/V
- Full-Scale Load: 10 kg
The sensitivity rating (2 mV/V) tells you how many millivolts of differential output you get per volt of excitation at maximum load.
$V_{out(max)} = V_{ex} \times \text{Sensitivity}$
$V_{out(max)} = 5.0V \times 2 \text{ mV/V} = \mathbf{10 \text{ mV}}$
At a 10 kg load, the differential voltage between the signal wires is only 10 millivolts. If you try to read this directly with an Arduino Uno's 10-bit ADC (which has a 0-5V range and ~4.88mV per step), your 10mV signal spans barely two digital steps. The resolution is useless, and the noise floor will bury the signal entirely. This is why the bridge output must feed into a dedicated instrumentation amplifier or a high-resolution delta-sigma ADC.
Where You Meet This in Practice
You will rarely build a Wheatstone bridge from scratch using discrete through-hole resistors unless you are doing it for a lab exercise. In practice, you meet this circuit embedded inside transducers that convert physical phenomena into electrical signals:
- Load Cells (Scales): From bathroom scales to industrial hopper weighers, metal beams are fitted with strain gauges in a full-bridge configuration. As the beam bends, two gauges stretch (resistance increases) and two compress (resistance decreases), doubling the output signal while canceling temperature drift.
- RTD Temperature Sensors: Precision PT100 or PT1000 resistance temperature detectors are often placed in one leg of a bridge to measure industrial process temperatures.
- Piezoresistive Pressure Sensors: Manifold absolute pressure (MAP) sensors in cars and medical blood pressure monitors use silicon diaphragms with integrated bridge resistors.
- Gas Detectors: Catalytic bead sensors for combustible gases use a bridge where one bead burns gas (changing resistance) and the other acts as a temperature-compensating reference.
Decision Tree: Picking the Right Bridge Readout IC
Because bridge outputs are in the microvolt or low millivolt range, selecting the right interface IC is the most critical decision in your design. Do not default to a standard op-amp; you need high common-mode rejection ratio (CMRR) and low offset drift. Use this decision path to select your readout component.
| If your project requires... | Then choose this architecture... | Concrete Part Number |
|---|---|---|
| A digital scale, load cell project, or slow-moving weight measurement via I2C/SPI to a microcontroller. | 24-bit Delta-Sigma ADC with integrated programmable gain amplifier (PGA). | HX711 (Avia Semiconductor) or NAU7802 (Nuvoton) |
| An analog control loop, 4-20mA transmitter, or you need to feed the bridge signal into an analog PID controller. | Precision Instrumentation Amplifier with an integrated voltage reference for bridge excitation. | INA125 (Texas Instruments) |
| High-speed dynamic strain measurement (e.g., vibration analysis, shock testing) at >10 kHz sampling. | High-bandwidth discrete instrumentation amp paired with a fast SAR ADC. | AD8421 (Analog Devices) + AD4000 SAR ADC |
| Industrial multi-channel RTD/Thermocouple/Bridge data acquisition with 50/60Hz rejection. | Multi-channel precision ADC with integrated excitation current sources and digital filters. | AD7124-8 (Analog Devices) |
The Default Recommendation: If you are a hobbyist, student, or maker building a scale, a coffee roaster load-cell trigger, or a DIY force gauge, stop evaluating and buy the HX711 breakout board. It costs under $3, includes the 128x/64x PGA, handles the 24-bit conversion, and has robust, copy-pasteable Arduino libraries available on GitHub. For professional analog panel meter designs, default to the TI INA125, which uniquely provides a precision voltage reference to excite the bridge and amplify the output in a single 16-pin DIP package.
Common Mistakes and Troubleshooting Bridge Circuits
Even with the right IC, bridge circuits are notoriously sensitive to physical layout and wiring errors. If your sensor data is noisy, drifting, or stuck at zero, check these specific failure modes:
1. Excitation Voltage Noise
The output of a bridge is directly proportional to the excitation voltage. If your 5V excitation line has 20mV of switching ripple from a cheap buck converter, that ripple will modulate directly onto your 10mV sensor signal. Fix: Power the bridge from a linear regulator (like an LM317 or the reference pin of your INA125), or use a ratio-metric ADC (like the HX711) that uses the excitation voltage as its ADC reference, mathematically canceling the noise.
2. Lead Wire Resistance in RTD Bridges
If you are using a Wheatstone bridge to read a PT100 RTD, the copper wires connecting the sensor to the board add resistance. A 10-meter run of 24 AWG wire adds about 0.8 ohms, which translates to a ~2°C temperature error. Fix: Abandon the 2-wire bridge setup. Use a 3-wire or 4-wire (Kelvin) configuration, which places the lead resistances in opposite arms of the bridge or outside the measurement loop entirely, canceling their effect.
3. Thermal EMFs (Seebeck Effect)
When you solder copper wires to the constantan or nichrome legs of a strain gauge, you create unintended thermocouples at the solder joints. If one side of your breadboard is warmer than the other (e.g., near a power resistor), these junctions generate microvolts of DC offset. Fix: Keep bridge wiring symmetrical, route signal wires away from heat sources, and use twisted-pair shielded cable for the differential output lines.
FAQ: Wheatstone Bridge Edge Cases
Can I use a Wheatstone bridge with AC excitation?
Yes. In fact, AC excitation (often at 1 kHz to 10 kHz) is used in high-precision industrial systems to avoid 1/f (flicker) noise and DC thermal EMF errors. The output is then demodulated using a synchronous lock-in amplifier. However, for 99% of DIY and microcontroller projects, DC excitation is standard and sufficient.
What is the difference between a quarter-bridge, half-bridge, and full-bridge?
A quarter-bridge has only one active strain gauge (the other three are fixed resistors on the PCB); it requires temperature compensation and yields the lowest output. A half-bridge has two active gauges (usually one in tension, one in compression), doubling the output. A full-bridge has four active gauges, quadrupling the output and providing the best temperature rejection. Always buy full-bridge load cells if your budget allows.
Why does my HX711 read negative numbers when I add weight?
This is a phase/polarity issue. The differential output wires (usually white and green on a standard load cell) are swapped. Simply reverse the E+ and E- or A+ and A- connections on your amplifier terminal block, or multiply the final software reading by -1.
Understanding the Wheatstone bridge transitions you from simply reading digital sensors to designing precision analog front-ends. By matching the correct bridge topology with a purpose-built readout IC like the HX711 or INA125, you can extract micro-strain and millidegree temperature data that standard microcontroller ADCs would never resolve. For further reading on bridge sensor interfaces, consult the SparkFun HX711 Hookup Guide for practical wiring diagrams, or review the foundational DC network theory in the All About Circuits textbook.
