Semiconductors and Components

# The Wheatstone Bridge: Still the preferred sensor-interface topology after 180 years

07 April 2016

It's very common to need to connect to a transducer or sensor, like a strain gauge, and then determine its precise value, or measure small changes around the component's nominal value. The Wheatstone bridge topology makes it easy to do so, even without our modern precision electronic components and circuitry. The simple schematic diagram of the Wheatstone bridge represents the most versatile circuit topology, widely used for comparing and measuring unknown resistances. Image source: Author

The Wheatstone bridge was developed around 1833 by Samuel Hunter Christie, then further studied, analyzed and popularized by Sir Charles Wheatstone over the next ten years. The bridge solved the problem of measuring the resistance value of unknown materials to high accuracy, in the days before the voltmeter (or anything even close to it) even existed. This was an era when our present-day understanding and characterization of voltage and current flow was just beginning, via Ohm's law (1827) and Kirchhoff's circuit laws (1845). Despite its age, it is still in widespread use in a form very close to its original.

The Wheatstone bridge allows the user to compare any unknown resistor to known values, despite the fact that there was no such instrument as the voltmeter, ammeter or ohmmeter. Instead, the instrument readout was a galvanometer, an extremely sensitive current-responding indicator-- still used today in some specialty situations. The galvanometer is especially well-suited to detecting what is called a null, which is zero current flow.

The basic bridge configuration, Figure 1, has four resistors arranged in a simple configuration. Rx is the unknown resistance to be measured, while R1, R2, and R3 are known. When the ratio of R2/R1 (called the "known leg") equals the ratio of the resistors in the unknown leg, Rx/R3, there is no voltage (potential difference) at the midpoint and therefore the current flow due to the excitation voltage is zero, which is easily observed using the galvanometer.

At that point, the bridge is said to be at null or in balance. Furthermore, the direction of current flow indicates if R2 is high or low compared to Rx. When the bridge is in balance, R2/R1 = Rx/R3 – what could be simpler?

The Wheatstone bridge is sometime drawn in a rectangular style, which is electrically equivalent but lacks the traditional, more-common appearance. Image source: AuthorThe bridge is most often drawn as a diamond (among Wheatstone's many contributions), but sometimes it is shown as a rectangle, Figure 2; the difference is esthetic but most engineers prefer the diamond style. Note that the four resistors do not have to be equal although in practice they are usually close in value; often R1and R2 are simply standard resistors, not the type being tested or matched. Also, the bridge can be used with non-resistive legs, such as capacitors or inductors, in which case the excitation voltage is AC, not DC.

It's an incredibly versatile, yet simple topology and can be used in two ways. Historically it was used to measure the value of an unknown resistance (you can see some of its many carefully crafted instruments at Reference 1). To make this measurement, R3 is comprised of a set of known, calibrated resistors such as from a user-switchable "decade" box or even using one-at-a-time substitution. Accuracy of the null readout depends on the accuracy of the known standards used, and there are some advanced techniques which allow other subtle errors, such as (voltage drop at the contacts) to be compensated or calibrated out of the measurement.

With the advent of electronic amplifiers and sensor interface circuitry, the bridge's use expanded. In a typical application, the amplifier "gains up" the signal at the bridge output (again, which is zero current/volts at null). As the resistance of the unknown Rx of bridge changes, such as from pressure applied to a strain gage, the output deviates from zero. This change is then amplified and can be digitized, if needed.

In this way, the value of the unknown resistance and the variable it represents, such as strain, can be determined in real time, without any need to manually adjust resistance R3 to achieve a null. Note that the bridge output change with the change is resistance is not linear, so some sort of linearization scheme, done using either hardwired circuitry or software, may be needed.

Typically, the nominal resistance of the bridge elements is between 50 and 250 Ω, but higher and lower values are used as well. Where highest precision is needed, circuit designers have devised ways to use active components to compensate for voltage drops at the contact points using what are called Kelvin connections.

Why not just two resistors? A basic voltage divider using just two components rather than the four of the Wheatstone bridge might seem a simpler alternative, but it has many inherent drawbacks which the bridge does not. Image source: Author

It may seem that using a four-element bridge is unnecessary when measuring changes in a sensor, and it should be possible to just use a basic voltage divider with a known resistor and the unknown value in series, Figure 3, with Vout = Vs × Rx/(R1 + Rx). In reality, this two-resistor configuration has many weaknesses and sources of error:

• The output voltage is a function of the supply voltage, which has inherent initial inaccuracy, will likely drift over time, and also have noise, all of which will diminish accuracy. In contrast, the bridge design inherently is immune to these shortcomings, because it is ratiometric and dependent only on the resistor ratios, not the supply voltage.
• With the voltage-divider approach, initial accuracy without calibration is limited, as the actual value of the two resistor sis not exact, yet the output is a function of their actual values. In contrast, the bridge depends on matching rather than absolute precision; again, the ratiometric function is the key.
• The change in output of the voltage-divider is a very small voltage on top of a large offset voltage. In general it is hard to see and amplify these small signals with their large DC component without issues of amplifier saturation and overranging. In the bridge, however, there is no offset at nominal operating point (there is a very small one, in practice) so the saturation problem is eliminated or greatly minimized.
• Any time/temperature-related drift of the resistors for the voltage divider will cause errors. With the bridge, however, there's' a simple way to compensate, by using a resistor or sensor in the corresponding ratio arm identical to the one being measured. For example, if the design has a strain gage, use an identical gage in the matching arm but do not have it in a strain-sensing placement. As the changes in both gages track in parallel, the ratiometric design of the bridge causes this drift to cancel itself out.

Other bridge features also considered

Bridge sensitivity is an issue that must be considered when observing the bridge output. It is usually specified in mV/V, and is the value of bridge output when the bridge is excited with one volt and the sensor is at full scale. Typical sensitivity values are 1 to 2 mV/V. Accuracy of a standard bridge is usually between 0.1 and 1% before any calibration is performed.

Power dissipation is also an issue, as it is a function of bridge voltage and arm resistance. A higher excitation voltage produces a higher output, which is good, but results in higher dissipation. This dissipation affects low-power operation, obviously, but also induces increased self-heating of the bridge elements. Even though the bridge is self-compensating for temperature drift to a large extent, it can become a problem if the different elements are not thermally coupled and at the same temperature.

The output of the bridge is not grounded, so any conditioning/amplification circuitry must be isolated (Reference 2) or have a differential input. Also, some sensors perform better using AC rather than DC excitation, which can then be demodulated synchronously to eliminate second- and third-order errors. A bridge interface IC such as the AD7730 provides all necessary interface, amplification, scaling, calibration, and digital I/O along with easy-to-use, high-resolution performance. Image source: Analog Devices, Inc.

Due to the widespread use of bridge circuits and their many benefits, IC vendors have developed many specialized interface devices which simplify using them, setting amplifier gain, and minimizing various residual error sources. For example, the AD7730 from Analog Devices, Figure 4, can be configured for AC or DC excitation, provides a user-settable differential amplifier followed by 24-bit A/D conversion, and provides the resultant data in various serial formats to the system microcontroller. Despite its internal complexity, it provides an easy-to-use bridge excitation and interface function along with filtering, calibration, and many other user options.

The simple yet clever bridge topology has been a valuable configuration and tools since the earliest days of development of the principles of basic electrical circuits. Despite its age, it is very often still the best solution to the ongoing challenge of precisely matching a unknown component against a known one, or capturing small changes in a sensor output despite noise, component imperfections, and supply variations.