Keywords: bridge circuits, bridges, Wheatstone bridge, sigma delta, sigma-delta converters
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TUTORIALS 3426

Abstract: Bridge circuits are a time-honored way to make accurate measurement of resistance and other analog values. This article covers the basics of bridge circuits and shows how to use them to make accurate measurements in practical environments. It details the key concerns of bridge-circuit applications such as noise, offset voltages and offset voltage drift, common-mode voltage, and excitation voltage. It describes how to interface bridges to high-resolution, analog-to-digital converters (ADCs) and the techniques for maximizing ADC capabilities.

NOTE: This is a two-part article. Part one reviews the basic bridge and focuses on bridges with low output signals, like those from bonded-wire or bonded-foil strain gauges. Part two, application note 3545, "Resistive Bridge Basics: Part Two," addresses high output bridges like those that use silicon resistors.

Equation 1 is not elegant, but can be simplified for most bridges in common use. Bridge outputs are the most sensitive to changes in resistance when Vo+ and Vo- equal 1/2 of Ve. This condition is easily achieved by using the same nominal value, R, for all four resistors. Resistance variations caused by the property being measured are accounted for by a delta R or dR term. Resistors with a dR term are cited as "active" resistors. In the following four cases, all the resistors have the same nominal value, R. One, two, or four of the resistors will be active, or have a dR term. In deriving these equations, dR is assumed to be positive. If the resistance actually decreases, then -dR used. In the special cases below, the magnitude of dR is the same for all active resistors.

Vo = Ve(R2/(R1 + R2) - R3/(R3 + R4)) (Eq. 1)

Vo = Ve(dR/R) A bridge with four active elements. (Eq. 2)

As might be expected, the bridge with one active element has 1/4 as much output signal as the bridge with four active elements. Another important characteristic of this configuration is the nonlinear output caused by the addition of a dR term in the denominator. This nonlinearity is small and predictable. If necessary, it can be corrected in software.

Vo = Ve(dR/(4R + 2dR)) A bridge with one active element. (Eq. 3)

In both the second and third cases above, only half of the bridge is active. The other half simply provides a reference voltage that is 1/2 of Ve. Consequently, it is not actually necessary for all four resistors to have the same nominal value. It is only important that both resistors on the left half of the bridge match and both resistors on the right half of the bridge match.

Vo = Ve(dR/(2R)) Two active elements with opposite response. (Eq. 4)

This nonlinearity is predictable, and can be removed with software or eliminated by driving the bridge with a current source rather than a voltage source. In Equation 6, Ie is the excitation current. It should be noted that Vo in Equation 6 is only a function of dR, not the ratio of dR/R as it was in the prior cases.

Vo = Ve(dR/(2R + dR) Two identical active elements in a voltage-driven bridge. (Eq. 5)

Understanding the four special cases above is useful when working with individual sensing elements. Many times, however, the sensor has an internal bridge with an unknown configuration. In these instances, knowing the exact configuration is not really important. The manufacturer will supply the necessary information, like sensitivity linearity error, common-mode voltage, etc. But why use a bridge in the first place? This question is easily answered by looking at the following example.

Vo = Ie(dR/2) Two identical active elements in a current driven bridge (Eq. 6)

The resistors in the load cell respond to more than just the applied load. Thermal expansion of the structure to which they are bonded and the TCR of the gauge material itself will cause resistance changes. These unwanted changes in resistance can be as large, or larger, than the change due to intended strain. If, however, these undesirable changes occur equally in all the bridge resistors, then their effect is negligible or nonexistent. An unwanted change of 200ppm, for instance, is equivalent to 10% of full scale in this example. But in Equation 2, changing R by 200ppm creates less than 1 LSB of difference on a 12-bit measurement. In many cases, the wanted change in resistance, dR, is directly proportional to the bulk resistance, R. In these cases, changing R by 200ppm should have no effect because the ratio of dR/R remains the same. The value of R could double and the output voltage would not be affected because dR would also double.

The above example shows how using a bridge can ease the task of measuring very small changes in resistance. The following section covers the major circuit concerns when measuring a bridge.

- Excitation voltage
- Common-mode voltage
- Offset voltage
- Offset drift
- Noise

An alternate approach uses an additional input channel on the ADC to measure the bridge's excitation voltage. Software can then compensate for changes in bridge voltage. Equation 7 shows the corrected output voltage, (Voc), as a function of the measured output voltage (Vom), the measured excitation voltage (Vem), and the excitation voltage at the time of calibration (Veo).

Voc = VomVeo/Vem (Eq. 7)

This type of automatic zero calibration is built into many modern ADCs and is extremely effective at removing ADC offsets. It does not, however, remove the offset of the bridge or the offset of any electronics between the bridge and the ADC.

A slightly more complicated form of offset correction uses a double-pole, double-throw switch between the bridge and the electronics (see

- Keeping noise out of the system (proper grounding, shielding, and wiring techniques)
- Reducing noise generated in the system (architecture, component selection, and bias levels)
- Reducing electronic noise (analog filters, common-mode rejection)
- Software compensation or DSP (algorithms that use multiple measurements to enhance the wanted signal and reject unwanted signals)

If a ratiometric system is not an option, these multichannel ADCs are an alternate solution. One ADC channel can be used to measure the output of the bridge and a second input channel can be used to measure the bridge's excitation voltage. Equation 7 above can then be used to correct for variations in Ve.

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APP 3426: TUTORIALS 3426,AN3426, AN 3426, APP3426, Appnote3426, Appnote 3426 |