## Quarter **Bridge**, Half **Bridge** and Full **Wheatstone** **Bridge** Strain Gauge Load Cell configurations.

**Wheatstone**

**bridge**. A

**Wheatstone**

**bridge**is a network of four resistive legs. One or more of these legs can be active sensing elements. Figure 1-1 shows a

**Wheatstone**

**bridge**circuit diagram.

**Figure 1-1**. Basic

**Wheatstone**

**Bridge**Circuit Diagram

The **Wheatstone** **bridge** is the electrical equivalent of two parallel voltage divider circuits. R1 and R2 compose one voltage divider circuit, and R4 and R3 compose the second voltage divider circuit. The output of a **Wheatstone** **bridge** is measured between the middle nodes of the two voltage dividers.

A physical phenomena, such as a change in strain applied to a specimen or a temperature shift, changes the resistance of the sensing elements in the **Wheatstone** **bridge**. The **Wheatstone** **bridge** configuration is used to help measure the small variations in resistance that the sensing elements produce corresponding to a physical change in the specimen.

Strain-gauge configurations are arranged as **Wheatstone** bridges. The gauge is the collection of all of the active elements of the **Wheatstone** **bridge**. There are three types of strain-gauge configurations: quarter-**bridge**, half-**bridge**, and full-**bridge**. The number of active element legs in the **Wheatstone** **bridge** determines the kind of **bridge** configuration. Refer to Table 1-1 to see how many active elements are in each configuration.

Each of these three configurations is subdivided into multiple configuration types. The orientation of the active elements and the kind of strain measured determines the configuration type

### Acronyms, Formulas, and Variable Definitions

In the figures and equations in this document, the acronyms, formulas, and variables are defined as:

*e*is the measured strain (+e is tensile strain and -e is compressive strain).

*e*is the simulated strain.

_{S}*GF*is the Gauge Factor, which should be specified by the gauge manufacturer.

*R*is the nominal gauge resistance, which should be specified by the gauge manufacturer.

_{g}*R*is the lead resistance. If lead lengths are long, RL can significantly impact measurement accuracy.

_{L}*Rs*is the shunt calibration resistor value.

*U*is the ratio of expected signal voltage to excitation voltage with the shunt calibration circuit engaged. Parameter U appears in the equations for simulated strain and is defined by the following equation:

*n*is the Poisson’s ratio, defined as the negative ratio of transverse strain to axial strain (longitudinal) strain.

*V*is the measured signal’s voltage.

_{CH}*V*is the excitation voltage.

_{EX}*V*is the voltage ratio that is used in the voltage to strain conversion equations and is defined by the following equation:

_{r}### Quarter-**Bridge** Type I

This section provides information for the quarter-**bridge** strain-gauge configuration type I. The quarter-**bridge** type I measures either axial or bending strain.

**Figure 1-2**. Quarter-

**Bridge**Type I Measuring Axial and Bending Strain

**bridge**type I has the following characteristics:

- A single active strain-gauge element is mounted in the principle direction of axial or bending strain.
- A passive quarter-
**bridge**completion resistor (dummy resistor) is required in addition to half-**bridge**completion. - Temperature variation in specimen decreases the accuracy of the measurements.
- Sensitivity at 1000 me is ~ 0.5 mV
_{out}/ V_{EX}input.

**Figure 1-3.**Quarter-

**Bridge**Type I Circuit Diagram

The following symbols apply to the circuit diagram and equations:

- R1 and R2 are half-
**bridge**completion resistors. - R3 is the quarter-
**bridge**completion resistor (dummy resistor). - R4 is the active strain-gauge element measuring tensile strain (+e).

To convert voltage readings to strain units use the following equation:

To simulate the effect on strain of applying a shunt resistor across R_{3}, use the following equation:

### Quarter-**Bridge** Type II

This section provides information for the quarter-**bridge** strain-gauge configuration type II.

The quarter-**bridge** type II measures either axial or bending strain.

**Figure 1-4.**Quarter-

**Bridge**Type II Measuring Axial and Bending Strain

A quarter-**bridge** type II has the following characteristics:

- One active strain-gauge element and one passive, temperature-sensing quarter-
**bridge**element (dummy gauge). The active element is mounted in the direction of axial or bending strain. The dummy gauge is mounted in close thermal contact with the strain specimen but not bonded to the specimen, and is usually mounted transverse (perpendicular) to the principle axis of strain. - This configuration is often confused with the half-
**bridge**type I configuration, with the difference being that in the half-**bridge**type I configuration the R3 element is active and bonded to the strain specimen to measure the effect of Poisson’s ratio. - Completion resistors provide half
**bridge**completion. - Compensates for temperature.
- Sensitivity at 1000 me is ~ 0.5 mV
_{out}/ V_{EX}input.

**Figure 1-5.**Quarter-

**Bridge**Type II Circuit Diagram

The following symbols apply to the circuit diagram and equations:

- R
_{1}and R_{2}are a half-**bridge**completion resistors. - R
_{3}is the quarter-**bridge**temperature-sensing element (dummy gauge). - R
_{4}is the active strain-gauge element measuring tensile strain (+e).

To convert voltage readings to strain units use the following equation:

_{3}, use the following equation:

### Half-**Bridge** Type I

This section provides information for the half-**bridge** strain-gauge configuration type I. The half-**bridge** type I measures either axial or bending strain.

**Figure 1-6.**Half-

**bridge**Type I Measuring Axial and Bending Strain

A half-**bridge** type I has the following characteristics:

- Two active strain-gauge elements. One is mounted in the direction of axial strain, the other acts as a Poisson gauge and is mounted transverse (perpendicular) to the principal axis of strain.
- Completion resistors provide half
**bridge**completion. - Sensitive to both axial and bending strain.
- Compensates for temperature
- Compensates for the aggregate effect on the principle strain measurement due to the Poisson’s ratio of the specimen material.
- Sensitivity at 1000 me is ~ 0.65 mV
_{out}/ V_{EX}input.

**Figure 1-7.**Half-

**Bridge**Type I Circuit Diagram

The following symbols apply to the circuit diagram and equations:

- R
_{1}and R_{2}are half-**bridge**completion resistors. - R
_{3}is the active strain-gauge element measuring compression from Poisson effect (–ne). - R
_{4}is the active strain-gauge element measuring tensile strain (+e).

To convert voltage readings to strain units use the following equation:

To simulate the effect on strain of applying a shunt resistor across R_{3}, use the following equation:

### Half-**Bridge** Type II

This section provides information for the half-**bridge** strain-gauge configuration type II.

The half-**bridge** type II only measures bending strain.

**Figure 1-8.**Half-

**Bridge**Type II Rejecting Axial and Measuring Bending Strain

A half-**bridge** type II configuration has the following characteristics:

- Two active strain-gauge elements. One is mounted in the direction of bending strain on one side of the strain specimen (top), the other is mounted in the direction of bending strain on the opposite side (bottom).
- Completion resistors provide half
**bridge**completion. - Sensitive to bending strain.
- Rejects axial strain.
- Compensates for temperature.
- Sensitivity at 1000 me is ~ 1 mV
_{out}/ V_{EX}input.

**Figure 1-9.**Half-

**Bridge**Type II Circuit Diagram

The following symbols apply to the circuit diagram and equations:

- R
_{1}and R_{2}are half-**bridge**completion resistors. - R
_{3}is the active strain-gauge element measuring compressive strain (–e). - R
_{4}is the active strain-gauge element measuring tensile strain (+e).

To convert voltage readings to strain units use the following equation:

To simulate the effect on strain of applying a shunt resistor across R_{3}, use the following equation:

### Full-**Bridge** I

This section provides information for the full-**bridge** strain-gauge configuration type I.

The full-**bridge** type I only measures bending strain.

**Figure 1-10.**Full-

**Bridge**Type I Rejecting Axial and Measuring Bending Strain

A full-**bridge** type I configuration has the following characteristics:

- Four active strain-gauge elements. Two are mounted in the direction of bending strain on one side of the strain specimen (top), the other two are mounted in the direction of bending strain on the opposite side (bottom).
- Highly sensitive to bending strain.
- Rejects axial strain.
- Compensates for temperature.
- Compensates for lead resistance.
- Sensitivity at 1000 me is ~ 2.0 mV
_{out}/ V_{EX}input.

**Figure 1-11.**Full-

**Bridge**Type I Circuit Diagram

The following symbols apply to the circuit diagram and equations:

- R
_{1}is an active strain-gauge element measuring compressive strain (–e). - R
_{2}is an active strain-gauge element measuring tensile strain (+e). - R
_{3}is an active strain-gauge element measuring compressive strain (–e).

R_{4} is an active strain-gauge element measuring tensile strain (+e).

To convert voltage readings to strain units use the following equation:

_{3}, use the following equation:

### Full-**Bridge** Type II

This section provides information for the full-**bridge** type II strain-gauge configuration.

The full-**bridge** type II only measures bending strain.

**Figure 1-12.**Full-

**Bridge**Type II Rejecting Axial and Measuring Bending Strain

A full-**bridge** type II configuration has the following characteristics:

- Four active strain-gauge elements. Two are mounted in the direction of bending strain with one on one side of the strain specimen (top), the other on the opposite side (bottom). The other two act together as a Poisson gauge and are mounted transverse (perpendicular) to the principal axis of strain with one on one side of the strain specimen (top), the other on the opposite side (bottom).
- Rejects axial strain.
- Compensates for temperature.
- Compensates for the aggregate effect on the principle strain measurement due to the Poisson’s ratio of the specimen material.
- Compensates for lead resistance.
- Sensitivity at 1000 me is ~ 1.3 mV
_{out}/ V_{EX}input.

**Figure 1-13.**Full-

**Bridge**Type II Circuit Diagram

The following symbols apply to the circuit diagram and equations:

- R
_{1}is an active strain-gauge element measuring compressive Poisson effect (–ne). - R
_{2}is an active strain-gauge element measuring tensile Poisson effect (+ne). - R
_{3}is an active strain-gauge element measuring compressive strain (–e). - R
_{}4 is an active strain-gauge element measuring tensile strain (+e).

To convert voltage readings to strain units use the following equation:

_{3}, use the following equation:

### Full-**Bridge** Type III

This section provides information for the full-**bridge** strain-gauge configuration type III.

The full-**bridge** type III only measures axial strain.

**Figure 1-14.**Full-

**Bridge**Type III Measuring Axial and Rejecting Bending Strain

A full-**bridge** type III configuration has the following characteristics:

- Four active strain-gauge elements. Two are mounted in the direction of axial strain with one on one side of the strain specimen (top), the other on the opposite side (bottom). The other two act together as a Poisson gauge and are mounted transverse (perpendicular) to the principal axis of strain with one on one side of the strain specimen (top), the other on the opposite side (bottom).
- Compensates for temperature.
- Rejects bending strain.
- Compensates for the aggregate effect on the principle strain measurement due to the Poisson’s ratio of the specimen material.
- Compensates for lead resistance.
- Sensitivity at 1000 me is ~ 1.3 mV
_{out}/ V_{EX}input.

**Figure 1-15.**Full-

**Bridge**Type III Circuit Diagram

The following symbols apply to the circuit diagram and equations:

- R
_{1}is an active strain-gauge element measuring compressive Poisson effect (–ne). - R
_{2}is an active strain-gauge element measuring tensile strain (+e). - R
_{3}is an active strain-gauge element measuring compressive Poisson effect (–ne). - R
_{4}is an active strain-gauge element measuring the tensile strain (+e).

To convert voltage readings to strain units use the following equation:

_{3}, use the following equation: