Instrumentation amplifiers serve as the workhorse of precision measurement systems. They are ideally suited to capture small voltage signals, such as those produced by sensors and transducers, even in the presence of large common-mode noise.

As an example of how instrumentation amplifiers work in a real-world application, we’ll examine the resistive strain gage (okay, “gage” should be “gauge,” but a nonviolent American revolt decreed the misspelling just, warranted and expedient).

Strain Gage Basics

Strain is a dimensionless measure of the deformation of an object under stress:

Although strain is a unitless quantity, it is often expressed as m/m or in/in. Typically, strain values are small quantities like 0.001, which could be expressed as 1000 µm/m, 1000 µin/in, or in some cases, simply as 1000 µ.

To measure strain, we use the fact that the resistance R of an electrical conductor depends directly on its resistivity r, its length l, and inversely with its cross-sectional area A.

If a conducting wire is placed in tension (stretched), its length will increase and its cross-sectional area will decrease, so its resistance will increase. Conversely, if the wire is compressed, its length will decrease, its cross-sectional area will increase, and its resistance will decrease.

By measuring the resistance of a conductor, a strain gage can determine strain.

The Wheatstone Bridge

The Wheatstone bridge circuit, consisting of four resistors in the arrangement pictured below, is the preferred circuit for measuring a small change in resistance like that developed by a strain gage. When an instrumentation amplifier is used to monitor the differential output voltage of a Wheatstone bridge, it draws essentially no current (because of its large input resistance) and so the Wheatstone bridge simplifies to two voltage dividers. The DC power supply is often called the bridge excitation voltage V_EXC.

Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

We can use voltage division to determine the differential voltage V_D developed by the bridge:

If all four resistors in the Wheatstone bridge are equal in value, the differential output voltage will be zero and the bridge is said to be in a null condition or balanced.

Wheatstone Bridge Active Arms

When one of the four fixed resistors in a Wheatstone bridge is replaced with a strain gage, it is called an active arm. The most common arrangement is a Wheatstone bridge with a single active arm, which is called a “quarter bridge” configuration.

The electronics involved in physical measurements are often located far from the physical parameter under measurement. For instance, a strain gage buried under the tarmac at a truck weigh station or within the structure of a bridge is unlikely to be located next to the electronics used to read the measurement.

This means that long lead wires are often needed to connect a strain gage to the Wheatstone bridge. Lead wire resistances vary with temperature and can greatly affect the accuracy of strain gage measurements, even though the lead wire resistance is much smaller than the bridge resistance.

We’ll first analyze the standard bridge shown above. Assume that each bridge resistor is a standard strain gage with a value of 350 Ω and that the excitation voltage is 5 V. The lead resistance is not included. The differential output voltage is zero and the bridge is in its null condition:

Now consider the added resistances of the lead wires, indicated by R_L1 and R_L2. The copper lead wires are similar in nature and are run as a twisted pair or a twisted shielded pair. Consequently, their resistances are nearly equal: R_L1 = R_L2 = R_L. This means that the total lead resistance in series with R₃ is 2R_L. Assuming that each lead has 1 Ω of resistance, the Wheatstone differential output voltage can be determined using voltage division:

Obviously, the resistance of the lead wires has thrown the bridge out of its null condition. While it is possible to readjust the circuit to its null condition with the lead wires in place, it will not hold, since temperature changes will produce drift.

However, we can compensate for this by adding a third wire to the sensor connection:

Lead wire R_L2 connects to the inverting input of the instrumentation amplifier (not shown above). The large input resistance of the instrumentation amplifier means that no current flow and no voltage drop across R_L2. Examination of the above circuit shows that R_L1, R₃, R_L3, and R₄ are in series. Voltage division yields the equation for V₁. Again, we assume that R_L1 = R_L3 = R_L = 1 Ω, R₁ = R₂ = R₃ = R₄ = 350 Ω, and V_EXC = 5 V:

The null condition is achieved with the lead wires in place. Further, if the lead wires exhibit the same temperature coefficient of resistance and experience the same temperature, perfect temperature compensation is achieved.

Gage Factor (GF)

Gage factor (GF) is an important strain gage parameter:

In this equation, the numerator is the fractional change in resistance with respect to the nominal value and the denominator is the fractional change in length with respect to its nominal value. For metal gages, the gage factor is always close to 2. For special alloys, the gage factor may be 10 or more. The gage factor is essentially constant with temperature.

Analysis of a Complete Sensor System

SGT-1/350 – TY41 data sheet. (Source: Omega.)

We’ll examine a full strain gage system using an Omega SGT -1/350 – TY43 strain gage. The above data sheet specifies that the nominal resistance (R_o) is 350 Ω, its maximum excitation voltage is 6 Vrms, and its gage factor is 2.

The sensor is used as a single active element, which means that we have a quarter bridge. To minimize noise pickup, we’ll use a three-wire, twisted shielded cable.

A precision 10 V voltage source is used for the excitation voltage. Tolerances in the bridge circuit can be trimmed out by using a multi-turn balance potentiometer (R₅) for the no-load condition. The potentiometer can adjust the bridge balance.

We take the gage factor equation and solve for the resistance change:

If the strain gage is in tension, the strain assumes positive values. Conversely, compression produces negative strain values. If we assume that we have a tension strain of 3000 µm/m, we can find the corresponding change in resistance:

This means that the strain gage resistance increases from 350 Ω to 352.1 Ω under 3000 µm/m. If the strain gage is placed under 3000 µm/m of compression (−3000 µm/m), the strain gage resistance decreases from 350 Ω to 347.9 Ω. The following table provides the strain gage resistance values.

The bridge output voltage is the differential input voltage v_D to the instrumentation amplifier. It can be determined by voltage division. (v₂ is the voltage at the noninverting input with respect to ground and v₁ is the voltage at the inverting input with respect to ground):

Next, we determine v₁:

The differential input voltage v_D can be determined:

Assume that we have tension strain of 3000 µm/m. From the resistance table above, R₃ = 352.10 Ω.

We can simulate the circuit in Multisim. The multimeters verify that v₂ is 5 V and that v_D is very close to our calculated value.

The AD620 instrumentation amplifier voltage gain equation is provided on the product data sheet (R₆is shown in the circuit below):

The instrumentation amplifier will present some DC offset voltage at its output. The AD620 instrumentation amplifier does not provide offset null input pins. However, like nearly all instrumentation amplifiers, it includes a reference input pin. The reference input can be either positive or negative and the applied voltage will be delivered to the output pin.

The circuit below includes two AD1580 bandgap voltage references (U2 and U3). The voltage reference devices are low-drift, low-noise, and virtually insensitive to temperature changes. The devices can be thought of as acting like precision Zener diodes. These devices have a nominal voltage drop of 1.225 V. The “bandgap” description comes from the fact that the ideal bandgap for silicon at 0 K is 1.22 eV.

Potentiometer R9 is adjusted to get the output of the instrumentation amplifier as close to 0 V as possible when no strain is applied to the strain gage (R3).

The last stage is a noninverting amplifier with a voltage gain of two. The output of the noninverting amplifier is monitored by a multimeter. Its voltage reading is in engineering units (for instance, 1.000 VDC is equal to 1000 µm/m).

We can simulate this design with Multisim:

Conclusion

We’ve covered a lot of ground in this series, including the challenges of electromagnetic interference, combatting common-mode noise, designing differential amplifiers and the superior instrumentation amps, and finally tying it all together with a look at real-world sensing applications.

In case you missed anything, or if you just want a refresher, check out the first three articles in this series:

Goodbye, EMI: Intro to Instrumentation Amplifiers

Make a Difference—Reject Common-Mode Noise

Instrumentation Amps: The Workhorse of Precision Measurement Systems