# Instrumentation Amps: The Workhorse of Precision Measurement Systems

Everything you need to know about designing and analyzing these noise-rejection circuits.

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In our quest to describe the instrumentation amplifier, we began by exploring electromagnetic interference (EMI) and what to do about it. We then examined the basis of instrumentation amplifiers, differential amplifiers, and defined common-mode noise and the common-mode rejection ratio (CMMR).

We’ve now set the stage for the instrumentation amplifier itself, the workhorse of precision measurement systems. Instrumentation amplifiers provide an easily adjustable voltage gain whose adjustment does not degrade the low-frequency common-mode rejection.

# Understanding the Instrumentation Amplifier

An instrumentation amplifier is a direct-coupled differential amplifier with matched input resistances (Rin(+) is equal to Rin(-)) and a differential voltage gain that can be adjusted by varying a single resistor (RG) without degrading the amplifier’s common-mode rejection.

Figure 1 shows the classic three-op amp implementation of an instrumentation amplifier.

Figure 1. Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

We can analyze the circuit in Figure 1 to determine the gain equation. The voltage transfer function (differential voltage gain) can be found by applying the superposition theorem. First, we set V1 equal to zero, and then find the components of Va and Vb produced by V2 acting alone (see Figure 2a).

Figure 2. Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

The inverting input terminal of AR2 is a virtual ground since it behaves as an inverting amplifier. As shown in Figure 2b, AR1 acts like a non-inverting amplifier with V2 as its input and Va‘ as its output. Equation 1 yields Va‘.

(1)

Because the differential voltage between the inverting and non-inverting input terminals of an operational (op) amp is approximately zero, the V2 source is effectively connected to AR2 as indicated in Figure 2c. AR2 works as an inverting amplifier and its output voltage is Vb‘.

(2)

In a similar fashion, we can find the components of Va and Vb produced by V1 with V2 equal to zero (see Figure 3). In this case, AR1 serves as an inverting amplifier, while AR2 behaves as a non-inverting amplifier. Equations 3 and 4 are based on this observation.

(3)
(4)

We find Va and Vb by summing the components algebraically:

(5)

(6)

Figure 3. Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

The output stage of the circuit is a unity-gain differential amplifier with Va and Vb as its inputs.  Hence, we can write the equation for VOUT directly.

(7)

We obtain the equation for VOUT in terms of V1 and V2 by substituting in Equations 5 and 6 for Va and Vb, respectively:

We distribute the minus sign through the Vb terms, then we distribute the V1 and V2 voltages:

The V1 and V2 terms are collected:

The differential voltage gain Avd is obtained by dividing both sides by (V2V1). (Because the Rout of AR3 is zero, Avd(oc) and Avd are equal.)

(8)

Figure 4. Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

Resistor RG is typically used as the gain-setting resistor. The attractive feature here is that RG can be varied without affecting the common-mode rejection of the circuit. While it is possible to build an instrumentation amplifier using op amps, the usual approach is to use integrated circuit versions. The data sheet for an Analog Devices AD620 instrumentation amplifier is provided in Figure 5.

Using Equation 8, we can find the voltage gain (the manufacturer indicated elsewhere that R is 24.7 kΩ):

Figure 5. Modified data sheet of AD620 instrumentation amplifier. (Source: Analog Devices.)

# Using EDA to Investigate the AD620 Instrumentation Amplifier

The Simulation Program with Integrated Circuit Emphasis (SPICE) model for the AD620 instrumentation amplifier is included in the Multisim library. As shown in Figure 6, it is in the Instrumentation Amplifier Family of the Analog Group.

Figure 6. Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

The Multisim circuit is given in Figure 7. The AD620 template does not identify the function of the pins. Consequently, the data sheet package information has been pasted on the schematic diagram for reference. The common-mode voltage is 1 V peak at 60 Hz. The differential input signal is 10 mV peak at 1 kHz. The voltage gain (Avd) was calculated previously to be 100.

Figure 7. Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

The circuit was simulated, and the oscilloscope display is provided in Figure 8. Even though there is a common-mode voltage that is 100 times larger than the differential input signal, the output signal is noise free.

Figure 8. Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

The output waveform is 1 V peak, which is perfect. The gain of 100 on a peak differential input voltage of 10 mV peak produces an output voltage of 1 V peak. As shown previously, a spectrum analyzer can be used to investigate circuit performance more fully. A virtual spectrum analyzer has been attached as indicated in Figure 9.

Figure 9. Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

If you are using Multisim, edit the start end frequencies as indicated in Figure 10. Click on Enter,  edit the Range and Resolution, and then run the simulation. By dragging the cursor to the positions shown in the figure, the peak values of the spectral components at 1 kHz and 60 Hz can be determined. Click on the left and right arrows to get as close as possible to the nominal frequencies.

Figure 10. Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

We can use the values provided by the spectrum analyzer to compute the common-mode rejection ratio:

These results are plausible. The manufacturer’s data sheet (see Figure 5) indicates a CMRR(dB) of 100 dB minimum with an Avd of 10.

# An Active Guard Drive Is a System to Drive the Shield

The CMRR of an instrumentation amplifier degrades with frequency. With power electronics, including more switching power supplies, converters and regulators, high-frequency common-mode noise abounds. An active guard drive combats the problem. Let’s see how it works.

The input portion of an instrumentation amplifier is shown in Figure 11. The two input op amps have a zero-differential voltage between their inverting and non-inverting inputs. This means that v2 appears at the top of the gain-setting resistor RG while v1 appears at its bottom. This means the voltage across RG is the differential voltage vD.

Figure 11. Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

In Figure 12, we model the differential input voltage and the common-source voltage. For clarity, the common-mode voltage source has been reversed to place its ground on its right side. The gain resistor RG is implemented by using two RG/2 resistors in series. Our immediate goal is to find voltage vx.

Kirchhoff’s voltage law is applied around the upper loop. Starting at the negative terminal of common-mode voltage source (ground), we move up and encounter the negative terminal of the upper differential source. We reach the non-inverting input terminal of the upper op amp. Its differential input voltage is zero. Since two equal-valued resistors in series are used for RG, they are each equal to RG/2 and drop one-half of the differential input voltage.

After we cross over the upper resistor, we reach the positive terminal of vx and then our ground starting point, which means we set the equation to zero. We write the Kirchhoff’s voltage law equation and solve for vX.

The voltage at the junction of the two resistors is equal to the common-mode voltage. As we will see, that voltage can be used to drive the shield.

Figure 12. Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

Figure 13a includes the model of the differential signal source and the common-mode voltage source. Observe the source resistance (rS) for the differential voltage source. Capacitor C1 is the stray capacitance of the Hi input signal conductor to the shield. Similarly, capacitor C2 represents the stray capacitance from the Lo input signal conductor to the shield.

To focus on the effects of the CMRR, we use the superposition theorem to set the differential input signal source to zero (see Figure 13b). Figure 13c describes the problem. The stray capacitances are rarely equal. This means the AC voltage division that occurs will deliver unequal portions of the common-mode noise to the non-inverting and inverting inputs of the instrumentation amplifier. Consequently, the CMRR will be degraded.

Figure 13. Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

Figure 13d shows an approach to maintain a high CMRR by making the stray capacitances irrelevant. Instead of taking the shield to ground, it is driven to the common-mode voltage.

Figure 13 (continued). Used with author’s permission from Discrete and Integrated Electronics Analysis and Design for Engineers and Engineering Technologists.

The implementation is indicated in Figure 13e. A voltage follower is used to buffer the gain resistors. The op amp should be a high-speed, wide-bandwidth unit. This is because common-mode noise can occur at frequencies much higher than 60 Hz. The op amp should be able to drive large capacitive loads. Shielded cables quite often have several picofarads per unit length (e.g., picofarads per foot or picofarads per meter). The common-mode rejection of an instrumentation amplifier is tremendous at low frequencies but degrades at higher frequencies.

# Review and Conclusions

Instrumentation amplifiers can reduce measurement uncertainty via noise rejection and proper shielding. Like the differential amplifier, the instrumentation amplifier rejects low-frequency common-mode noise.

To change the voltage gain of a differential amplifier, two resistors must be changed. To preserve good common-mode rejection, the two resistors must be matched closely. The instrumentation amplifier also amplifies its differential input signal and yields a large common-mode rejection. The prime advantage of the instrumentation amplifier is that only a single resistor must be changed to change the differential voltage gain. Further, there is no attendant degradation of the common-mode rejection.

Electronic design automation (EDA) like Multisim can simulate the operation of the instrumentation amplifier. By obtaining the output spectral response, we can determine the differential voltage gain, the common-mode voltage gain, and the common-mode rejection ratio. Stray capacitances exist within the shielding incorporated in an instrumentation amplifier system. A lack of symmetry often occurs, which impairs the common-mode noise rejection. This can be negated by reducing the voltage across the stray capacitances, which can be accomplished by driving the shield at the common-mode voltage.

In our fourth and final installment on instrumentation amplifiers, we’ll examine strain gauges and measurement temperature compensation, as well as provide a detailed analysis of a precision application.