Instrumentation Amplifiers.

Design File DF03, January, 2006

While the Op-Amp may be the work horse of analog active circuit design in general, the Instrumentation Amplifier, a specialized kind of op-amp based design, is the work horse of sensor interfacing. With balanced high impedance inputs, isolated feedback networks and excellent CMR (common mode rejection) specs, the Instrumentation amplifier is the best choice for interfacing high impedance bridge sensors.

Notes:

The Standard Non-inverting Op-Amp.

Simple single-ended low input impedance sensors which reference to ground usually present no problems interfacing to a standard non-inverting op-amp.

Figure 1 shows a single ended sensor connected to a standard non-inverting op-amp. The main design consideration is to choose a gain setting that allows the op-amp performs in a linear fashion and properly track and amplify the response of the sensor.

The gain of the op-amp is familiar formula:

A = (R2 + R3) / R3.

As we all know (or should know!) all op-amp inputs require some DC bias current to operate. Because bias current can cause a slight voltage drop R1 is typically chosen so that:

R1 = R2 || R3

This value will equalize the ibias × R voltage drops at the inputs. If the source impedance is high, then R1 is chosen so that:

R1 + Rs = R2 || R3

The input impedance is Rin + R1. Since R1 is usually insignificant in comparison to the very high input impedance of the op-amp, other than a small bias current, the sensor has a minimal load presented by the op-amp.

Bridge Sensors.

But what if the sensor is not singled, and not referenced to ground (or a fixed voltage)?

Figure 2 shows a typical bridge circuit. The output of the bridge is the difference signal between vb and va. Looking at the circuit, we suspect there is a common mode voltage, which will probably vary so a simple DC offset is not going to fix this. The standard non-inverting op-amp circuit above will poorly at best - if at all.

If what we are interested in is the difference between va and vb - this requires a different kind of amplifier called a difference or subtracting amplifier to amplify the sensor signal.

If RS is extremely high as in the case of a microphone, R1 should be connected as a terminating resistance, and the sensor should be AC coupled. The feedback network will need to changed for AC operation. Detailed treatment of this subject is beyond this ap-note. See ref. below more information.

The Difference Amplifier.

Fig 3 Shows an op-amp implemented as a difference amplifier. The output signal vo is comprised of the gain signals vo2' + vo1.

Deriving the transfer function of this circuit is straight forward. Using superposition, with v2 = 0:

vo = vo1 = -(v1 × R2 / R1)

Now, with v1 = 0:

vo = vo2 = v2' × (R1 + R2) / R2

= v2 × (R4) / (R4 + R3) × (R2 + R1) / R2

If we choose R3 = R1 and R4 = R2, then:

vo2 = v2 × R2 / R1

With both signals present,

v0 = vo2 + v01

= v2 × R2 / R1 + -(v1 × R2 / R1)

= (v2 - v1) × R2 / R1

The output is the difference of the input voltage as we wanted, but the problem with this configuration is that the input impedances are unequal. v1 sees an input impedance of R1, typical of an inverting amplifier, while v2, because of the very high input impedance typical of a non-inverting amplifier input, sees an input impedance of R3 + R4.

Since it is the ratio of the resistances which determine gain, it is possible to select equal resistor ratios for the amplifier gain but choose R4 + R3 = R1 for equal input impedances.

The input resistance seen by the sensor is.

Rin = R1 + R3 + R4.

This will work fine as long as the source resistance is low compared to the input resistance. However, this may not be the case.

The common mode input impedance Rcom is R1 || (R3 + R4). If the ratios of R1/R2 and R3/R4 match exactly, the common mode voltage component is amplified exactly the same at each input, and is subtracted by the difference amplifier.

In both cases, the low impedance of the amplifier input is a result of the feedback network, not the op-amp itself. If the connected sensor is inherently a low impedance type, like a voltage source, the low impedance of the combined amplifier input and feedback network should present no problem.

For high impedance sensors however impedance mis-match can be a problem. A differential amplifier configuration which isolates the feedback network and presents just balanced high impedance inputs to the sensor output would be a better solution. This is what an instrumentation amplifier does.

Typically there is always some mis-match. R4 can be made adjustable for common mode nulling the output. If DC level shifting is required, instead of ground, R4 can be connected to a DC bias voltage to DC shift the output.

The Instrumentation Amplifier.

Analog Devices defines an instrumentation amplifier or I-amp as "a closed loop gain block that has a differential input and an output terminal that is single-ended with respect to a reference terminal." Also, unlike an op-amp which sets it closed loop gain by a external resistor network connected between its input and output, an I-amp uses an internal isolated gain network.

In Figure 4, a classic three op-amp instrumentation amplifier is shown. The three op-amp is the most straight forward implementation of an Instrumentation Amplifier. It consists of two non-inverting input buffer amplifiers, followed by a difference amplifier. It should be noted that there are a number of other implementations using two amplifiers for example, each with their own weaknesses and strong points, but still preserving the basic definition of an Instrumentation Amplifier above.

There are three major advantages to this circuit arrangement. First, if the buffer amplifiers are matched, the input impedances are identical, and very high. Second, the feedback network is completely isolated from the signal inputs. Finally, as we will see, the gain of the amplifier is set by a single resistor Rg.

Analysis of the circuit is straight forward.

Using superposition, when vin+ = 0:

va = vin- x (R1 + Rg) / Rg

vb = vin- x (R1' / Rg)

When vin- = 0,

vb = vin+ × (R1' + Rg) / Rg

va = vin+ × (R1 / Rg)

Combining terms and subtracting we get::

(vb - va) = (Vin+ × ((R1'+ Rg) / Rg ) - Vin- x (R1' / Rg))

- (Vin- x ((R1 + Rg) / Rg) - Vin+ x (R1 / Rg))

If R1 = R1'

= Vin+ x (2R1 / Rg + 1) - Vin- x (2R1 / Rg + 1)

= (Vin+ - Vin-) x (2R1 / Rg + 1)

We know from above that the output of the difference amplifier stage, if the resistors are matched:

Vout = (vb - va) × (R3 / R2)

Substituting for vb and va, we get

Vout = (Vin+ - Vin-) x (2R1 / Rg + 1) × (R3 / R2)

We know that common mode rejection depends upon close matching of the resistors of the difference amplifier, but what effect does a mis- match of R1 and R1' at the inputs have on common mode voltage error? It turns out none.

Vcm = (vb - va) = (Vin+ × ((R1' + Rg) / Rg ) - Vin- × (R1' / Rg)) - (Vin- × ((R1 + Rg) / Rg) - Vin+ × (R1/Rg))

but Vcm = Vin+ = Vin- by definition

Voutc = Vcm ((R1'+ Rg)/Rg - R1'/Rg - R1'/Rg - ( R1+Rg)/Rg + R1/Rg) )

= Vcm (R1'/Rg + 1 - R1'/Rg - R1/Rg - 1 + R1'/Rg)

= Vcm (0)

The gain of the amplifier can be set by the single resistor Rg, with no increased common mode voltage error.

An integrated solution

You could easily build an instrumentation amplifier like figure 4. However you would still need to carefully match resistors R2, R2', R3 and R3' of the difference amplifier for acceptable CMR performance. Luckily, a number of IC vendors provide integrated solutions which implement the complete difference amplifier and associated feedback network internally.

Figure 5 shows Analogs Devices® AD623 Instrumentation Amplifier. The AD623 is an integrated version of the classic three op-amp instrumentation, with some input refinements in an eight pin package.

A real world application.

Figure 6 shows one the instrumentation amplifier channels on the MB2001 Dual Channel I-Amp MechaBlox board. It is based upon Analogs Devices® AD623 Instrumentation Amplifier in a single-end power supply configuration.

The gain of the amplifier is set by the combination of R6 and the variable resistor R8. The gain is variable from 2 to 1000 (R6 limits the gain to 1000).

In figure 4, resistor R3' is shown connected to ground. If instead, a DC bias voltage is applied, the output can be DC shifted. Pin 5 of the I-amp in figure 5 performs this function. In figure 6, Op-amp U11, a voltage follower, provides the offset voltage. Since the output of the I-amp is input to one of the 10bit single-ended Analog to digital converters (ADC) of the onboard microprocessor, the DC level shift allows the sensor mid-range output to be set to a swing point in the midrange of the ADC, allowing full use of the ADC range.

Op-amp U9 adds one system refinement, it creates a midrange voltage for a driven shield, if a shielded cable is used to connect the sensor. Note that even if the shield is connected to ground instead of the shield drive output, it should only be connected at one place! The shield should not carry an current.

Conclusion

With balanced high impedance inputs, isolated feedback networks and excellent CMR specs, the Instrumentation Amplifier is the best choice for interfacing high impedance bridge sensors.

References: A good book on Op-Amps is:
Bell, Davis A., "Operational Amplifiers"
1990, Prentis-Hall

For I-amp applications:
A Designer's Guide to Instrumentation Amplifiers
2nd Edition, Analog Devices
available on line Analog Devices Website