The circuit in Figure 3.40 is the classic implementation for an instrumentation amplifier. Its analysis when the three op amps are ideal leads to.. By eliminatingV6, Vn, and Vc in the preceding equations, we have... From this we find that the common mode rejectilon is maximal when

If in addition 2RrlRz : ZRtlRz: G, then we have

This shows that we can change the differential mode gain by means of R2 (although not in a linear way) without affecting the CMRR.

The condition to prevent saturation in any of the first stage op amps is different from that found in two-op-amp instrumentation amplifiers. From the corresponding expressions for Va and Vs, we can deduce that thE com- mon mode input signal is amplified by I in the first stage:

Therefore E" car. be higher than in two-op-amp instrumentation amplifl- ers, provided that Ve and Vn are kept below the saturation level for op amps. In practice we have neither perfect resistor matching nor ideal op amps.

This does not have any serious repercussions on input impedances that always reach very high values both in common mode and differential mode. The common mode rejection, however, is affected by matching of resistors in the differential input to single ended stage (the second one), matching of

input op amps, and by CMRR of the op amp in the second stage. It can be shown that in a similar way to that expressed by (3.55), all these factors combine by adding their reciprocals [8]:

Subscripts I and 2 refer to input op amps and subscript 3 to that in the second stage. Resistor imbalance is quantified by

From (3.69) it follows that it is advisable to use a dual op amp at the input stage instead of two individual units because that will increase the chances of having CMRRI : CMRRz, thus increasing the total CMRR.

The effect of tolerairces in resistors can be analyzed from (3.70). If a tolerance a is assumed for all resistors, the worst-case condition would be when the denominator in (3.70) is maximal, corresponding to the situation R+ :rR(l * a), R7 : kR(l * a),R5 : kR(l - a),Ro :R(l - a). Theresultis then Example: If we desire a differential mode gain of 1000 and use 57o tolerance resistors, how do the values for G and ft influence the maximal CMRR that can be achieved? From (3.66),

If the three op amps are considered to be ideal, from (3.69) and (3.72)it follows that

RUMUS

Therefore cMRR1s1a1 : 1000(k + l)10.2k: 5000(k + 1)lk. when k: l, we achieve 80 dB; when k : 10, we achieve aboutT4 dB. It is thus better to design a high gain for the first stage, unless other factors (drifts, noise) suggest low gain.

To avoid the need for low tolerance resistors, whenever a high CMRR is of interest, one of the four resistors in the differential stage (usually Rz) is an adjustable one. Another option is to use a second stage that already includes the entire differential stage, namely, the op amp and the resistors. That is the case, for example, with Burr-Brown Corp. models INA 105, INA 117, and 3627. These components can also be used in different applications, whether differential or not, because they make accessible one terminal of each inter- nal resistor [9].

When the circuit in Figure 3.40 is built from discrete parts, we should consider the following. Bipolar input op amps are usually more linear and have lower offset voltage and drifts than FET input op amps. However, FET input op amps have lower bias currents and higher input impedances. In any case it is important for these two op amps to be matched in CMRR, equation (3.69) and in offset voltage. The need for offset vbltage matching can be justified from (3.67) and (3.68) if they are rewritten when the offset voltage for each op amp is taken into account. Their contribution to the output voltage, together with that of the offset voltage for the second stage is then

There are several IC instrumentation amplifiers based on the circuit in Figure 3.40. For example, models INA 101, INA 102, INA 104, and INA 110 of Burr-Brown Corp. and model AD 522 of Analog Devices Inc. With these it is easy to achieve a CMRR of 90 dB, at60Hz and with a differential gain of 1.

The three-op-amp structure for instrumentation amplifiers is the most popular one. Some IC manufacturers even produce units containing; resis- tor network, sometimes digitally programmable, playing the role of Rz. Then it is possible to change the gain by means of a digital control from the Data Acquisition System. In that case they are called programmable gain instru- mentation amplifiers.