The Differential Amplifiers in Instrumentation amplifier
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Most resistance sensor bridges are supplied by a grounded voltage or curreht source. Therefore the amplifier at the bridge's output should not have any of its input terminals grounded. In addition we will show later that it is best for input termi...
Most resistance sensor bridges are supplied by a grounded voltage or curreht source. Therefore the amplifier at the bridge's output should not have any of its input terminals grounded. In addition we will show later that it is best for input terminals to have high and similar impedances to ground. An amplifier having these characteristics is called a differential amplifier.
Figure 3.36 shows a very simple circuit to implement a differential ampli- fier. We assume that the op amp is ideal (Vr: V); then the output voltage is
To illustrate the differential properties of the circuit, it is convenient to write the output as a function of the differential input voltage Ed : Ez - Er. In order to do this, we must make the following substitutions in
where E" is the common mode voltage. Substitution of (3.48) and (3.49) in (3.47) yields an equation where there is one factor multiplying E" and an- other multiplying Ea. The first factor is called common mode gain, G", and the second factor differential mode gain, G6. That is,
Their expressions for the circuit in Figure 3.36 are
In a differential amplifier we wish to amplify the difference between the input voltages but not the common mode signal. Thus we must have G" : 0, which is obtained when
Then V. : kEo. Because the matching expressed by (3.53) is difficult to fulfill exactly, the circuit's ability to reject common mode signals will be limited rather than infinite. It is quantified by means of the Common Mode Rejection Ratio (CMRR), defined as the differential gain divided by the common mode gain. For Figure 3.36 it is given by
The CMRR is usually expressed in decibels. We obtain that by taking the decimal logarithm of the previous expression and multiplying the result by 20. If in Figure 3.36 the op amp is not ideal we must substitute the model in Figure 3.37, where the common mode gain for the op amp (A.) is obtained from the CMRR in the specification sheets. For the p.A74l, for example, Aa : 50,000 minimum at dc, and CMRR : 70 dB minimum. Therefore
Using this model for the op amp, the analysis of Figure 3.36 is more cumbersome. But we can follow the same steps that lead us before to equa- tions (3.47-3.50), now defining V6 and V" from Vl and V2. Fortunately, after simplifying and reordering, from the flnal equation we obtain a very simple rule,
That is, the CMRR for resistors, equation (3.54), and for the op aup add in "parallel"; that is, their reciprocals add. Each CMRR must be expressed as a fraction, not in decibels.
The circuit of Figure 3.36 can be directly applied to a sensor bridge, where E1 and E2are the voltages at the bridge output terminals. It is also possible to arrange connections in order to identify output bridge voltages with Vr and V2, zs shown in Figure 3.38a.
For Figure 3.36, note that by assuming an ideal op amp, the input imped- ances seen by sources E1 and E2are respectively R1 and R3 * Ra, implying that Rz and Ra will have to be very large resistors if high input impedance and high gain are required. A high input impedance is required in order to reduce loading effects in voltage measurements. The requirement for a high gain is due to the low amplitude for the bridge output. It would certainly be possible to arrange several gain stages in cascade in order to obtain the amplitude needed at the ADC input, but drifts and noise effects in amplifiers are lower when the gain is concentrated in the flrst amplifying stages (see chapter 7). Figure 3.38b shows the equivalent circuit for analyzing Figure 3.384. If, as usual, we want to have % : 0 when x : 0, then we must have Rz : Rl (: R). By applying (3.54), we obtain
Thus the CMRR for this circuit degrades when the bridge imbalance increases. If, for example, we want a differential mode gain of 100 when x : 0.01, the resulting CMRR will be approximately 86 dB. Therefore the actual common mode gain, G", is about 5 x 10-3. If the supply voltage for the bridge is 20 V, then the common mode voltage at the bridge output will be 2012: l0 V. The voltage contribution at the amplifier output will be 50 mV on a signal voltage of 5 v, even with an ideal op amp. This contribution is proportional to x, so the result is a small change in gain. For large values of x the nonlinearity is increased.
Both the circuit in Figure 3.38a and that in Figure 3.36 show the additional shortcoming of the need for modifying two resistors whenever the differen- tial mode gain is to be changed. Even more, this niodiflcation must be per- formed without degrading the matching required by equation (3.57). This lack of flexibility has lead to the development of better alternatives, imple- mented in circuits generally called instrumentation amplifiers.
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