Many sensors, such as the dynamic microphone we used in ELEC 241 or the piezoelectric transducers we'll use in this exercise, produce an output voltage directly. Others, such as the carbon button microphone from 241 or the pressure sensor in this exercise, change their resistance in response to changes in the measured parameter. To produce a signal which we can process it is necessary to convert this change in resistance to a voltage.
One way to do this is with a voltage divider:
If the internal reference voltage for the MSP430 A/D converter is set to 2.5 V, the minimum resolvable change in voltage will be about 2.4 mV. This means that the smallest change in resistance that we can measure is or about 0.39%. This doesn't seem like much of a limitation, but the pressure sensor we will be using has a full-scale resistance change of only 0.25%, so we would be unable to measure any changes.
The root of the problem is that the total change in the voltage is only a small fraction of the range of the A/D converter. But since this value is located in the middle of the range, we can't amplify without exceeding the range of the A/D converter. What we need to do is amplify the changes in about its nominal value.
Suppose that we add a second voltage divider to the above circuit:
One circuit that will amplify , is the difference amplifier:
For this circuit . If and , then . But if the resistances aren't exactly matched, we will have different gains for the inverting and non inverting inputs. Suppose that . Assume that is the larger of the two and that Let be the average of and and let . Then or . is the differential gain and is called the common-mode gain. The common-mode rejection ratio (CMRR) in decibels is defined as .
The following circuit combines high input impedance, high common mode rejection, and single resistor gain programming. It is often referred to as the "three op amp" or "classic" instrumentation amplifier.