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Figure 1514 Inductive coupling and equivalent-circuit representation
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Noise Reduction Various techniques exist for minimizing the effect of undesired interference, in addition to proper wiring and grounding procedures The two most common methods are shielding and the use of twisted-pair wire A shielded cable is
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Figure 1513 Capacitive coupling and equivalent-circuit representation
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Part II
Electronics
shown in Figure 1515 The shield is made of a copper braid or of foil and is usually grounded at the source end but not at the instrument end, because this would result in a ground loop The shield can protect the signal from a signi cant amount of electromagnetic interference, especially at lower frequencies Shielded cables with various numbers of conductors are available commercially However, shielding cannot prevent inductive coupling The simplest method for minimizing inductive coupling is the use of twisted-pair wire; the reason for using twisted pair is that untwisted wire can offer large loops that can couple a substantial amount of electromagnetic radiation (see Section 161) Twisting drastically reduces the loop area, and with it the interference Twisted pair is available commercially
+ V S _
Shield
Signal source
Measurement system
Figure 1515 Shielding
SIGNAL CONDITIONING
A properly wired, grounded, and shielded sensor connection is a necessary rst stage of any well-designed measurement system The next stage consists of any signal conditioning that may be required to manipulate the sensor output into a form appropriate for the intended use Very often, the sensor output is meant to be fed into a digital computer, as illustrated in Figure 151 In this case, it is important to condition the signal so that it is compatible with the process of data acquisition Two of the most important signal-conditioning functions are ampli cation and ltering Both are discussed in the present section Instrumentation Ampli ers An instrumentation ampli er (IA) is a differential ampli er with very high input impedance, low bias current, and programmable gain that nds widespread application when low-level signals with large common-mode components are to be ampli ed in noisy environments This situation occurs frequently when a lowlevel transducer signal needs to be preampli ed, prior to further signal conditioning (eg, ltering) Instrumentation ampli ers were brie y introduced in 12 (see Example 124), as an extension of the differential ampli er You may recall that the IA introduced in Example 124 consisted of two stages, the rst composed of two noninverting ampli ers, the second of a differential ampli er Although the design in 12 is useful and is sometimes employed in practice, it suffers from a few drawbacks, most notably the requirement for very precisely matched resistors and source impedances to obtain the maximum possible cancellation of the common-mode signal If the resistors are not matched exactly, the commonmode rejection ratio of the ampli er is signi cantly reduced, as the following will demonstrate The ampli er of Figure 1516 has properly matched resistors (R2 = R2 , RF = RF ), except for resistors R and R , which differ by an amount R such that
v'b R iS R2 v _
RF iF
R1 v + +
vout
R'2 _ + v'a R' R'F
Figure 1516 Discrete op-amp instrumentation ampli er
15
Electronic Instrumentation and Measurements
R = R + R Let us compute the closed-loop gain for the ampli er As shown in Example 124, the input-stage noninverting ampli ers have a closed-loop gain given by A= vb v 2R2 = a =1+ vb va R1 (154)
To compute the output voltage, we observe that the voltage at the noninverting terminal is v+ = RF RF + R + R va (155)
and since the inverting-terminal voltage is v = v + , the feedback current is given by iF =
RF vout RF +R+ vout v = RF RF
v R a
(156)
and the source current is iS = vb vb v = R
RF v RF +R+ R a
(157)
Applying KCL at the inverting node (under the usual assumption that the input current going into the op-amp is negligible), we set iF = iS and obtain the expression vout va = RF RF + R + = 1+ RF R R vb RF va + R R RF + R + R vb R R
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