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vi Calculate the voltage gain ( gain =
ideal op amp. Figure 2 + + − ! " =
= − = + − = = +
+ = + # $% "
− − = − −
& − =
− ' () + & − = & + − & − & "
+ = +
+
+ = +
+
* − & & & − & & − = & " = = & +
+
+ & − = , +
,
, − = ,
= −, , )
− ) /.&
. page 2 of 4 ENME 351 HW#5 Solutions Electronics & Instrumentation II Problem 3 For the circuit shown in Figure 3, assume the operational amplifiers are ideal.
v
(a) Calculate the voltage gain ( gain = out )
v in
(b) Calculate the input impedance. Solution page 3 of 4 ENME 351 HW#5 Solutions Electronics & Instrumentation II Problem 4
A strain gauge with gauge factor GF and nominal resistance R is used to measure strain
on a specimen as shown in Figure 4 (b). The strain gauge is connected to a bridge circuit
and an amplifier as shown in Figure 4 (a). Assume the op-amp is ideal. Derive an
expression for the output voltage Vout. Is the relationship between the output voltage and
the change in gauge resistance linear or nonlinear? (a) Solution: Figure 4 (b) Since the op amp is ideal and there is negative feedback,
i− =i+ =0 V + =V − Summing point constraint i
V+ V− 0 i V
V
R
= in V − = in
R +R
2
2
Writing KVL at output loop:
V
V
V out = −RG i +V − = −(R + ∆R ) in + in
2R
2
V
∆R
V
= − in −
V in + in
2 2R
2
∆R
V out = −
V in
(V out is a linear function of ∆R )
2R
V + =V in Remark Recall that for a quarter bridge circuit with one strain gauge, the output voltage is a
nonlinear function of ∆R . Therefore, the op amp in the circuit linearizes the output
voltage as a function of ∆R . page 4 of 4...

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