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HW5 Solutions

# Figure 2

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Unformatted text preview: an 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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