92 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems
A–3–6. Obtain the transfer function of the op-amp circuit shown in Figure 3–26.
Solution.The voltage at point Ais
The Laplace-transformed version of this last equation is
The voltage at point Bis
Since and we must have Thus
Hence
A–3–7. Obtain the transfer function Eo(s)/Ei(s)of the op-amp system shown in Figure 3–27 in terms of
complex impedances Z 1 ,Z 2 ,Z 3 , and Z 4. Using the equation derived, obtain the transfer function
Eo(s)/Ei(s)of the op-amp system shown in Figure 3–26.
Solution.From Figure 3–27, we find
Ei(s)-EA(s)
Z 3
=
EA(s)-Eo(s)
Z 4
Eo(s)
Ei(s)
=-
R 2 Cs- 1
R 2 Cs+ 1
=-
s-
1
R 2 C
s+
1
R 2 C
1
2
CEi(s)+Eo(s)D=
1
R 2 Cs+ 1
Ei(s)
CEB(s)-EA(s)DK=Eo(s) K1, EA(s)=EB(s).
EB(s)=
1
Cs
R 2 +
1
Cs
Ei(s)=
1
R 2 Cs+ 1
Ei(s)
EA(s)=
1
2
CEi(s)+Eo(s)D
eA=
1
2
Aei-eoB+eo
Eo(s)Ei(s)
+
C
A
B
R 1
R 1
R 2
ei
eo
Figure 3–26
Operational-
amplifier circuit.
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