Modern Control Engineering

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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