Section 3–3 / Mathematical Modeling of Electrical Systems 81
Impedance Approach to Obtaining Transfer Functions. Consider the op-amp
circuit shown in Figure 3–17. Similar to the case of electrical circuits we discussed ear-
lier, the impedance approach can be applied to op-amp circuits to obtain their transfer
functions. For the circuit shown in Figure 3–17, we have
Since we have
(3–34)
Eo(s)
Ei(s)
=-
Z 2 (s)
Z 1 (s)
E¿(s)0,
Ei(s)-E¿(s)
Z 1
=
E¿(s)-Eo(s)
Z 2
+
Eo(s)
I(s)
I(s)
Ei(s)
E 9 (s)
Z 1 (s)
Z 2 (s)
Figure 3–17
Operational-
amplifier circuit.
EXAMPLE 3–9 Referring to the op-amp circuit shown in Figure 3–16, obtain the transfer function Eo(s)/Ei(s)by
use of the impedance approach.
The complex impedances Z 1 (s)andZ 2 (s)for this circuit are
and
The transfer function Eo(s)/Ei(s)is, therefore, obtained as
which is, of course, the same as that obtained in Example 3-8.
Eo(s)
Ei(s)
=-
Z 2 (s)
Z 1 (s)
=-
R 2
R 1
1
R 2 Cs+ 1
Z 2 (s)=
1
Cs+
1
R 2
=
R 2
R 2 Cs+ 1
Z 1 (s)=R 1