Modern Control Engineering

90 Chapter 3 / Mathematical Modeling of Mechanical Systems and Electrical Systems

A comparison of the transfer functions shows that the systems shown in Figures 3–23(a) and (b)

are analogous.

A–3–5. Obtain the transfer functions Eo(s)/Ei(s)of the bridged T networks shown in Figures 3–24(a)

and (b).

Solution.The bridged Tnetworks shown can both be represented by the network of

Figure 3–25(a), where we used complex impedances. This network may be modified to that shown

in Figure 3–25(b).

In Figure 3–25(b), note that

I 1 =I 2 +I 3 , I 2 Z 1 =AZ 3 +Z 4 BI 3

RR

C 1

CC

C 2

ei eo

(a)

R 1

R 2

ei eo

(b)

Figure 3–24

BridgedTnetworks.

Z 1

Z 4

Z 3

Z 2

Z 1

Ei(s)

Z 4

Z 3

Z 2

I 3

I 1 I 2

I 1

I 3

I 3

I 2

I 1

I 1

ei eo

Eo(s)

(a)

(b)

Figure 3–25

(a) Bridged T

network in terms of

complex impedances;

(b) equivalent

network.

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