PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

260 Practical MATLAB® Applications for Engineers

R.3.67 Let the load impedance of an arbitrary network be ZL = RL + jXL, where RL can be
adjusted (variable), and let the load reactance XL be fi xed, where XL ≠ XTH. Then
maximum power delivered to the load ZL occurs when RL is (adjusted) to

RRXXL
TH^2 ()TH L^2

and the power delivered to the load is then

P

VR

RL

TH X

2

4

where

R

RR

X

TH L

(^2)
R.3.68 A Y impedance structure can be transformed into a ∆ equivalent impedance struc-
ture (refer to Figure 3.38) by the following set of equations:

Z

ZZ ZZ ZZ

Z

AB BC CA

C

1



Z

ZZ ZZ ZZ

Z

AB BC CA

B

2



Z

ZZ ZZ ZZ

Z

AB BC CA

A

3



Observe that a ∆ confi guration is a structure consisting of three nodes (A, B, and C)
and three elements Z 1 , Z 2 , and Z 3 , where each node is the connection point of two
elements. For example, node A is the connection point of Z 1 and Z 2.
A Y confi guration is a four-node structure, where each of the ∆ nodes (A, B,
and C) is connected to one element ZA, ZB, and ZC, and the fourth node (the center
node) is the connection point of the three elements ZA, ZB, and ZC.

Z 2 Z 3

Z 1

ZA

ZC

Z

B

A B

C

FIGURE 3.38
Y–∆ structures.