13.10.2012 Views

boylistad

boylistad

boylistad

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

816 ⏐⏐⏐ NETWORK THEOREMS (ac)<br />

+<br />

E<br />

–<br />

I<br />

R 1<br />

hI<br />

+ V = 0 –<br />

E oc<br />

FIG. 18.77<br />

Determining E oc for the network of Fig. 18.75.<br />

+<br />

–<br />

E � IR1 � Isc R2 � 0<br />

and IR1 � Isc R2 � E<br />

or I �<br />

so Isc ��(1 � h)I ��(1 � h) �� � R1 �<br />

or R1Isc ��(1 � h)Isc R2 � (1 � h)E<br />

Isc[R1 � (1 � h)R2] � (1 � h)E<br />

(1 � h)E<br />

Isc ��� �IN R1 � (1 � h)R2 Z N<br />

I sc R 2 � E<br />

��<br />

R1<br />

Method 1: Eoc is determined from the network of Fig. 18.77. By<br />

Kirchhoff’s current law,<br />

0 � I � hI or I(h � 1) � 0<br />

For h, a positive constant I must equal zero to satisfy the above.<br />

Therefore,<br />

I � 0 and hI � 0<br />

and Eoc � E<br />

Eoc E R1 � (1 � h)R2 with ZN ���–––– �––––<br />

Isc (1 � h)E (1 � h)<br />

�� R1 � ( 1 �<br />

h)R 2<br />

I sc R 2 � E<br />

Method 2: Note Fig. 18.78. By Kirchhoff’s current law,<br />

Ig � I � hI � (1 � h)I<br />

+<br />

– V R1<br />

R 1<br />

I<br />

–<br />

V R2<br />

R 2<br />

+<br />

hI E<br />

Z g<br />

N –<br />

FIG. 18.78<br />

Determining the Norton impedance using the approach Z N � E g/ E g.<br />

By Kirchhoff’s voltage law,<br />

Eg � IgR2 � IR1 � 0<br />

or I �<br />

Substituting, we have<br />

E g � I gR 2<br />

��<br />

R1<br />

Ig � (1 � h)I � (1 � h) �� � R1 �<br />

and I gR 1 � (1 � h)E g � (1 � h)I gR 2<br />

I g<br />

E g � I gR 2<br />

+<br />

Th

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!