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1154 ⏐⏐⏐ SYSTEM ANALYSIS: AN INTRODUCTION<br />

Channel 1<br />

E g<br />

+<br />

–<br />

50 mV ∠0°<br />

(p-p)<br />

–<br />

R s<br />

10 �<br />

(a)<br />

Z i<br />

+<br />

+<br />

E i<br />

–<br />

Solution:<br />

VRs � Eg � Eo � 2 V � 1.92 V � 0.08 V � 80 mV<br />

Io � IRs � � �40 mA<br />

Zo � � Eo<br />

� � � 1<br />

VRs 80 mV<br />

� �<br />

Rs 2 k�<br />

. 92V<br />

� � 48 k�<br />

40<br />

mA<br />

I o<br />

EXAMPLE 26.3 The input characteristics for the system of Fig.<br />

26.10(a) are unknown. Using the oscilloscope measurements of Fig.<br />

26.10(b), determine the input impedance for the system. If a reactive<br />

component exists, determine its magnitude and whether it is inductive<br />

or capacitive.<br />

Channel 2<br />

Two-port<br />

system<br />

FIG. 26.10<br />

Example 26.3.<br />

150°<br />

E g<br />

Eg : Vertical sensitivity = 10 mV/div.<br />

VRs : Vertical sensitivity = 1 mV/div.<br />

(b)<br />

Solution: The magnitude of Zi: VRs( p-p) 2 mV<br />

Ii( p-p) � IRs( �����200 mA<br />

p-p)<br />

Rs<br />

10 �<br />

E i<br />

50<br />

mV<br />

Zi � � � � � �� � 250 �<br />

Ii Ii 200<br />

mA<br />

The angle of Zi: The phase angle between Eg and VRs (or IRs � Ii) is<br />

180° � 150° � 30°<br />

with E g leading I i, so the system is inductive. Therefore,<br />

E g<br />

Zi � 250 � �30°<br />

� 216.51 ��j 125 � � R � j XL V Rs

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