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Z i, from which the resistive and reactive components can be determined
using a few basic geometric relationships. The reactive nature (inductive
or capacitive) of the input impedance can be determined when the
angle between E i and I i is computed. For a dual-trace oscilloscope, if
E g leads V Rs (E i leads I i), the network is inductive; if the reverse is true,
the network is capacitive.
Red
E g
Black
+
––
Black
FIG. 26.7
Determining Z i using an oscilloscope.
To determine the angle associated with Z o, the sensing resistor must
again be moved to the bottom to form a common ground with the supply
E g. Then, using the approximation E g � E o, the magnitude and
angle of Z o can be determined.
EXAMPLE 26.1 Given the DMM measurements appearing in Fig.
26.8, determine the input impedance Zi for the system if the input
impedance is known to be purely resistive.
Solution:
VRs � Eg � Ei � 100 mV � 96 mV � 4 mV
Ii � IRs � � �40 mA
Zi � Ri � � Ei
� � � 9
VRs 4 mV
� �
Rs 100 �
6 mV
� � 2.4 k�
40
mA
I i
R s
I i
Red
I i
+
EXAMPLE 26.2 Using the provided DMM measurements of Fig.
26.9, determine the output impedance Z o for the system if the output
impedance is known to be purely resistive.
E i = 0 V
Two-port
system
+
E i
–
FIG. 26.9
Example 26.2.
Two-port
system
Channel 2: V Rs
Channel 1: E s
Share common
ground
+
Rs 2 k�
+
Eo = 1.92 V Eg 2 V
–
Z o
THE IMPEDANCE PARAMETERS Z i AND Z o ⏐⏐⏐ 1153
–
E g
+
–
R s
100 �
100 mV
+
E i = 96 mV
Z i
–
FIG. 26.8
Example 26.1.
Two-port
system