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Zi � � Ei
�
(ohms, �) (26.1)
with I i the current resulting from the application of a voltage E i.
The output impedance Z o is defined by
Zo � � Eo
�
E i � 0 V
(ohms, �) (26.2)
with I o the current resulting from the application of a voltage E o to the
output terminals, with E i set to zero.
Note that both I i and I o are defined as entering the package. This is
common practice for a number of system analysis methods to avoid
concern about the actual direction for each current and also to define Z i
and Z o as positive quantities in Eqs. (26.1) and (26.2), respectively. If I o
were chosen to be leaving the system, Z o as defined in Eq. (26.2) would
have to have a negative sign.
An experimental setup for determining Z i for any two input terminals
is provided in Fig. 26.5. The sensing resistor R s is chosen small
enough not to disturb the basic operation of the system or to require too
large a voltage E g to establish the desired level of E i. Under operating
conditions, the voltage across R s is E g � E i, and the current through the
sensing resistor is
VRs �
Rs
I Rs � �
E g � E i
� Rs
Ei �
Ii
But Ii � IRs and Zi � � Ei �IRs
E g
+
–
I Rs
I o
R s
I i
V Rs I i
Z i
+
E i
–
FIG. 26.5
Determining Z i.
Two-port
system
The sole purpose of the sensing resistor, therefore, was to determine I i
using purely voltage measurements.
As we progress through this chapter, keep in mind that we cannot
use an ohmmeter to measure Z i or Z o since we are dealing with ac systems
whose impedance may be sensitive to the applied frequency. Ohmmeters
can be used to measure resistance in a dc or an ac network, but
recall that ohmmeters are employed only on a de-energized network,
and their internal source is a dc battery.
The output impedance Z o can be determined experimentally using the
setup of Fig. 26.6. Note that a sensing resistor is introduced again, with
E g being an applied voltage to establish typical operating conditions. In
addition, note that the input signal must be set to zero, as defined by Eq.
THE IMPEDANCE PARAMETERS Z i AND Z o ⏐⏐⏐ 1151