boylistad

1156 ⏐⏐⏐ SYSTEM ANALYSIS: AN INTRODUCTION
+
–
A vNL E i
R o
+
E o
–
R L
FIG. 26.14
Applying a load to the output of Fig. 26.13.
If we expand Eq. (26.5) as follows:
Eo �
Eg
Eo �
Eg
A vT � � (1) � � � � ⋅
Ei �
Eg
then A vT � A v (if loaded)
Ei or AvT � AvNL � (if unloaded)
Eg
The relationship between Ei and Eg can be determined from Fig.
26.12 if we recognize that Ei is across the input impedance Zi and thus
apply the voltage divider rule as follows:
Zi(Eg) Ei ��
Zi � Rg Ei Zi or � ��
Eg Zi � Rg Substituting into the above relationships will result in
Zi AvT � Av�� Zi � Rg Zi AvT � AvNL�� Zi � Rg Eo Ei � �
Eg Ei
Eo �
Ei
E i
� Eg
(if loaded) (26.6)
(if unloaded) (26.7)
A two-port equivalent model for an unloaded system based on the
definitions of Z i, Z o, and A vNL is provided in Fig. 26.13. Both Z i and Z o
appear as resistive values since this is typically the case for most electronic
amplifiers. However, both Z i and Z o can have reactive components
and not invalidate the equivalency of the model.
+
E i
–
I i
Z i
R i
+
AvNLEi –
Z o
R o
FIG. 26.13
Equivalent model for two-port amplifier.
The input impedance is defined by Z i � E i/I i and the voltage E o �
A vNL E i in the absence of a load, resulting in A vNL � E o/E i as defined.
The output impedance is defined with E i set to zero volts, resulting in
A vNL E i � 0 V, which permits the use of a short-circuit equivalent for the
controlled source. The result is Z o � E o/I o, as defined, and the parameters
and structure of the equivalent model are validated.
If a load is applied as in Fig. 26.14, an application of the voltage
divider rule will result in
I 2
+
E o
–