Download Current and Voltage Gain

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Current and Voltage Gain
Of the four amplifier parameters we have discussed
( Ri , Ro , Avo , Ais ), only three are independent. Once we know any
three of the parameters, we can determine the remaining value.
For example, say we have determined the input resistance Ri,
output resistance Ro , and open-circuit voltage gain Avo of the
amplifier. We can determine from these values alone the
short-circuit current gain Ais of this amplifier!
To see this, let’s begin with our first amplifier model:
ii (t)
+
vi
-
Ro
+
-
Ri
Avo vi
We know that the short-circuit current gain is defined as:
Ais 
ios
ii
We can determine the short-circuit output current ios by simply
shorting the output of the model and determining the output
current:
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Rs
vs (t)
+
-
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ii (t)
+
vi
-
Ro
Ri
+
-
ios (t)
Avo vi
The short-circuit output current is obviously:
ios 
Likewise, the input voltage vi can be written in terms of the
input current as:
vi 
and therefore the short-circuit output current becomes:
ios 
Thus, the short-circuit current gain is determined to be:
Ais 
A
ios Ri
 Avo
ii
Ro
Ais is determined from Ri , Ro , and Avo !
a
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Note that we can use this result to derive our second amplifier
model (i.e., model with dependent current source). Starting
with our original model:
ii (t)
+
vi
-
Ro
Ri
+
-
Avo vi
We replace the output section with its Norton’s equivalent
circuit:
ii (t)
+
vi
-
Ri
Avo vi
Ro
Ro
Note that the dependent current source can be written in of
input current ii and the short-circuit current gain Ais:
Avovi
R
 Avo i ii  Ais ii
Ro
Ro
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So that we now have an alternative linear amplifier model, one
using the amplifier parameters Ais, Ri and Ro:
io (t)
ii (t)
+
vi
-
Ri
Ais ii
Ro
vo(t)