2/7/2011
Current and voltage amplifiers lecture
1/11
Current and Voltage Amplifiers
Q: I’ll admit to being dog-gone confused.
You say that every amplifier can be described equally
well in terms of either its open-circuit voltage gain Avo,
or its short-circuit current gain Ais.
Yet, amps I have seen are denoted specifically as either
a dad-gum current amplifier or a gul-darn voltage
amplifier.
Are voltage and current amplifiers separate devices, and
if so, what are the differences between them?
A: Any amplifier can be used as either a current amp or as a voltage amp.
However, we will find that an amp that works well as one does not generally work
well as the other! Hence, we can in general classify amps as either voltage amps
or current amps.
Jim Stiles
The Univ. of Kansas
Dept. of EECS
2/7/2011
Current and voltage amplifiers lecture
2/11
Define a gain
To see the difference we first need to provide some definitions.
First, consider the following circuit:
iout (t )
iin (t )
Rs
+
vs (t )
+
-
+
vin (t )
RL
−
vout (t )
−
Q: Isn’t that just Avo ??
We define a voltage gain Av as:
Av vout (t )
v s (t )
A: NO! Notice that the output of the amplifier is not open circuited.
Jim Stiles
The Univ. of Kansas
Dept. of EECS
2/7/2011
Current and voltage amplifiers lecture
3/11
This is what the model is for
Likewise, the source voltage vs is not generally equal to the input voltage vin.
We must use a circuit model to determine voltage gain Av .
Although we can use either model, we will find it easier to analyze the voltage
gain if we use the model with the dependent voltage source:
Rs
vs (t )
Jim Stiles
+
-
iin (t )
+
vin (t )
−
Rout
Rin
+
-
iout (t )
+
Avo vin
The Univ. of Kansas
RL
vout (t )
−
Dept. of EECS
2/7/2011
Current and voltage amplifiers lecture
4/11
The result
Analyzing the input section of this circuit, we find:
Rin
⎝ Rs + Rin
⎛
vin = ⎜
???
⎞
⎟ vs
⎠
and analyzing the output:
vout
⎛ RL
=⎜
⎜R +R
L
⎝ out
⎞
⎟⎟ Avo vin
⎠
combining the two expressions we get:
⎛
vout = ⎜⎜
RL
⎝ Rout
⎞
⎟A
+ RL ⎟⎠ vo
⎛ Rin
⎜
⎝ Rs + Rin
⎞
⎟ vs
⎠
and therefore the voltage gain Av is:
Av Jim Stiles
vout (t )
vs (t )
⎛ RL
=⎜
⎜
⎝ Rout + RL
⎞
⎟⎟ Avo
⎠
⎛ Rin ⎞
⎜
⎟
R
R
+
in ⎠
⎝ s
The Univ. of Kansas
Dept. of EECS
2/7/2011
Current and voltage amplifiers lecture
5/11
How to maximize voltage gain
Note in the above expression that the first and third product terms are limited:
⎛ RL
0≤⎜
⎜R +R
L
⎝ out
⎞
⎟⎟ ≤ 1
⎠
and
⎛ Rin ⎞
0≤⎜
⎟≤1
⎝ Rs + Rin ⎠
We find that each of these terms will approach their maximum value (i.e., one)
when:
Rout RL
and
Rin Rs
Thus, if the input resistance is very large (>>Rs) and the output resistance is
very small (<<RL), the voltage gain for this circuit will be maximized and have a
value approximately equal to the open-circuit voltage gain!
vo ≈ Avo vs
Jim Stiles
iff Rout RL and Rin Rs
The Univ. of Kansas
Dept. of EECS
2/7/2011
Current and voltage amplifiers lecture
6/11
A good voltage amplifier
Thus, we can infer three characteristics of a good voltage amplifier:
1. Very large input resistance ( Rin Rs ).
2. Very small output resistance ( Rout RL ).
3. Large open-circuit voltage gain ( Avo 1 ).
Jim Stiles
The Univ. of Kansas
Dept. of EECS
2/7/2011
Current and voltage amplifiers lecture
7/11
Now for current gain
Now let’s consider a second circuit:
iin (t )
iout (t )
+
is (t )
Rs
+
vin (t )
RL
−
vout (t )
−
We define current gain Ai as:
Ai iout (t )
is (t )
Note that this gain is not equal to the short-circuit current gain Ais. This
current gain Ai depends on the source and load resistances, as well as the
amplifier parameters.
Therefore, we must use a circuit model to determine current gain Ai .
Jim Stiles
The Univ. of Kansas
Dept. of EECS
2/7/2011
Current and voltage amplifiers lecture
8/11
Use the other model
Although we can use either model, we will find it easier to analyze the current
gain if we use the model with the dependent current source:
iin (t )
iout (t )
+
is (t )
Rs
vin (t )
+
Rin
Ais iin
−
Rout
RL
vout (t )
−
Analyzing the input section, we can use current division to determine:
⎛
Rs
⎞
⎟ is
R
R
+
in ⎠
⎝ s
iin = ⎜
We likewise can use current division to analyze the output section:
iout
Jim Stiles
⎛ Rout
=⎜
⎜R +R
L
⎝ out
⎞
⎟⎟ Ais iin
⎠
The Univ. of Kansas
Dept. of EECS
2/7/2011
Current and voltage amplifiers lecture
9/11
How to maximize current gain
Combining these results, we find that:
⎛
iout = ⎜⎜
Rout
⎝ Rout
⎞
⎟⎟ Ais
+ RL ⎠
⎛ Rs
⎜
⎝ Rs + Rin
⎞
⎟ is
⎠
and therefore the current gain Ai is:
Ai io (t )
⎛ Rout
=⎜
is (t ) ⎜⎝ Rout + RL
⎞
⎟⎟ Ais
⎠
⎛ Rs ⎞
⎜
⎟
R
R
+
in ⎠
⎝ s
Note in the above expression that the first and third product terms are limited:
⎛ Rout
0≤⎜
⎜R +R
L
⎝ out
⎞
⎟⎟ ≤ 1
⎠
and
⎛ Rs ⎞
0≤⎜
⎟≤1
+
R
R
in ⎠
⎝ s
We find that each of these terms will approach their maximum value (i.e., one)
when:
Rout RL
Jim Stiles
and
Rin Rs
The Univ. of Kansas
Dept. of EECS
2/7/2011
Current and voltage amplifiers lecture
10/11
The ideal current amp
Thus, if the input resistance is very small (<<Rs) and the output resistance is
very large (>>RL), the voltage gain for this circuit will be maximized and have a
value approximately equal to the short-circuit current gain!
iout ≈ Ais is
iff Rout RL and Rin Rs
Thus, we can infer three characteristics of a good current amplifier:
1. Very small input resistance ( Ri Rs ).
2. Very large output resistance ( Ro RL ).
3. Large short-circuit current gain ( Ais 1 ).
Note the ideal resistances are opposite to those of the ideal voltage
amplifier!
Jim Stiles
The Univ. of Kansas
Dept. of EECS
2/7/2011
Current and voltage amplifiers lecture
11/11
You can trust ol’ Roy!
It’s actually quite simple.
An amplifier with low input resistance and high
output resistance will typically provide great
current gain but lousy voltage gain.
Conversely, an amplifier with high input
resistance and low output resistance will
typically make a great voltage amplifier but a
dog-gone poor current amp.
Jim Stiles
The Univ. of Kansas
Dept. of EECS