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The Common Source Amp
with a Current Source
VDD
Now consider this NMOS
amplifier using a current source.
I
* Note no resistors or
vO(t)
capacitors are present!
Q1
* This is a common source
amplifier.
+
_
vi(t)
* ID stability is not a
VG
problem!
Q: I don’t understand! Wouldn’t the small-signal circuit be:
vo(t) =???
Q1
vi(t)
+
_
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A: Remember, every real current source (as with every
voltage source) has a source resistance ro . A more accurate
current source model is therefore:
ro
I
Ideally, ro = ¥ . However, for good current sources, this
output resistance is large (e.g., ro = 100 KΩ ). Thus, we mostly
ignore this value (i.e., approximate it as ro = ¥ ), but there
are some circuits where this resistance makes quite a
difference.
VDD
This is one of those circuits!
ro
I
Therefore, a more accurate
amplifier circuit schematic is:
vO(t)
Q1
vi(t)
VG
+
_
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And so the small-signal circuit becomes the familiar:
ro
vo(t)
Q1
vi(t)
+
-
Therefore, with the hybrid-pi model:
id
G1
D1
+
vi
+
-
vgs1
-
vo
gm v gs 1
ro 1
ro
S1
Q: But, we implement a current source using a current
mirror. What is the output resistance ro of a current mirror?
A: Implementing a PMOS current mirror, we find that our
amplifier circuit:
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VDD
I
vO(t)
Q1
+
_
vi(t)
VG
is specifically:
VSS
-
Q3
-
VSS
VGS2
VGS3
+
+
Q2
vO(t)
Iref
Q4
Q1
vi (t)
VG
+
_
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Q: Yikes! Where did all those transistors come from? What
is it that they do?
A: Transistors Q2, Q3, and Q4 form the current mirror that
acts as the current source. Note that transistor Q4 is an
enhancement load—it acts as the resistor in the current
mirror circuit.
Note this amplifier circuit is entirely made of NMOS and
PMOS transistors—we can “easily” implement this amplifier as
an integrated circuit!
Q: So again, what is the source resistance ro of this current
source?
A: Let’s determine the small-signal circuit for this
integrated circuit amplifier and find out!
Q: But there are four (count em’) transistors in this circuit,
determining the small-signal circuit must take forever!
A: Actually no.
The important thing to realize when analyzing this circuit is
that the gate-to-source voltage for transistors Q2, Q3, and
Q4 are DC values!
Q: ??
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A: In other words, the small signal voltages v gs for each
transistor are equal to zero:
v gs 2 = v gs 3 = v gs 4 = 0
Q: But doesn’t the small-signal source vi (t ) create smallsignal voltages and currents throughout the amplifier?
A: For some of the circuit yes, but for most of the circuit no!
Note that for transistor Q1 there will be small-signal voltages
v gs 1(t ) and vds 1(t ), along with id 1(t ). Likewise for transistor
Q2, a small-signal voltage vds 2(t ) and current id 2(t ) will occur.
VSS
- VSS
VGS 3 + 0
-
VGS 2 + 0
+
-
+
VDS 3 + 0 Q3
Q2
VDS 2 + vds 2
+
+
I ref + id
+
Iref + 0
+
+
+
Q4 V + 0
DS 4
-
VGS 4 + 0
-
vO(t)
vi (t)
+
_
Q1 VDS 1 + vds 1
-
VGS 1 + v gs 1
-
VG
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But, for the remainder of the voltages and currents in this
circuit (e.g., VDS 4 , VGS 2 , ID 3 ), the small-signal component is
zero!
Q: But wait! How can there be a small-signal drain current
id 2(t ) through transistor Q2 , without a corresponding smallsignal gate-to-source voltage v gs 2(t )?
A: Transistor Q2, is the important device in this analysis.
Note its gate-to-source voltage is a DC value (no small-signal
component!), yet there must be (by KCL) a small-signal drain
current id 2(t )!
This is a case where we must consider the MOSFET output
resistance ro 2 . The small-signal drain current for a PMOS
device is:
id 2 = gm 2 v gs 2 -
vds 2
ro 2
Since v gs 2 = 0 , this equation simplifies to:
id 2 = -
vds 2
ro 2
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Equivalently, the small-signal PMOS model is:
S2
-
-
vgs2
+
G2
ro 2
vds2
+
gm v gs
D2
Thus for v gs 2 = 0 , the small-signal model becomes:
S2
-
-
G2
ro 2
vds2
+
vgs2 =0
+
D2
Or, simplifying further:
id
S2
-
ro 2
vds2
+
id 2 = D2
vds 2
ro 2
id
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Thus, the small-signal model of the entire current mirror is
simply the output resistance of the MOSFET Q2 !
ro 2
vo(t)
Q1
vi (t)
+
-
Comparing this to the earlier analysis--with a current source
of output resistance ro :
ro
vo(t)
Q1
vi(t)
+
-
It is evident that the output resistance of the current mirror
is simply equal to the output resistance of MOSFET Q2 !!!!
ro = ro 2
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And so this circuit:
VSS
VSS
Q2
Q3
vO(t)
Iref
Q4
Q1
+
_
vi (t)
VG
VDD
is equivalent to this circuit:
Iref
ro 2 
vO(t)
Q1
vi(t)
VG
+
_
1
 Iref
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The resulting small-signal circuit of this amp is:
vo
+
vi
+
-
vgs1
-
gm 1 v gs 1
ro 1 ro 2
And so the open-circuit voltage gain is:
Avo = - gm 1 (ro 1 ro 2 ) = 2 K1 Iref (ro 1 ro 2 )
Note this result is far different (i.e., larger) than the result
when using the enhancement load for RD:
Avo  
K1
K2
However, we find that the output and input resistances of
this amplifier are the same as with the enhancement load:
Ri  
Ro  ro 1 ro 2
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