# Set 5B: Difference Amplifiers (Part B) ```Differential Amplifier Implementation
on ICs
Difference Amplifiers are quite popular as
building blocks of ICs
 They are much less sensitive to noise (CMRR &gt;&gt;1).
 They allow direct coupling of stages (no need for
coupling and/or by-pass capacitors).
Typical implementation in an IC
Two outputs
Single ended output
Need to get rid of R’s
Biasing with a Current Mirror – Bias
VG is the bias voltage
at gates of Q1 and Q2
VG = 0 if no bias is
applied (e.g., first stage)
Bias
Half circuit
(common mode)
VGS = VG − VS
Current mirror is in
the Source Circuit
0.5 I o = I D =
1
k n′ (VGS − Vtn ) 2 (1 + λVDS )
2
VDD = I D RD + VDS + VS
DS-KVL
Can be solved to find VDS and VS (and VGS)
Does not require a precise circuit to set VG
Biasing with a Current Mirror – Small Signal
Small Signal
Analyzed before
Current mirror is in
the Source Circuit
Biasing with a Current Mirror
Why is the current mirror in the source circuit?
Current mirror is in
the Drain Circuit
Current mirror is in
the Source Circuit
Recall: For CS amplifier we
argued that current source
should not be located in
the source circuit!
Biasing with a Current Mirror
Why is the current mirror in the source circuit?
Difference Amp.
 ro3 does not affect the differential gain
 Need a large “RSS ” to get a high CMRR
|A |
CMRR = d = 1 + 2 g m1 RSS + RD / ro1
| Ac |
= 1 + 2 g m1ro 3 + RD / ro1
CS Amp. With current source
in the source circuit
 A large resistor in the source circuit
reduces the gain substantially
Av = −
g m1 R D
1 + g m1ro 2 + R D / ro1
Biasing with a Current Mirror
Why is the current mirror in the source circuit?
Difference Amp.
CS Amp. With current source
in the drain circuit
 It does not require a precise circuit to set VG
 We can set VG = 0 . Ideal for first stage as it
would not require coupling capacitors
 Requires precise bias
voltage for Q1
(differential output)
We need to replace RD with active loads.
Choices are:
Diode Connected transistor*
 RD= 1/gm
 Not useful as the gain is
Ad = − g m R D
 Large gain as RD= ro
Ad = − g m R D
 But above is really a leg of a
current mirror!
*See Sedra &amp; Smith, Problem 8.20
Note: Circuit is incorrect. Gates Q3 and Q4 should NOT be connected to each other
Current source (mirror) as active load
 For NMOS difference amplifier, we need PMOS
 Q1 should see the drain of Q3 (in order to
see large R)
 Bias current should flow into the drain of Q1
(and thus out of drain of Q3)
 For PMOS difference amplifier, we need NMOS
 This is Similar to a CS amplifier.
Q3 and Q4 should be identical
to get a symmetric circuit
Current source (mirror) as active load
Requires careful biasing
• Q1 and Q2 are identical and
VGS1 = VGS 2
• Thus, I D 2 = I D1 = I o / 2
•
I D 3 = I D1 = I o / 2
•
I D4 = I D2 = Io / 2
• Note: VSG 3 = VSG 3 = VDD − VG 3
Q3 and Q4 are identical
Q1 and Q2 are identical
 Q3 and Q4 should be
identical.
 Q3, Q4, and Q5 parameters
(i.e., W/L) and VG3 should be
chosen carefully such that
I D3 = I D 4 = I o / 2
Current source (mirror) as active load
Example Implementation on IC
PMOS Amps
NMOS Amps,
PMOS current source
NMOS current
Current source (mirror) as active load
Small Signal Response
Differential Mode
vo1 = − g m1ro3 (−0.5vd ) = 0.5 g m1ro3vd
vo 2 = −vo1 = −0.5 g m1ro3vd
Common Mode
vo 2 − vo1
= − g m1r o 3
vd
vo1
g m1ro 3
=−
1 + 2 g m1ro 5 + ro 3 / ro1
vc
vo1 = vo 2
Ac =
vo 2 − vo1
=0
vc
CMRR =
=∞
| Ac |
Cascode Difference amplifier
ro 5 + ro 7 + g m 5 ro 5 ro 7
≈ g m 5 ro 5 ro 7
Small
signal
Cascode Difference amplifier*
Differential Mode
vo1 = − g m1 ( g m 3 ro3 ro1 || g m 5 ro5 ro7 )(−0.5vd )
vo 2 = −vo1
vo 2 − vo1
= − g m1 ( g m 3 ro3 ro1 || g m 5 ro5 ro7 )
vd
Common Mode
vo1 = vo 2
Ac =
* See Sedra &amp; Smith, Chap 12.2 for a
folded cascode version
vo 2 − vo1
=0
vc
Exercise: Calculate vo1 for
common mode
Active load for a single-ended output
Works fine but require biasing of
Q3 and Q4 (i.e., VG3)
“Popular” active load for single-ended output
 Does not require biasing of Q3 and Q4
(i.e., VG3)
 Gets a similar gain and CMRR
 But, circuit is NOT symmetric (half-circuit
does not work!)
Active load for a single-ended output
Small Signal
Note ro4 = ro3 and gm4 = gm3
Diode-connected
transistor
Active load for a single-ended output
Small Signal
Note ro4 = ro3 and gm4 = gm3
ro2 = ro1 and gm2 = gm1
Circuit is NOT symmetric
CANNOT use “half-circuit”
Differential Gain
ro4 = ro3 and gm4 = gm3
ro2 = ro1 and gm2 = gm1
vgs1 = − 0.5vd − v5
vgs2 = + 0.5vd − v5
v g 3 − v5
Node vg3
g m 3v g 3 + g m1 (−0.5vd − v5 ) +
Node vo
g m 3v g 3 +
Node v5
v5 v5 − v g 3 v5 − vo
+
+
− g m1 (−0.5vd − v5 ) − g m1 (+0.5vd − v5 ) = 0
ro 5
ro1
ro1
ro1
=0
vo
v −v
+ g m1 (+0.5vd − v5 ) + o 5 = 0
ro 3
ro1
Differential Gain
Rearranging terms:


1 
1 
vg 3  g m 3 +  + v5  − g m1 −  = +0.5 g m1vd
ro1 
ro1 



 1
1 
1 



v g 3 ( g m 3 ) + v5  − g m1 −  + vo  +  = −0.5 g m1vd
ro1 

 ro 3 ro1 
 1 

 1 
2
1 
v g 3  −  + v5  + 2 g m1 + +  + vo  −  = 0
ro1 ro 5 
 ro1 

 ro1 
Dropping 1/ro terms compared with gm
v g 3 ( g m 3 ) + v5 (− g m1 ) = +0.5 g m1vd
 1
1 
v g 3 ( g m 3 ) + v5 (− g m1 ) + vo  +  = −0.5 g m1vd
 ro 3 ro1 
 1 
 1 
v g 3  −  + v5 (+ 2 g m1 ) + vo  −  = 0
 ro1 
 ro1 
Dropping v5 /ro5 term implies
that very little current flows into
ro5 (can remove ro5 from the
circuit as done in the textbook)
Differential Gain
v g 3 ( g m 3 ) + v5 (− g m1 ) = +0.5 g m1vd
 1
1 
v g 3 ( g m 3 ) + v5 (− g m1 ) + vo  +  = −0.5 g m1vd
 ro 3 ro1 
 1 
 1 


v g 3  −  + v5 (+ 2 g m1 ) + vo  −  = 0
 ro1 
 ro1 
Subtracting second equation from the first*:
vo
= − g m1vd
ro1 || ro 3
⇒ vo = − g m1 (ro1 || ro 3 )vd ⇒ Ad = − g m1 (ro1 || ro 3 )
2 g m 3v g 3 +
vo
vo
= 0 ⇒ vg 3 = −
ro 3
2 g m 3 ro 3
vg 3 = +
Note: vg3 &lt;&lt; vo
g m1 (ro1 || ro 3 )
g m1
vd ≈
vd
2 g m 3 ro 3
4 g m 3 ro
Textbook Eq. 7.1.40
is incorrect
* This is sloppy math as if subtract 2nd equation from first before dropping ro terms, a vg3 term
appears in the above equation. Fortunately, as vg3 &lt;&lt; vo, ignoring vg3 term is justified
Common-Mode Gain
ro4 = ro3 and gm4 = gm3
ro2 = ro1 and gm2 = gm1
vgs1 = − 0.5vd − v5
vgs2 = + 0.5vd − v5
vg 3 − v5
Node vg3
g m 3vg 3 + g m1 (vc − v5 ) +
Node vo
g m 3v g 3 +
Node v5
v5 v5 − vg 3 v5 − vo
+
+
− g m1 (vc − v5 ) − g m1 (vc − v5 ) = 0
ro 5
ro1
ro1
ro1
=0
vo
v −v
+ g m1 (vc − v5 ) + o 5 = 0
ro 3
ro1
Common-Mode Gain
g m 3vg 3 + g m1 (vc − v5 ) +
g m 3v g 3 +
vg 3 − v5
ro1
=0
vo
v −v
+ g m1 (vc − v5 ) + o 5 = 0
ro1
ro 3
v5 v5 − vg 3 v5 − vo
+
+
− g m1 (vc − v5 ) − g m1 (vc − v5 ) = 0
ro 5
ro1
ro1
Subtracting second equation from the first and dropping 1/ro terms compared with gm
vo
=0 ⇒
ro1 || ro 3
Ac = 0 ⇒ CMRR = ∞
Solving equations without dropping 1/ro terms compared with gm
vo =
1
2 g m 3 ro 5
vc ⇒
Ac =
1
2 g m 3 ro 5
⇒ CMRR = 2 g m 3 ro 5 g m1 (ro1 || ro 3 )
Output Resistance
Attach a source vx to the
output and calculate ix)
Node vg3 g m 3vg 3 + g m1 (−v5 ) +
vg 3 − v5
ro1
=0
vx
v −v
+ g m1 (−v5 ) + x 5 = ix
ro1
ro 3
Node vx
g m 3v g 3 +
Node v5
v5 v5 − v g 3 v5 − v x
+
+
− g m1 (−v5 ) − g m1 (−v5 ) = 0
ro 5
ro1
ro1
Subtracting second equation
from the first and dropping
1/ro terms compared with gm
vx
= ix
ro1 || ro 3
Ro =
vx
= ro1 || ro 3
ix
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