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4. Active Loads and IC MOS Amplifiers
ECE 102, Winter 2011, F. Najmabadi
Reading: Sedra & Smith: Chapter 7 (MOS portions)
Progress towards an IC relevant amplifier
Resistors and capacitors take a lot of space on ICs:o Minimize (i.e., very few) R & C and small sizes (e.g., nF or smaller)
o Get rid of coupling capacitors by direct coupling between stages (makes biasing design complicated)
o Replace Rs with a current sourceo Still need to get rid of Cs!o What to do about RD?
Current mirrors are the principle method for biasing in ICs
Identical MOS: Same k’n and Vt
Q1 is always in saturationVDS1 = VGS > VGS – Vt
Q2 has to be in saturation for current mirror to workVDS2 > VGS – Vt
refo ILWLWI
1
2
)/()/(
=
Small signal model of Current Mirrors
Small signal response of an ideal current source is an open circuit!
However, Current mirrors are NOT ideal current sources as we used λvDS << 1 in our “bias” analysis
Bias Model Small Signal Model
Real Circuit
refo ILWLWI
1
2
)/()/(
=
Small signal model of Current Mirrors
0
in flows :D1at KCL
111
11
=⇒−== gsogsmgsD
ogsm
vrvgvvrvg
Real Circuit Small Signal Model
2orR =circuitopen is sourcecurrent 0 2 gsmgs vgv ⇒=
Current sourcebecomes open circuit
But what happens if we replace Irefcurrent source with “practical” elements?
Not a Practical Circuit Practical Circuit
Would practical elements that fix Iref change the small signal response?
Small signal response of a practical current mirror
Practical Circuit
0 )||(
||in flows :D1at KCL
111
11
=⇒−== gsDogsmgsD
Dogsm
vRrvgvvRrvg
2orR =circuitopen is sourcecurrent 0 2 gsmgs vgv ⇒=
Generalized Small signal Model ofCurrent Mirrors
Any circuit that “fixes Iref”
V ..
)1()( )/('21
saturationin Q1
.
G1
12
111
11
1
→⇒=⇒==⇒
+−=
⇒=
==
GGGSGS
DStnGSnD
GSDS
refD
vconstvconstvv
vVvLWki
vvconstii
λ
Small Signal Model
Summary of Current Mirrors
Bias Model Small Signal Model
refo ILWLWI
1
2
)/()/(
=
Bias current goes through this leg
Signal current goes through this leg(∞ capacitor)
It is sufficient to consideronly Q2 in circuit calculations
PMOS Version:
Summary of Current Mirrors
NMOS Version:
“Intuitive” Model
It is sufficient to consideronly Q2 in circuit calculations
Biasing a CS Stage: Can we place a current mirror in the source circuit?
Typical bias of a discrete CS amplifier
Placing a current mirror in the source circuit will not Work!
Current mirror Bias works fine!
o A large R in the source circuit for small signal reducing the gain by (1+ gm1 rO2)
Bias Small Signal
We need to Bias a CS Stage by placing a current mirror in the drain circuit!
Signal
Current mirror provides RD !
Current mirror sets ID = Io
However, a precise bias voltage should be applied to the Gate (corresponding to the ID set by the current source)
Several ways to do this
Bias
Basic gain cell in IC
NMOS Version:
PMOS Version:)||( 211 oomv rrgA −=
Bias point of CS amp with current mirror
||22
2
tpSGOV
GDDSG
VVVVVV−=
−=
222 2 )/('
21
OVVLWkI pD =
222
111
111
//
/2
DAo
DAo
OVDm
IVrIVr
VIg
===
2/1
1
11
21
)/('2
=
=
LWkI V
II
n
DOV
DD
Ignore Channel Width Modulation,o Fast and relatively accurate
method to find gm1 , ro1 and ro2o Cannot find VDS1 and VDS2
Bias point of CS amp with current mirror
Include Channel Width Modulation,o Lengthy Analysiso Gives VDS1 and VDS2o See S&S Example 7.2 (pp500-504)o Can gain insight with load-line analysis
iD2
vDS2
Bias point of CS amp with current mirror
12 DSSDDD vvV +=
Setting Vss = 0 (For simplicity), the load line (or load curve!) equation for Q1 is (note iD1 = iD2)
Biasing CS amp with current mirror allows a very large RD without increasing VDD
Q2 in triodeQ2 in saturation
Load line for a discrete resistor of value ro2
Needed VDD
Biasing a Source Follower in ICs
Current mirror Bias works fine! Small signal OK
Common-Drain (Source Follower) stages are biased with current mirror in the source circuit (as above)
Common-Gate stages are biased with current mirror in the drain circuit similar to CS amplifier.
PMOS version of Basic gain cell in IC
NMOS CS Amp PMOS CS Amp NMOS CD Amp PMOS CD Amp
Implementation of CS and Follower configurations on IC
Cascode Amplifiers and Current Mirrors
Cascode amplifier is a two-stage, CS-CG configuration
Cascode Configuration
CG stage
CS stage
signalbias
Cascode amplifier is a two-stage, CS-CG configuration
Cascode Configuration
CG stage
CS stage
Small Signal Model
Small Signal Model configured as two-stage amplifier
Open-Loop gain of a Cascode amplifier
122 )1( vrgv omo ⋅+=⇒
22112211 )1( omomomomi
ovo rgrgrgrg
vvA ⋅⋅⋅−≈⋅+⋅⋅−==
Node Voltage Method:
0122
1 =⋅−− vg
rvv
mo
oNode vo:
0011
1 =+⋅+ imo
vgrv
Node v1: iom vrgv 111 ⋅−=⇒
By KCL around Q2
Open Loop Gain (RL →∞, io = 0):
Output Resistance of a Cascode amplifier
1122 )1( oomoo rrgrR +⋅+=
RRgr mo ++ )1(
21221 oomooo rrgrrR ++=
Exercise: Compute Ro from the small signal circuit of the previous slide(Attach a voltage source vx to the output and compute ix, see S&S pp 509-510)
R
Amplifier models*Voltage Amplifier
Current Amplifier
Transconductance Amplifier
0for == oivoo ivAv
Avo : Open-Loop voltage gain
0for == oimo vvGi
Gm : Short-circuit transconductance
0for == oiiso viAi
Ais : Short-circuit current gain
Ideal Amplifier
Ri →∞Ro = 0
Ri →∞Ro →∞
Ri = 0 Ro →∞
* See S&S pp 26-27
Amplifier modelsVoltage Amplifier
Current Amplifier
Transconductance Amplifier
isiovo
imis
omvo
ARRARGARGA
)/(===
From the point of view of circuit analysis: amplifier models are identical (The output stages are
Thevenin/Norton Equivalent)
omvo
oimivoo
RGARvGvAvi
====
0For 0
Avo , Ais , and Gm are related to each other
Amplifier models*Voltage Amplifier
Transconductance Amplifier
0for == oivoo ivAv
0for == oimo vvGi
Alternate method to compute Avo:1. Set RL = 0 (short output)2. Compute Gm = io/vi3. Avo = Gm Ro
omvo RGA =
Example: CS amplifier gain from Gm
gsmo vgi ⋅−=
oo rR =
omomvo rgRGA −==
gsmimo vGvGi ==
gsmgsm vgvG −=
mm gG −=
CS Amplifier
Alternate method to compute Avo:1. Set RL = 0 (short output)2. Compute Gm = io/vi3. Avo = Gm Ro
Short circuit
Transconductance Amplifier
Gm = − gm because current source is flipped
0
Cascode amplifier gain from Gm
1
11
1
111
oim
ogsmo r
vvgrvvgi −⋅−=−⋅−=
21221
2211 ) 1(
oomoo
omom
i
om rrgrr
rgrgviG
+++
−==
21221 oomooo rrgrrR ++=22112211 )1( omomomomomvo rgrgrgrgRGA −≈+−==
121 and vvvv gsigs −==
Node equation at v1
imoooo
moo
immoo
ogsmgsm
o
vgrrrr
grrv
vgvgrr
rvvgvg
rv
22121
1211
11221
2
12211
1
1
11
0
++−=
−=
++
=+−+
KCL at D1
Insight into operation of Cascode amplifier
For simplicity assume ro1 = ro2 = ro and gm1 = gm2 = gm
CG section has kept Gm the same (i.e., since Gm = io/vi , same current is passed through) but has increased Ro substantially resulting in a large increase in overall open-loop voltage gain!
CG section acted as a current buffer!
Cascode amplifier needs a large load!
mom
omom
oomoo
omomm g
rgrgrg
rrgrrrgrgG −=−≈
+++
−= 221221
2211 )() 1.(
221221 )2( omomooomooo rgrgrrrgrrR ≈+=++=Cascode amplifier:
oomm rRgG =−= and 1CS amplifier (1st
stage of cascode):
Distribution of the gain in a Cascode Amp.
)||( 222 Lomv RrgA =
22222
221 1
1 om
L
mom
LoiL rg
Rgrg
RrRR +≈+
+==
)||( 2111 iomv RrgA −=
21 vvv AAA =
CG stages “reduces” the load seen by the CS stage by gm2ro2
CG StageCS Stage
Cascode Amplifier needs a large load
)||( 222 Lomv RrgA =22222
221 1
1 om
L
mom
LoiL rg
Rgrg
RrRR +≈+
+==)||( 2111 iomv RrgA −=
For simplicity assume ro1 = ro2 = ro and gm1 = gm2 = gm
∞ ∞ − gmro gmro − (gmro)2
(gmro) ro = Ro ro − 0.5gmro gmro − 0.5(gmro)2
ro 2/gm − 2 0.5 gmro − gmro
RL Ri2 = RL1 Av1(CS) Av2 (CG) Av= Av1 Av2
Max. Gain
Same gainas a CS Amp.
PracticalGain
Cascode amplifier is a two-stage, CS-CG configuration
Cascode Configuration
CG stage
CS stage
Small Signal Model
Small Signal Model configured as two-stage amplifier
Cascode Amplifier needs a large load
)||( 222 Lomv RrgA =22222
221 1
1 om
L
mom
LoiL rg
Rgrg
RrRR +≈+
+==)||( 2111 iomv RrgA −=
For simplicity assume ro1 = ro2 = ro and gm1 = gm2 = gm
∞ ∞ − gmro gmro − (gmro)2
(gmro) ro = Ro ro − 0.5gmro gmro − 0.5(gmro)2
ro 2/gm − 2 0.5 gmro − gmro
RL Ri2 = RL1 Av1(CS) Av2 (CG) Av= Av1 Av2
Max. Gain
Same gainas a CS Amp.
PracticalGain
Cascode amplifier needs a large load to get a high gain
RL = ro3
Av ≈ − gmro
Gain did not increase compared to a CS amplifier.
This is still a useful circuit because of its high gain-bandwidth (we see this later).
To get a high gain, Av = − 0.5(gmro)2 , we need to increase the small-signal resistance of the current mirror to ≈ (gmro) roo Cascode current mirror
Current Mirror
Cascode
Cascode Current mirror Identical MOS: Same k’n and Vt ,
and
Usually: (W/L)1 = (W/L)3 and (W/L)2 = (W/L)4
1
2
3
4
)/()/(
)/()/(
LWLW
LWLW
=
Q1 and Q3 are always in saturation Q2 and Q4 have to be in saturation
for current mirror to work VDS2 > VGS – Vt
VDS4 > VGS – Vt
Straight forward to show
refo ILWLWI
1
2
)/()/(
=
Exercise: For VSS = 0, show that a single current mirror (no cascoding) works only if VD2 > VOV and a cascode current mirror requires VD4 > Vt + 2VOV
Small signal resistance of a cascode current mirror is quite large
Equivalentcircuit
Small-signalcircuit
2244 )1( oomoo rrgrR +⋅+=
Cascode amplifier with a cascode current mirror
Cascodeamplifier
Cascodecurrent mirror
Signal
Bias
Cascode amplifier with a cascode current mirror
A high gain, Av ≈ − 0.5(gmro)2 , high gain-bandwidth circuit.
Draw-back: Low voltage headroom because 4 MOS should be in active for a given VDD
Cascodeamplifier
Cascodecurrent mirror
4433 )1( oomo rrgr +⋅+
Folded Cascode increases voltage overhead
PMOS CG stageNMOS CS stageBiased with I1 – I2
Exercise: Draw the small-signal circuit of a folded cascode and show that it is exactly the same as a regular cascode.