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Cascode amplifier is a popular building block of ICs
Cascode amplifier is a two-stage, CS-CG configuration
CG stage
CS stage
signal bias
Cascode Configuration
21 DD II =
Small Signal Model of a Cascode Amplifier
Cascode Configuration
CG stage
CS stage
Small Signal Model
* Text book solves the Cascode amplifier using the small signal model. Text book introduces Gm method to simplify the analysis. We will find Avo from small signal model. However, the solution and insight into Cascode amplifiers can be easily obtained using fundamental MOS configurations!
Open-Loop gain of a Cascode amplifier (using NMOS small signal model)
122 )1( vrgv omo ⋅+=⇒
)1( 22112211 omomomomi
ovo rgrgrgrg
vvA ⋅⋅⋅−≈⋅+⋅⋅−==
Node Voltage Method:
0122
1 =⋅−− vg
rvv
mo
oNode vo:
0011
1 =+⋅+ imo
vgrvNode v1:
iom vrgv 111 ⋅−=⇒
By KCL around Q2
Open Loop Gain (RL → ∞, io = 0):
Exercise: Compute Ro from the small signal circuit (Attach a voltage source vx to the output and compute ix, see S&S pp 509-510)
Distribution of the gain in a Cascode Amp.
)||(/ 2212 Lomov RrgvvA ≈=
22
221 1 om
LoiL rg
RrRR+
+==
)||(/ 21111 iomiv RrgvvA −==
/ 21 vviov AAvvA ==
CG stages “reduces” the load seen by the CS stage by gm2ro2
Cascode Configuration
CG stage
CS stage
Open Loop Gain: (RL → ∞)
2211111
22
221222
, 1
,
omomvoomv
om
LoiLomv
rgrgArgArg
RrRRrgA
−=−=
∞=+
+===
Output Resistance of a Cascode amplifier
1122 )1( oomoo rrgrR +⋅+=
RRgr mo ++= )1(
21221 oomooo rrgrrR ++=
R
Cascode Amplifier needs a large load
)||( 222 Lomv RrgA =22
221 1 om
LoiL rg
RrRR+
+== )||( 2111 iomv RrgA −=
For simplicity assume ro1 = ro2 = ro and gm1 = gm2 = gm
∞ gmro ∞ − gmro − (gmro)2
(gmro) ro = Ro gmro ro − 0.5gmro − 0.5(gmro)2
ro 0.5 gmro 2/gm − 2 − gmro
RL Av2(CG) Ri2 = RL1 Av1 (CS) Av= Av1 Av2
Max. Gain
Same gain as a single CS Amp.
Practical Gain
212 oomo rrgR ≈
For comparison, a two-stage CS-amplifier (CS-CS) has a gain of 0.5 (gmro)2 for RL = ro and a gain of (gmro)2 for RL = gmro
2. o Cascode amplifier needs a large load (RL = gmro
2 ). o Cascode amplifiers are popular because of their large gain-bandwidth
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) ro
o Cascode current mirror
Current Mirror
Cascode
refo ILWLWI
1
2
)/()/(
=
Cascode Current mirror Identical MOS: Same µCox and Vt , and
Usually: (W/L)1 = (W/L)3 and (W/L)2 = (W/L)4
o vGS1 = vGS3 = vGS
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
o VDS2 > VGS – Vt
o VDS4 > VGS – Vt
Straight forward to show Exercise: Show that a single current mirror (no cascoding) works only if VD2 > VOV −VSS
and a cascode current mirror requires VD4 > 2VOV −VSS
Small signal resistance of a cascode current mirror is quite large
Equivalent circuit
Small-signal circuit
)1( 2244 oomoo rrgrR +⋅+=
Cascode amplifier with a cascode current mirror/active load
Signal
Bias
Cascode current mirror
Cascode amplifier
4321 DDDD IIII ===
4433 )1( oomo rrgr +⋅+
Gain of a Cascode amplifier with a cascode current mirror/active load
A high gain, Av ≈ − 0.5(gmro)2 , high gain-bandwidth circuit.
Draw-back: Low voltage headroom because 4 MOS should be in saturation for a given VDD
Cascode amplifier
Cascode current mirror
222212 )||(/ omLomov rgRrgvvA ≈≈=
22
433
22
4433221
1 )1(
om
oom
om
oomooiL
rgrrg
rgrrgrrRR
≈
++⋅++
==
)||(/22
4331111
om
oomomiv rg
rrgrgvvA −==
433212
432132121
oomoom
oooommmvvv rrgrrg
rrrrgggAAA+
−==
Value for the same gm and ro
omv rgA ≈2
oiL rRR ≈= 21
omv rgA 5.01 −=
2)( 5.0 omv rgA −=