6. Cascode Amplifiers and
Cascode Current Mirrors
Sedra & Smith Sec. 7 (MOS portion)
(S&S 5th Ed: Sec. 6 MOS portion & ignore frequency
response)
ECE 102, Fall 2012, F. Najmabadi
Cascode amplifier
is a popular building block of ICs
Cascode Configuration
Signal circuit: Current source
becomes an open circuit
CG stage
signal
CS stage
Cascode amplifier is a two-stage, CS-CG configuration
F. Najmabadi, ECE102, Fall 2012 (2/17)
bias
I D1 = I D 2
Small Signal Model of a Cascode Amplifier
CG stage
Small Signal Model
CS stage
 Lengthy analysis to find Av (and a complicated equation). Simpler to compute open-loop gain (Avo)
and Ro.
 Text book introduces Gm method to find Avo (See S&S Sec. 1)
 Here will find Avo directly from the small signal model.
 However, the solution of and insight into Cascode amplifiers are best obtained using fundamental
MOS configurations!
Note that Avo and Ro calculated here are meant to find Av and guide the choice of the
active load. Avo and Ro should be re-calculated for a practical circuit (see slides 14 & 15)
F. Najmabadi, ECE102, Fall 2012 (3/17)
Open-Loop gain of a Cascode amplifier
(using small signal model)
Open Loop Gain
(R’L → ∞, io = 0):
By KCL around Q2
Node Voltage Method:
Node vo:
Node v1:
vo − v1
− g m 2 v1 = 0
ro 2
v1
+ g m1vi + 0 = 0
ro1
Avo =
F. Najmabadi, ECE102, Fall 2012 (4/17)
⇒ vo = (1 + g m 2 ro 2 ) v1
⇒ v1 = − g m1ro1 vi
vo
= − g m1ro1 × (1 + g m 2 ro 2 ) ≈ − g m1ro1 g m 2 ro 2
vi
Output Resistance of a Cascode amplifier
(using small signal model)
Set vi = 0, attach a voltage source vx ,
compute ix, Ro = vx / ix
vi = vgs1 = 0 → gm1 vgs1 current source becomes open circuit
By KCL around Q2
KVL : vgs 2 = −ix ro1
KCL : i2 = ix − g m 2 vgs 2 = ix + ix g m 2 ro1 = ix (1 + g m 2 ro1 )
KVL : vx = i2 ro 2 + ix ro1 = ix (1 + g m 2 ro1 )ro 2 + ix ro1
vx = ix [(1 + g m 2 ro1 )ro 2 + ro1 ]
Ro =
vx
= ro1 + ro 2 + g m 2 ro1 ro 2
ix
Note: Av = Avo ×
F. Najmabadi, ECE102, Fall 2012 (5/17)
RL′ + Ro
RL′
Gain of a Cascode Amplifier
(using MOS Fundamental Configurations)
Cascode (signal circuit)
CG stages “reduces” the load
seen by the CS stage by gm2ro2
CG stage
CS stage
Av 2 = vo / v1 ≈ g m 2 (ro 2 || RL′ )
Av1 = v1 / vi = − g m1 (ro1 || Ri 2 )
RL1 = Ri 2 =
ro 2 + RL′
1 + g m 2 ro 2
Av = vo / vi = Av1 Av 2 = − g m1 g m 2 (ro1 || Ri 2 ) (ro 2 || RL′ )
ro 2 + RL′
= ∞ → Avo = − g m1ro1 g m 2 ro 2
Note: Open Loop Gain: (R’L → ∞) RL1 = Ri 2 =
1 + g m 2 ro 2
F. Najmabadi, ECE102, Fall 2012 (6/17-)
Output Resistance of a Cascode amplifier
(from Elementary R forms)
= ro (1 + g m R ) + R
R
Ro = ro 2 (1 + g m 2 ro1 ) + ro1
Ro = ro1 + ro 2 + g m 2 ro1 ro 2
Ro = ro 2 (1 + g m 2 ro1 ) + ro1
Ro ≈ g m 2 ro 2 ro1 + ro1 = ro1 (1 + g m 2 ro 2 )
Ro ≈ g m 2 ro1 ro 2
F. Najmabadi, ECE102, Fall 2012 (7/17)
Cascode Amplifier needs a large load
Av 2 = g m 2 (ro 2 || RL′ )
RL1 = Ri 2 =
ro 2 + RL′
1 + g m 2 ro 2
Av1 = − g m1 (ro1 || Ri 2 )
Ro ≈ g m 2 ro1 ro 2
For simplicity assume ro1 = ro2 = ro and gm1 = gm2 = gm
R’L
Av2(CG)
Ri2 = RL1
Av1 (CS)
Av= Av1 Av2
∞
gmro
∞
− gmro
− (gmro)2
Max. Gain
(gmro) ro = Ro
gmro
ro
− 0.5gmro
− 0.5(gmro)2
Practical
Gain
ro
0.5 gmro
2/gm
−2
− gmro
Same gain
as a single
CS Amp.
 For comparison, a two-stage CS-amplifier (CS-CS) has a gain of 0.5 (gmro)2 for
R’L = ro and a gain of (gmro)2 for R’L = gmro2.
o Cascode amplifier needs a large load (R’L = gmro2 ).
F. Najmabadi, ECE102, Fall 2012 (8/17)
Cascode amplifier needs a large load to
get a high gain
Current
Mirror
Cascode
R’L = 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
F. Najmabadi, ECE102, Fall 2012 (9/17)
Cascode Current mirror
 Identical MOS: Same µCox and Vt , &
o vGS1 = vGS2 & vGS3 = vGS4
(W / L) 4 (W / L) 2
=
(W / L) 3 (W / L)1
 Usually: (W/L)1 = (W/L)3 and (W/L)2 = (W/L)4
o vGS1 = vGS2 = vGS3 = vGS4 = vGS
 Q1 and Q3 are always in saturation
 Q2 and Q4 both have to be in saturation for current mirror to
work
o VDS2 > VGS – Vt
o VDS4 > VGS – Vt
 Straight forward to show
Io =
(W / L) 2
I ref
(W / L)1
Exercise: Show that a single current mirror (no cascoding) works only if VD2 > VOV −VSS
and a cascode current mirror requires VD4 > 2VOV −VSS
F. Najmabadi, ECE102, Fall 2012 (10/17)
Small signal resistance of a cascode
current mirror is quite large
R = ro 4 (1 + g m 4 ro 2 ) + ro 2
R
Transistor numbering is different in different circuits
Be careful in applying formulas!
It is best to use elementary R forms to find R instead of formula above.
F. Najmabadi, ECE102, Fall 2012 (11/17)
PMOS cascode current mirror is similar to
NMOS version
NMOS Cascode current mirror
F. Najmabadi, ECE102, Fall 2012 (12/17)
PMOS Cascode current mirror
Cascode amplifier with a
cascode current mirror/active load
Bias
Cascode
current mirror
Signal
Cascode
amplifier
I D1 = I D 2 = I D 3 = I D 4
F. Najmabadi, ECE102, Fall 2012 (13/17)
Exercise: Draw the circuit for a PMOS cascode with a cascode current
mirror (cascode current mirror would be made of NMOS).
Gain of a Cascode amplifier with a
cascode current mirror/active load
Value for the same
gm and ro
Q2 (CG Amp)
Av 2 = vo / v1 ≈ g m 2 (ro 2 || RL′ ) ≈ g m 2 ro 2
Cascode
current mirror
RL1 = Ri 2 =
ro 3 (1 + g m 3ro 4 ) + ro 4
Cascode
amplifier
≈
Av 2 ≈ g m ro
ro 2 + ro 3 (1 + g m 3 ro 4 ) + ro 4
1 + g m 2 ro 2
g m 3 ro 3 ro 4
g m 2 ro 2
RL1 = Ri 2 ≈ ro
Q1 (CS Amp)
v1
Ri 2
Av1 = v1 / vi = − g m1 (ro1 ||
Avo = Av1 Av 2 = −
F. Najmabadi, ECE102, Fall 2012 (14/17)
g m 3 ro 3 ro 4
)
g m 2 ro 2
g m1 g m 2 g m 3 ro1ro 2 ro 3 ro 4
g m 2 ro1ro 2 + g m 3 ro 3 ro 4
Av1 = −0.5 g m ro
Avo = −0.5 ( g m ro ) 2
Output Resistance of a Cascode amplifier
with a cascode current mirror/active load
Value for the
same gm and ro
R1
R1 = ro 3 (1 + g m 3 ro 4 ) + ro 4
R 1 ≈ g m ro2
R 2 = ro 2 (1 + g m 2 ro1 ) + ro1
R 2 ≈ g m ro2
R2
Ro = R 1 || R 2
F. Najmabadi, ECE102, Fall 2012 (15/17)
Ro = 0.5 g m ro2
Why Cascode Amplifiers are popular?
Cascode Amp.
Avo = −0.5 ( g m ro ) 2
Ro = 0.5 g m ro2
2-stage CS Amp.
Drawbacks:
 While Avo are similar, Cascode has a very
Ro (MΩ level).
o should be followed with a CS or CD
stage (infinite load for cascode)
o BJT cascodes are not useful.
Avo = +0.25( g m ro ) 2
Ro = r o
 Low voltage headroom (VDD across 4 MOS)
o Folded cascodes solve this.
Benefits:
 Much better high-frequency response
(high gain-bandwidth).*
 Simpler biasing.
F. Najmabadi, ECE102, Fall 2012 (16/17)
* We will see this later in our discussion of frequency response.
Folded Cascode increases voltage overhead*
Bias
Signal
CG stage
I2
I1 – I2
I2
I1 – I2
CS stage
NMOS CS stage
Biased with I1 – I2
PMOS CG stage
Biased with I2
F. Najmabadi, ECE102, Fall 2012 (17/17)
* Folded cascode only helps the voltage overhead issue
for difference amplifiers (see S&S pages 999-1000)