6. Cascode Amplifiers and Cascode Current Mirrors

ECE 102, Fall 2012, F. Najmabadi

Sedra & Smith Sec. 7 (MOS portion)

(S&S 5th Ed: Sec. 6 MOS portion & ignore frequency response)

Cascode amplifier is a popular building block of ICs

F. Najmabadi, ECE102, Fall 2012 (2/17)

Cascode amplifier is a two-stage, CS-CG configuration

CG stage

CS stage

signal bias

Cascode Configuration

21 DD II =

Signal circuit: Current source becomes an open circuit

Small Signal Model of a Cascode Amplifier

F. Najmabadi, ECE102, Fall 2012 (3/17)

CG stage

CS stage

Small Signal Model

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)

Open-Loop gain of a Cascode amplifier (using small signal model)

F. Najmabadi, ECE102, Fall 2012 (4/17)

122 )1( vrgv omo +=⇒

)1( 22112211 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 (R’L → ∞, io = 0):

Output Resistance of a Cascode amplifier (using small signal model)

F. Najmabadi, ECE102, Fall 2012 (5/17)

21221 oomoox

xo rrgrr

ivR ++==

])1[( )1( : KVL

)1( : KCL

: KVL

1212

1212122

1212222

12

ooomxx

oxoomxoxox

omxomxxgsmx

oxgs

rrrgivrirrgiririv

rgirgiivgiiriv

++=++=+=

+=+=−=

−=

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

L

oLvov R

RRAA′

+′×=Note:

Gain of a Cascode Amplifier (using MOS Fundamental Configurations)

F. Najmabadi, ECE102, Fall 2012 (6/17-)

)||(/ 2212 Lomov RrgvvA ′≈=

22

221 1

om

LoiL rg

RrRR+

′+==

)||(/ 21111 iomiv RrgvvA −==

)||( )||( / 2212121 Loiommvviov RrRrggAAvvA ′−===

CG stages “reduces” the load seen by the CS stage by gm2ro2

Cascode (signal circuit) CG stage CS stage

Note: Open Loop Gain: (R’L → ∞) 221122

221

1

omomvoom

LoiL rgrgA

rgRrRR −=→∞=

+′+

==

Output Resistance of a Cascode amplifier (from Elementary R forms)

F. Najmabadi, ECE102, Fall 2012 (7/17)

1122 )1( oomoo rrgrR ++=

RRgr mo ++= )1(

21221 oomooo rrgrrR ++=

R

)1( )1(

2211122

1122

omoooomo

oomoo

rgrrrrgRrrgrR

+=+≈++=

212 oomo rrgR ≈

Cascode Amplifier needs a large load

F. Najmabadi, ECE102, Fall 2012 (8/17)

)||( 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

R’L 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 R’L = ro and a gain of (gmro)2 for R’L = gmro

2.

o Cascode amplifier needs a large load (R’L = gmro2 ).

Cascode amplifier needs a large load to get a high gain

F. Najmabadi, ECE102, Fall 2012 (9/17)

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

Current Mirror

Cascode

refo ILWLWI

1

2

)/()/(

=

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

Cascode Current mirror

F. Najmabadi, ECE102, Fall 2012 (10/17)

Identical MOS: Same µCox and Vt , &

o vGS1 = vGS2 & vGS3 = vGS4 Usually: (W/L)1 = (W/L)3 and (W/L)2 = (W/L)4

o vGS1 = vGS2 = vGS3 = vGS4 = vGS

1

2

3

4

)/()/(

)/()/(

LWLW

LWLW

=

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

F. Najmabadi, ECE102, Fall 2012 (11/17)

)1( 2244 oomo rrgrR ++=

R

Transistor numbering is different in different circuits Be careful in applying formulas! It is best to use elementary R forms to find instead of formula above. R

PMOS cascode current mirror is similar to NMOS version

F. Najmabadi, ECE102, Fall 2012 (12/17)

NMOS Cascode current mirror PMOS Cascode current mirror

Cascode amplifier with a cascode current mirror/active load

F. Najmabadi, ECE102, Fall 2012 (13/17)

Signal

Bias

Cascode current mirror

Cascode amplifier

4321 DDDD IIII ===

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

F. Najmabadi, ECE102, Fall 2012 (14/17)

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

oooommmvvvo rrgrrg

rrrrgggAAA+

−==

Value for the same gm and ro

omv rgA ≈2

oiL rRR ≈= 21

omv rgA 5.01 −=

2)( 5.0 omvo rgA −=

1v2iR

Q2 (CG Amp)

4433 )1( oomo rrgr ++

Q1 (CS Amp)

Output Resistance of a Cascode amplifier with a cascode current mirror/active load

F. Najmabadi, ECE102, Fall 2012 (15/17)

44331 )1( oomo rrgrR ++=

2 ||1 RRRo =

Value for the same gm and ro

21 omrgR ≈

25.0 omo rgR =

1R11222 )1( oomo rrgrR ++=

22 omrgR ≈

2R

Why Cascode Amplifiers are popular?

F. Najmabadi, ECE102, Fall 2012 (16/17)

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.

Low voltage headroom (VDD across 4 MOS)

o Folded cascodes solve this.

Benefits:

Much better high-frequency response (high gain-bandwidth).*

Simpler biasing.

2

2

5.0

)( 5.0

omo

omvo

rgRrgA

=

−=

Cascode Amp.

oo

omvo

rRrgA

=+= 2)(25.0

2-stage CS Amp.

* We will see this later in our discussion of frequency response.

Folded Cascode increases voltage overhead*

F. Najmabadi, ECE102, Fall 2012 (17/17)

Bias

I2

I1 – I2 I2

I1 – I2

NMOS CS stage Biased with I1 – I2

Signal

CG stage

CS stage

PMOS CG stage Biased with I2

* Folded cascode only helps the voltage overhead issue for difference amplifiers (see S&S pages 999-1000)