EECS 105 Fall 2003, Lecture 22
Lecture 22:
Multistage Amps
Prof. Niknejad
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Lecture Outline
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Department of EECS
Finish Current Mirrors
An Example Using Cascodes
Multistage Amps
Cascode Amplifier: Magic!
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
The Integrated “Current Mirror”
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High Res
Low Resis
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M1 and M2 have the same
VGS
If we neglect CLM (λ=0),
then the drain currents are
equal
Since λ is small, the
currents will nearly mirror
one another even if Vout is
not equal to VGS1
We say that the current IREF
is mirrored into iOUT
Notice that the mirror
works for small and large
signals!
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Current Mirror as Current Source
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The output current of M2 is only weakly dependent on
vOUT due to high output resistance of FET
M2 acts like a current source to the rest of the circuit
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Small-Signal Resistance of I-Source
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Improved Current Sources
Goal: increase roc
Approach: look at amplifier output resistance
results … to see topologies that boost resistance
Rout  ro
Looks like the output
impedance of a commonsource amplifier with source
degeneration
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Effect of Source Degeneration
vt  (it  g m vgs )ro  vRS
vgs  vRS
1
Req 
gm
vRS  it RS
vt  (it  gm RS it )ro  it RS
vt
Ro   1  g m RS  ro
it
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Equivalent resistance loading gate is dominated by
the diode resistance … assume this is a small
impedance
Output impedance is boosted by factor 1  gm RS 
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Cascode (or Stacked) Current Source
Insight: VGS2 = constant AND
VDS2 = constant
Small-Signal Resistance roc:
Ro  1  gm RS  ro
Ro  1  gm ro  ro
Ro  g m r02  ro
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Drawback of Cascode I-Source
Minimum output voltage to keep both transistors in
saturation: V
V
V
OUT , MIN
DS 4, MIN
DS 2, MIN
VDS 2, MIN  VGS 2  VT 0  VDSAT 2
iOUT
VD 4  VDSAT 2  VGS 4  VGS 2  VGS 4  VT 0
VOUT , MIN  VGS 2  VGS 4  VT 0
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vOUT
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Current Sinks and Sources
Sink: output current goes
to ground
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Source: output current comes
from voltage supply
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Current Mirrors
Idea: we only need one reference current to set up all the
current sources and sinks needed for a multistage amplifier.
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Multistage Amplifiers
Necessary to meet typical specifications for any of the 4 types
We have 2 flavors (NMOS, PMOS) of CS, CG, and CD and
the npn versions of CE, CB, and CC (for a BiCMOS
process)
What are the constraints?
1. Input/output resistance matching
1. DC coupling (no passive elements to block the signal)
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Summary of Cascaded Amplifiers
General goals:
1. Boost the gain parameter (except for buffers)
2. Optimize the input and output resistances
Rin
Voltage:
Current:
Transconductance:
Transresistance:
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0

0
Rout
0


0
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Start: Two-Stage Voltage Amplifier
• Use two-port models to explore whether the combination
“works”
CE2
CE1
CE1,2
Results of new 2-port: Rin = Rin1, Rout = Rout2
Av  Gm1  Rin 2 || Rout1    Gm2 Rout 2 
Av  Gm1Gm2  Rin 2 || Rout1  Rout 2 
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Add a Third Stage: CC
Goal: reduce the output resistance
(important spec. for a voltage amp)
CE2
CE1
CC3
Output resistance:
Rout 
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R
r || r
1
1
 S 
 o 2 oc 2
g m3 
g m3

University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Using CMOS Stages
CS2
CS1
CD3
Input resistance: 
Voltage gain (2-port parameter):
Av   gm1  ro1 || roc1   gm2  ro 2 || roc 2 
Output resistance:
Rout 
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1
g m  g mb
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Multistage Current Buffers
Are two cascaded common-base stages better than
one?
CB1
CB2
Input resistance: Rin = Rin1
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Two-Port Models
Rout  Rout 2  r02 1  g m 2 r 2 || RS 2  || roc2
Output impedance of stage #1 (large)
Rout  r02  gm2r 2  || roc 2   o ro 2  || roc 2
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Common-Gate 2nd Stage
Rout  Rout 2  r02 1  g m 2 RS 2  || roc2
Rout  Rout 2  r02 1  gm2ro1 || roc1  || roc 2
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Second Design Issue: DC Coupling
Constraint: large inductors and capacitors are not
available
Output of one stage is directly connected to the
input of the next stage  must consider DC
levels … why?
3.2V
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Alternative CG-CC Cascade
Use a PMOS CD Stage: DC level shifts upward
3.2V
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
CG Cascade: DC Biasing
Two stages can have different supply currents
Extreme case:
IBIAS2 = 0 A
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
CG Cascade: Sharing a Supply
First stage has no current
supply of its own  its output
resistance is modified
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
The Cascode Configuration
Common source / common gate
cascade is one version of a cascode
(all have shared supplies)
DC bias:
Two-port model: first stage
has no current supply of its own
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Cascode Two-Port Model
CS1*
CG2
Output resistance of first stage = Rout,CS *  R down,CS  ro1
Rout
roc 2 || (1  gm ro1 )ro 2
Gm  g m1
Rin  
Why is the cascode such an important configuration?
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Miller Capacitance of Input Stage
Find the Miller capacitance for Cgd1
Input resistance to
common-gate
second stage is low 
gain across
Cgd1 is small.
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Two-Port Model with Capacitors
Miller capacitance:
AvCgd 1
CM  (1  AvCgd1 )Cgd1
g m1
1
  g m1 (
|| ro1 )  
 1
gm2
gm2
CM  2C gd 1
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Generating Multiple DC Voltages
Stack-up diode-connected
MOSFETs or BJTs and
run a reference current
through them  pick off
voltages from gates or
bases as references
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Multistage Amplifier Design Examples
Start with basic two-stage transconductance
amplifier:
Why do this combination?
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Two-Stage Amplifier Topology
Direct DC connection: use NMOS then PMOS
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Current Supply Design
Assume that the reference is a
“sink” set by a resistor
Must mirror the reference
current and generate a sink for
iSUP 2
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Use Basic Current Supplies
Department of EECS
University of California, Berkeley
EECS 105 Fall 2003, Lecture 22
Prof. A. Niknejad
Complete Amplifier Topology
What’s missing? The device dimensions and the bias
voltage and reference resistor
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University of California, Berkeley