2-Stage Opamp Design & Modeling: ESE 568 Lecture

1
ESE 568: Mixed Signal Design and
Modeling
Lec 6: September 19th, 2018
Basic 2-stage Opamp (con’t) and Advanced
Opamp Design
Penn ESE 568 Fall 2018 – Khanna adapted from Perrot
CPPSim Lecture notes
Basic 2-stage Opamp
Basic 2-Stage Opamp
! This is a common “workhorse” opamp for
medium!performance!applications
" Relatively simple structure with reasonable performance!
3 Penn ESE 568 Fall 2018 - Khanna
Basic 2-Stage Opamp
! Key issue: two-stages lead to two poles that are
relatively close to each other
" This leads to very poor phase margin
! Inclusion of a compensation capacitor across
the!second stage leads!to pole splitting such that
stable!performance can be achieved
" A compensation resistor is also desirable to help!eliminate
the impact of a!RHP zero that occurs due
to!compensation
4 Penn ESE 568 Fall 2018 - Khanna
2-Stage Opamp Frequency Response
5 Penn ESE 568 Fall 2018 - Khanna
Key Specifications of Opamps (Open Loop)
! DC small signal gain
! Unity gain frequency
! Dominant pole frequency
! Parasitic pole frequencies
6 Penn ESE 568 Fall 2018 - Khanna

2
2-Stage Opamp Frequency Response
7 Penn ESE 568 Fall 2018 - Khanna
DC gain
Dominant pole
Unity-gain frequency
Parasitic pole
2-Stage Opamp Frequency Response
8 Penn ESE 568 Fall 2018 - Khanna
Dominant Pole
ω
0=gm1
CC
Unity-gain frequency
DC gain
Parasitic pole
Key Specifications of Opamps (Closed Loop)
! Offset voltage
! Settling time (closed loop bandwidth)
! Common-Mode Rejection Ratio (CMRR)
! Power Supply Rejection Ratio (PSRR)
! Equivalent Input-Referred Noise
9 Penn ESE 568 Fall 2018 - Khanna
2-Stage Opamp
10 Penn ESE 568 Fall 2018 - Khanna
! Settling Time/Slew Rate
2-Stage Opamp – Slew Rate
11 Penn ESE 568 Fall 2018 - Khanna
2-Stage Opamp
12 Penn ESE 568 Fall 2018 - Khanna
! Settling Time/Slew Rate
SR ≡dvout
dt max
=
ICCmax
CC
=ID5
CC

3
Finite Slew Rate Effect
! Ex. Unity-gain Follower
13 Penn ESE 568 Fall 2018 - Khanna
vI=Asin( ω t)
dvo
dt MAX
=A ω
Unity Gain Freq and Slew Rate
! Relationship between unity gain frequency and slew
rate:
14 Penn ESE 568 Fall 2018 - Khanna
ω
0=gm1
CC
SR =ID5
CC
Unity Gain Freq and Slew Rate
! Relationship between unity gain frequency and slew
rate:
! For 45° phase margin:
15 Penn ESE 568 Fall 2018 - Khanna
ω
0=gm1
CC
SR =ID5
CC
SR =ID5
gm1
ω
0
ω
0=p2
SR =ID5
gm1
p2
p2≈ − gm7CC
C1C2+C1CC+CCC2
≈−gm7
C2
2-Stage Opamp Offset: Systematic
16 Penn ESE 568 Fall 2018 - Khanna
2-Stage Opamp Offset: Systematic
17 Penn ESE 568 Fall 2018 - Khanna
2-Stage Opamp Offset: Random
18 Penn ESE 568 Fall 2018 - Khanna
VOS =ΔVt(1−2)
+ΔVt(3−4)
gm3
gm1
#
$
%&
'
(
+(VGS −Vt)(1−2)
2
−Δ W
L(1−2 )
W
L(1−2 )
−
ΔW
L(3−4)
W
L(3−4)
#
$
%
%
%
%
&
'
(
(
(
(

4
2-Stage Opamp Offset: Random
19 Penn ESE 568 Fall 2018 - Khanna
VOS =ΔVt(1−2)
+ΔVt( 3−4)
gm3
gm1
#
$
%&
'
(
+(VGS −Vt)(1−2)
2
−Δ W
L(1−2 )
W
L(1−2 )
−
ΔW
L(3−4)
W
L(3−4)
#
$
%
%
%
%
&
'
(
(
(
(
Minimize by making
gm3,4<gm1,2
Minimize by operating
input transistors at small
Vgs-Vt
2-Stage Opamp CMRR
20 Penn ESE 568 Fall 2018 - Khanna
2-Stage Opamp CMRR
21 Penn ESE 568 Fall 2018 - Khanna
2-Stage Opamp PSRR+
22 Penn ESE 568 Fall 2018 - Khanna
2-Stage Opamp PSRR+
23 Penn ESE 568 Fall 2018 - Khanna
2-Stage Opamp PSRR-
24 Penn ESE 568 Fall 2018 - Khanna

5
2-Stage Opamp PSRR-
25 Penn ESE 568 Fall 2018 - Khanna
@ high frequencies M6 looks diode connected
2-Stage Opamp Noise Analysis
! Each opamp stage will contribute noise
" Typically the spectral density of the noise will be of the same order at
each stage
26 Penn ESE 568 Fall 2018 - Khanna
2-Stage Opamp Noise Analysis
! Each opamp stage will contribute noise
" Typically the spectral density of the noise will be of the same order at
each stage
! Input referral of the noise reveals that the second!stage noise
will!have much less impact than the first!stage noise
" Input-referred noise calculations of an opamp need only!focus on the
first!stage
27 Penn ESE 568 Fall 2018 - Khanna
Noise Sources
! Shot Noise
" Discrete random event of charge jumping potential
barrier (i.e PN junction)
! Thermal Noise
" Random thermal motion of electrons
! Flicker Noise: 1/F Noise
" Usually due to impurities causing traps in material which
capture and emit carriers randomly
28 Penn ESE 568 Fall 2018 - Khanna
MOSFET Noise Model
29 Penn ESE 568 Fall 2018 - Khanna
! Flicker noise as voltage on the gate
! Thermal noise as current in the channel
MOSFET Noise Model
30 Penn ESE 568 Fall 2018 - Khanna
! Flicker noise as voltage on the gate
! Thermal noise as current in the channel