Transcript 607 Lect 12 LDO

ECEN 607(ESS)
Low Drop-Out Voltage Regulators
Analog and Mixed-Signal Center, Texas A&M University
1
Power Management
• Why do we need power management?
– Batteries discharge “almost” linearly with time.
– Circuits with reduced power supply that are time dependent
operate poorly. Optimal circuit performance can not be obtained.
– Mobile applications impose saving power as much as possible.
Thus, the sleep-mode and full-power mode must be carefully
controlled.
– What is the objective of a power converter?
• To provide a regulated output voltage
Voltage
Battery (i.e. Li-ion)
Regulated Voltage
Time
2
What are the conventional power converters?
– Low drop-out linear regulator (LDO)
– Switch-inductor regulator (switching regulators)
– Switch-capacitor regulator (charge pump)
Why do we need different Power Converters Types?
– Different applications
– Desired efficiency and output ripple
Can we combine them?
+
Battery
-
SR
LDO
VREGULATED
+
Battery
-
CP
LDO
VREGULATED
+
Battery
-
LDO
CP
VREGULATED
What is the purpose of combining several converters?
3
Linear Regulator: Principles
+
– Vo must be constant and
RC
RLOAD
VBAT
VO
R  R
C
LOAD
– VBAT is changing as a function of time
VO 
-
RLOAD
VBAT
RLOAD  RC
Thus in order to keep constant Vo, the value of the controlling resistor
RC yields:
V

V V 
V 
  R  

R  R  
 1  R  
V

 V

V 
BAT
C
BAT
LOAD
O
LOAD
O
LDO
LOAD
O
O
How can we automatically pick the value of RC such that Vo= Vdesired, regRC
voltage?
+
VC
VBAT
Feedback
Control
RLOAD
VO
-
4
How can we implement RC and the Feedback
Control?
ID
NMOS Transistor
PMOS Transistor
VGS
a
b
a
a
b
VC = VGS
ILOAD
VC = -VGS = VSG
Vdo = ILOADRC
VDO,n= VSAT+Vgs
b
VDO,p= VSD(SAT)
Can we implement RC as follows? For which applications?
RC1
RC2
a
RC1
b
VC
MN
RC2
a
b
MP
VC
MN and MP are transistors operating in the Ohmic region. Discuss the option5.
How the feedback control could be implemented?
VO
Error Amplifier
VO
R1
Error Amplifier
R1
VC,NMOS
VC,PMOS
R2
R2
VREF
VREF
• Remarks
– Make sure the closed loop is negative
– For an ideal op amp gain, the differential input is zero, i.e.
R
V
V
R R
2
O
REF
1
2
0
OR
V
O UT
V
REG
 R
 V  1 
 R
1
O
2

V

REF
– VREF is a Bandgap voltage which is also supplied by VBAT=VIN.
6
The efficiency is defined as:

P
V I

P
V I
OUT
OUT
IN
IN
LOAD

LOAD
V
V V

V
V
OUT
IN
IN
 1
DO
IN
V
V
DO
BAT
• Where VDO is the voltage drop across the pass transistor,
i.e. VDS
• The output error voltage (EVO) is defined as:
E 
VO
R
R R
C
C
100%
LOAD
OR
E 
VO
V
OUT  MAX
V
V
OUT  LOAD
100%
OUT  MAX
7
LDO Analysis
•
Let us analyze the basic LDO architecture. First, we will consider ideal
components, then the non-idealities are introduced together with the
accompanied design challenges to tackle
VIN
Error Amplifier
VIN = VBAT
Ref
VX
PMOS Pass Transistor
R1
VDIV
R2
Basic LDO Topology
rop
AEA( VDIV - VREF)
VIN
AEA
gm( Vx – ViN )
Vo
R1
Io
VDIV
Load (RL)
RL
R2
Small Signal Representation
1
1

1

1
1 


VO  
   VIN   g m   VDIV   g m AEA   g m AEAVREF
 R1

 rop RL R1 
 rop

1 1 V
VDIV     O  0
 R1 R2  R1
(1)
(2)
8
Solving the (1) and (2), Vo becomes:
Vin (1  APT )   V REF APT AEA 
rop
 [1  APT AEA  ]
RL
 g m rop ,   R2 /( R1  R2 ), and ( R1  R2 )  RL
Vo 
Where:
APT
Thus Vo can be expressed as:
Vo 
If
Vin APT 
V A A 
 REF PT EA
 (1  APT AEA )  (1  APT AEA )
T  APT AEA 
Vo yields:
Vo 
VinT / AEA
V T
 REF
 (1  T )  (1  T )
T is the open loop gain. Furthermore for T >>1
Vo 
Vin
V
 REF
AEA 

Observe that Vin is attenuated by AEA and Vref is not.
9
Line Regulation
The line regulation is a steady-state specification. It can be defined as:
LR 
Vo
APT
APT


Vin  (1  APT AEA ) 1  APT AEA
L 
R
V
1

V A
o
in
EA
For a practical case with non-idealities such as offset Op-Amp voltage Vos
and reference voltage error i.e. Vref ; the line regulator becomes:

Vo
R  V  Vos 
1


 1  1  REF
Vin AEA  R2 
Vin

Observe that designers should also minimize: Vos
and provide Vref to be independent of VBAT and temperature and process variations.
10
Note that Rc given in page 3 for a transistor can be expressed as:
RC 
 V  Vo
VDS
V
 RLoad DS  RLoad  BAT
I OUT
Vo
 Vo



In order to maintain the regulation the transistor must operate properly
NMOS case
Vin 
VDS 
VC 

ID  Io 
Exercise: Repeat the above case for a PMOS case
11
Load/Line Regulation
Let us assume the error amplifier is a transconductance amplifier of
value GEA and α is the current gain of the pass transistor i.e.
Io
Thus
Vo  I o Req  I o ( R1  R2 ) // RL 
Vo  I o RL
R1
Furthermore:
I o  G EAVDIV Req  G EA R2 /( R1  R2 )Vo
GEA
Vin
∆VDIV
Then, the load regulation can be expressed
as:

Vo
1  R1


 1
I o GEA  R2

Vo+∆Vo
R2
VREF
Or line regulation:

Vo
1  R1
1


 1
Vin GEA  R2
 RDS  RL
12
RL
RL
Efficiency Calculation
Example of efficiency: A 3.3V LDO with 3.7 V < Vin < 4.71V, 100mA < Io < 150mA
Io,q (maximum quiescent current) = 100 μA


I o max  Vout,nominal
( I o max  I o ,q )  Vin,max
150mA  3.3
 100  70%
(150mA  100A)  4.71
The output current can be represented as a pulse for simulation purposes
Io,max
OR
Io,min
Io,max
Io,min
t0
t1
t0 t1
t3 t4
13
LDO ESR Stability
One of the most challenging problems in designing LDO is the stability problems
due to the closed loop and the parasitic components associated with the pass
transistor and the error amplifier. In fact to compensate the loop stability a large
external capacitor is often connected at the output. i.e.
Vo
Z CL ( s) 
1  s / wL
sC L
Im
RESR
Re
CL
w L  1 / RESRC L
-wL
Where CL is of the order of μF with a small equivalent series resistor (RESR).
14
LDO Parameters 1
• Dropout voltage (Vdo); This is the difference between the minimum
voltage the input DC supply can attain and the regulated output
voltage.
•
Input rail range; This is the input supply voltage range that can be
regulated. The lower limit is dependent on the dropout voltage and
upper limit on the process capability.
•
Output current range; This is the output current handling capability
of the regulated output voltage. The minimum current limit is mainly
dependent on the stability requirements and the maximum limit
dependent on Safe Operating Area (SOA) of pass FET and also
maintaining output voltage in regulation.
•
Output capacitor range; This is the specified output capacitance the
regulator is expected to accommodate without going unstable for a
given load current range.
•
Output regulated voltage range; This is the output voltage variation
the regulator guarantees. When output voltage is in this range, it is
said to be in regulation.
•
Load regulation; This is the variation in output voltage as current moves from min to
max
15
LDO Parameters 2
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Line regulation; This the variation in output voltage as supply
voltage is varied from minimum to maximum.
PSR; Power Supply Rejection ( or ripple rejection) is a measure of the
ac coupling between the input supply voltage on the output voltage.
Load/Line transient regulation; This is a measure of the response speed
of the regulator when subjected to a fast load/Vsupply change.
Short circuit current limit; This is the current drawn when the
output voltage is short circuited to ground. The lower limit is
determined by the maximum regulated load current and the upper
limit is mainly determined by the SOA and specified requirements
Power Efficiency; This is the ratio of the output load power
consumption to input supply power. Linear regulators are not really
efficient especially at high input supply voltages.
Overshoot: It is important to minimized high transient voltages at start-up
and during load and line transients.
Thermal Shut down: This is needed to protect the part from damage
16
Conventional LDO: Modeling
Close Loop Schematic
Open Loop Transfer Function: TF  H1  H 2  H 3  H 4
VIN
Error Amplifier
VREF
PND1CGs
p
Rds
PD
H3 
Vout
B
A
1EF
m1
1
C
PND2
g R
R C s 1
H 
CGD
R1
D
CL
z
RL
1EH
R2
RESR
VTest
Loop Breaking Point for Stability Analysis
Open Loop Block Diagram
H2 
p
p
R A CGS
 g m3 R A
  AV  1CGD  s  1
 g mp RPAR RESRC L   s  RPAR 
RPAR  RESR C L  s  1
Av  g mp  R par
H4 
RPAR  Rds R1  R2 RL
R2
R2  R1
Rds 
1
I ds
RPAR : Output impedance
RL : Load resistance
RDS : Drain to source impedance of the pass transistor
R1 &R2 : Feedback Resistors
Vdropout  200mV  VDSSATPass  200mV
Vdropout : Minimum voltage drop across the input and output
terminalsof the LDO with shich the system is able to regulate.
VDSSATPass : Vdsat of the pass transistor
ID 
Note: The error amplifier is a two-stage amplifier without miller compensation
2I D
1
W 
W 
 p Cox  VDSSATPass2    
2
L
 L   p Cox  VDSSATPass2
W 
g  2  C  i
L
mp
p
ox
load
17
Error Amplifier AEA
R
OUT
Dominant pole
Cgate
R
01
Two stage amplifier without miller compensation
A g R g R
o
Notes:
1.
2.
m1
GBW 
01
m8
g R g
C
m1
o1
out
m8
gate
CGATE is connected to output node.
Miller Compensation is not required since the dominant pole
is at the output.
18
Matlab/Simulink Macromodel
Pass Transistor Dominant Pole / Compensation Zero
Transconductance
Non-dominat Pole
due to Pass Transistor
Gate Capacitance
Error Amplifier
Nondominant Pole
Feedback
Factor
Formulas and Component Values
K
R2
R1  R2
R1  420 K
R2  240 K
resr  5
C  10F
Cgd  30 pF
Vdsat  200 mV
Cgs  50 pF
R p  64k
iload  50 mA
Ra  7.36 M
C p  100 fF
  0.1
Gm3  1.35mA / V
o
Gm1  15.62 A / V
R 
DS
1
  i
load

 44e  3 
g  80e  6  
i
0
.
6
e

6


mp
load
RL 

Vout
iload
Vout  3.3V
19
Simulation Results From Simulink
z
Loop Gain and Phase
P
P
ND 2
ND 1
P
D
Loop Gain ~ 100dB
Fu ~ 2.7MHz
Phase boost due to Compensation Zero

1
 Z 
C R

L
ESR



PM ~ 90°
20
Open Loop Gain and Phase Under Load Variation
Notes:
1-Open Loop System
2- Load Variation (iload varies from 10mA to 50mA)
3- The load variation (iload) was simulated in Matlab using a “for loop”
21
Simulation Results From Matlab
Step Response
Vout varies from 0 to 3.3V
Vin varies from 0 to 3.5V
22
Power Supply Rejection
Vsupply

Problem:
 Low frequency and high frequency noise affects the operation of the highly
sensitive circuits
 External noise is mainly coupled through the supply lines
 A regulator (LDO) is mandatory with high PSR
23
Power Supply Rejection Existing Solutions
VIN

VIN
VIN
VVDD
IN
Current Solutions:
 RC filtering: Larger drop-out voltage, and larger power consumption
 Cascading of LDO: Larger area, power consumption, larger dropout voltage
 Combined RC filtering and cascading: Larger area and power
consumption, larger drop-out voltage and complexity
24
Enhancing PSR over a wide frequency range
Proposed Topology
•
The NMOS cascode, MNC, shields
the entire regulator from fluctuations
in the power supply.
•
MNC gate needs to be biased at a
voltage above the supply using a
charge pump.
•
MNC acts as a voltage follower for
noise at its gate, it is critical to
shield the gate of MNC from supply
fluctuations using an RC filter to
shunt supply ripple to ground.
G. A. Rincon-Mora, V. Gupta, “A 5mA 0.6mA CMOS Miller-Compensated LDO Regulator with -27dB Worst-Case
25
Power-Supply Rejection Using 60pF of On-Chip Capacitance ,” ISSCC, feb. 2007.
Enhancing PSR over a wide frequency range
•
With the help of an NMOS cascode, a charge pump, a voltage reference and
an RC filter to shield the entire regulator from power supply fluctuations, a
5mA LDO regulator utilizing 60pF of on-chip capacitance achieves a worstcase PSR performance of -27dB over 50MHz.
G. A. Rincon-Mora, V. Gupta, “A 5mA 0.6mA CMOS Miller-Compensated LDO Regulator with -27dB Worst-Case
26
Power-Supply Rejection Using 60pF of On-Chip Capacitance ,” ISSCC, feb. 2007.
Stability and PSR Simulations
• Stability test (Open Loop)
Frequency Response
Open loop gain shows a low pass frequency response
AC signal is injected here
Loop Gain ~ 65dB
Fu ~ 10MHz
PM ~ 60°
27
Stability and PSR Simulations (Continue)
• PSR simulation
AC signal is injected here
PSR versus Frequency
PSR curve shows a Quasi-Band Pass frequency
response
it is less than -40 dB up to 10KHz, -30 dB at 100 KHz
28
Different Compensation Techniques for Stability
Purposes
•
Internal zero generation using a differentiator
– An auxiliary fast loop (differentiator) provides both a fast transient detector path
as well as internal ac compensation.
– The simplest coupling network might be a unity gain current buffer.
– Cf senses the changes in the output voltage in the form of a current that is then
injected into pass transistor gate capacitance.
Robert J. Milliken, Jose Silva-Martínez, and Edgar Sánchez-Sinencio “Full on-chip CMOS low-dropout voltage regulator,”
29
IEEE Trans. on Circuits and Systems – I, pp 1879-1890, vol. 54, Issue 9, Sept. 2007.
Different Compensation Techniques
•
Capacitive feedback for frequency compensation
– It introduces a left hand plane zero in the feedback loop to replace the zero generated
by ESR of the output capacitor.
– the capacitor is split into two frequency-dependent voltage-controlled current sources
(VCCS) and grounded capacitors.
– Instead of adding a pole–zero pair with zero at lower frequency than the pole, in this
technique only a zero is added.
– It needs a frequency dependent voltage control current source (VCCS).
30
Chaitanya K. Chava, and Jose Silva-Martinez, “A frequency compensation scheme for LDO voltage regulators,”
IEEE Trans. on Circuits and Systems – I, vol. 51, No.6, pp. 1041-1050, June 2004.
Different Compensation Techniques
•
DFC frequency compensation
– It is a pole-splitting compensation technique especially designed for compensating
amplifier with large-capacitive load.
– DFC block composed of a negative gain stage with a compensation capacitor Cm2,
and it is connected at output of the first stage. Another compensation capacitor Cm1
is required to achieve pole-splitting effect.
– The feedback-resistive network creates a medium frequency zero for improving the
LDO stability.
31
K. N. Leung, and P.K.T. Mok, “A capacitor-free CMOS low-dropout regulator with damping-factor-control frequency compensation,”
IEEE J. Solid-State Circuits, vol.38, no.10, pp.1691-1702, Oct. 2003.
Different Compensation Techniques
•
Pole-zero tracking frequency compensation
– To have pole-zero cancellation, the position of the output pole po and compensation
zero zc should match each other.
– The resistor is implemented using a transistor Mc in the linear region, where its
value is controlled by the gate terminal.
K. C. Kwok, P. K. T. Mok. “Pole-zero tracking frequency compensation for low dropout regulator,”
2002 IEEE International Symposium on Circuits and Systems, Vol. IV, pp. 735-738,May 2002.
32
Fast Transient Response
•
•
A current-efficient adaptively biased regulation scheme is implemented using a lowvoltage high-speed super current mirror. It does not require a compensation
capacitor.
The adaptively error amplifier drives a small transconductance (MA9) to modulate the
output current IOUT through a transient-enhanced super current mirror.
Yat Lei Lam, Wing-Hung Ki, “A 0.9V 0.35µm Adaptively Biased CMOS LDO Regulator with Fast
Transient Response,” 2008 IEEE International Solid-State Circuit Conference, February 2008.
33
Noise in Linear Regulators
•
LDO noise is sometimes confused with PSRR


•
PSRR is the amount of ripple on the output coming from the ripple of the input.
On the other hand, noise is purely a physical phenomenon that occurs with the transistors and resistors
(ideally, capacitors are noise free) on a very fundamental level.
Primary noise sources:
1. Bandgap-Reference (Primary source of noise)
 Possible solution: add a low-pass filter (LPF) to the output of the bandgap.
– Drawback: it can slow down the output startup.
2. The resistor divider ( thermal noise = 4KTR )
 Possible solution: Use resistors as small as possible.
– Drawback: Smaller resistors burn more current through the feedback divider.
 Possible solution: add a capacitor across the top resistor in the resistor feedback divider. At high
frequencies it reduces the close loop gain and thus the noise.
– Drawback: it could slow down start-up time significantly, since the capacitor would have to be
charged by the current in the resistor divider.
3. Input stage of the error amplifier (thermal and flicker noise)
 Possible Solution: Large input drivers.
– Drawback: larger area.
•
Second order noise sources:
–
Load current and output capacitance (Phase Margin)
•
Low phase margin will cause peaking in the close-loop gain and since the close-loop gain amplifies this
noise, the total output noise increases.
34
Reference: J. C. Teel, “Understanding noise in linear regulators” Analog Application Journal, 2Q 2005, www.ti.com/aaj
LDO Design Example
Conventional LDO
Error Amplifier
VREF
Parameters
Specifications
VIN
3.5V
VOUT
3.3V
ILoad
0mA-50mA
IQ
< 100µA
Technology
0.5µm CMOS
Pass Transistor
VOUT
R1
CL
RL
R2
RESR
35
Design Flow Diagram
Vin
Vout
RL
Vdropout
W/L
CGate
ILoad
Design Error Amplifier
RDS
Cp
Rp
RA
Calculate non dominant poles: PND1, PND2
Adjust poles and zeros locations using CL and RESR
Check stability
Check transient, PSR, load regulation, line regulation, …
36
LDO Design Example
Since
ID 
Vdropout  200mV  VDSSATPass  200mV
2I D
1
W 
W 
 p Cox  VDSSATPass2    
2
L
 L   p Cox  VDSSATPass2
Assuming µPCox= 65µA/V2
the pass transistor size can be calculated by:
W
 38,462
L
In order to minimize the gate capacitance, we use minimum length L = 0.6µm
W  38462  0.6m  23mm
The gate capacitance of the pass transistor is given by the following equation:
C  C  g  R  1C
gate
where
2
C  W  L  C
3
GS
ox
GS
mp
par
GD
C W  L C
GD
D
ox
RPAR  Rds R1  R2 RL
Rds 
1
I ds
37
Design Example (Continue)
The values of CGS and CGD can be also obtained if we run a dc simulation and verify the operating
point of the pass transistor. Using the last method, we found:
R 
DS
1
 15
g
C  26 pF
C  7.6 pF
GS
GD
ds
R1 and R2 are calculated using :
V
 R
 1 
 R
2
OUT
1

  V

REF
Assuming a reference voltage of 1.2V and choosing R1 = 240K, We found R2 = 420K .
R 
L
V
I
OUT
LOAD

3.3V
 66
50mA
W 
G  2  C  i
L
mp
p
C
ox
gate
load
R  15 420 K  240 K 66  12
PAR
 23e  3 
 130e  6  
  50e  3  50mA / V
 0.6e  6 
2
 C  g  R  1C  36.5 pF
GS
mp
par
GD
38
Design Example (Continue)
Error Amplifier Design and Considerations
–
High DC Gain to guarantee high loop gain over the range of loads (AV > 60dB)
–
Low output impedance for higher frequency pole created with CGS of pass transistor
–
Internal poles must be kept at high frequencies, preferably > fU of the system (~1MHz)
–
Low DC current consumption
–
Low Noise
Error Amplifier schematic
The error amplifier is implemented using a two stage without miller compensation topology
in order to achieve a gain larger than 60dB and GBW =7MHz using 0.5µm CMOS technology
39
Design Example (Continue)
Error Amplifier Simulation Results
Phase Plot
Magnitude Plot
A  65dB
o
GBW  7.6MHz
PM  51
Note: This results were obtained using Cgate = 36.5pF as the load
40
Design Example (Continue)
z
Pole / Zero Locations
P
ND 2
Dominant Pole Location
1
P 
2 R  R
D
PAR
ESR
C
 1.2 KHz
ND 1
P 
ND 2
A
Gate
P
D
1
 7.3MHz
RC
p
L
 5.3KHz
ND 1
Second non-dominant pole location
p
Zero location
First non-dominant pole location
1
P 
RC
P
Z
1
 3.2 KHz
R C
ESR
L
Notes:
1- RA was obtained from simulations. Basically, it is the output resistance of the error amplifier.
2-PND2 is greater than 7.3MHz since the phase margin of the amplifier is around 51°. This is
good news since we want this pole to be located above the gain bandwidth product of the
overall system.
3- RESR equal 5 was chosen for stability reasons (see next slide).
41
Design Example (Continue)
Stability versus RESR
UGB versus RESR
Phase margin versus RESR
Note: RESR was swept from 0 to 10
42
Design Example (Continue)
System Simulation Results
Magnitude Plot (IL=50mA)
Phase Plot (IL=50mA)
Phase Margin = 55°
DC Gain = 74dB
UGB = 6.3MHz
Magnitude Plot (IL=100µA)
Phase Plot (IL=100µA)
Phase Margin = 90°
DC Gain = 75dB
UGB = 172KHz
43
Design Example (Continue)
System Simulation Results
VIN Step Plot
IL Step Plot
V  3.30352V
V  3.30206V
4
2
V  3.30238V
3
V  3.30238V
1
Load Regulation =
V  V 1.17mV

 0.0234V / A
I I
50mA
V V
313V

 0.0031V / V
I I
100mV
2
L2
Line Regulation =
2
L2
1
L1
1
L1
Notes:
1- VIN step from 3.4 to 3.5V
2- ILOAD step from 0 to 50mA
44
Design Example (Continue)
System Simulation Results
PSR versus Frequency
PSR @ 100KHz = -35dB
45
Summary of the Results
Parameters
Results
VIN
3.5V
VOUT
3.3V
ILoad_max
ILoad_min
50mA
0mA
IQ
30µA
PSRR@100KHz
-35dB
Line Regulation
0.0031V/V
Load Regulation
0.0234V/A
TR
1µs
Technology
0.5µm CMOS
46
Current Efficient LDO
For low IL, for R1+R2 >> Ro_pass
w p1 
1
Ro _ passCo

I L
Co
For no-load current
w p3 
g mQ1
C par

2 KI bias
C par
Note that RL is significantly larger
Ro _ pass //( R1  R2 )  Ro _ pass
 W   p Cox
K  
 L p 2
Loop Gain:
Av  AEA g mp Ro _ pass
Av  AEA
2 KI L
I L
Av  AEA
2

AEA  g ma Roa
K
IL
47
Current Efficient LDO
GB  Avw p1  AEA g mp Ro _ pass / Ro _ passCo
GB  AEA g mp / Co  2 AEA KI L / Co  2 g ma Roa KI L / Co
Note that GB will change as
margin. i.e.,
I L changes, this effects modify the pole-zero locations and the phase
GBMAX  2 AEA KI L ,max / Co
; w p1 
GBMIN  2 AEA KI L,min / Co
; w p1 
Due to current mirror when load current exist, then we have
w p 3,load 
2 KI bias  I L / N
;
C par
1
C par KN 2 I bias  NI L
The zero is located at: w z |Cb Co 


Co
make
w p 3,load
I L

w p1 GB
,
I L I L
2
or
C 
2
  par  KN 2 I bias  C par
NI L  1
 Co 
2
1
Co RESR
Another pole is located at the output of the AEA, w p 2 
1
RoaC pa
G. A. Rincon-Mora, P. E. Allen, “A low-voltage, low quiescent current, low drop-out regulator,”
IEEE J. Solid-State Circuits, vol.33, no.1, pp.36-44, Jan. 1998.
48
To determine the stability one can consider the open loop gain defined as:
Aopen

s 
A 1  
v
 w 


v

s 
s 
s
1 
1 
1 
 w  w  w



Avo
vo
A
open
fb
z
ref
p1
p2
p3




wp1
where
w w w w
Avo  g ma Roa g mp Ro _ pass
p1
z
p2

p3
wz
wp2
wp3
1
R
1
R
2
1
Stability imposes the following conditions:
open
M
o

o
A ( jw )  1
Or
open
o
where
w  GB
o
  180  ARGA  jw 

M
open
w 
  tan
w 
  180  tan 

open
ARG  A ( jw )  0
Where wo is defined as:
Phase Margin:
A ( jw )  1
1
z
1
w

w

p1

  tan


1
w

w

p2

  tan


1
w

w

p3




49
For
w  w  GB ; 
o
M
w
 180    tan 
w
1
o
M
is the arbitrary phase margin

  tan  A   tan

1
vo
z
1
 GB 


 w   tan


p2
1
 GB 


w 


p3
In order to determine an approximated relation between wp3 and GB several assumptions are
required.
Avo >> 1, Then tan-1(Avo)  90°
wo Avow p1
R

 ESR Avo
wz
wz
Ro _ pass
RoaC pa
wo
 Avo
wz
Ro _ passCo
Thus one can write
 R

 RoaC pa

 GB 

 90  MX  tan 1  ESR Avo   tan 1 
Avo    tan 1 
R

R

w 
C
 o _ pass

 o _ pass o

 p3 
50
Cadence Simulation
•
This current efficient LDO is implemented using 0.5 μm CMOS process
•
The LDO provides a 3.3 V regulated output voltage from a 3.5 V supply, for
a load current IL ranging from 250 μA to 25mA
•
The current in the buffer ranges from 20μA (which is only the bias current) in
case of ILmin to 180µA in case of ILmax.
•
The output voltage for load
current alternating between ILmin
and ILmax is shown.
51
Cadence Simulation
iload  25mA
Vout  3.3V
Loop Gain ~ 52dB
Fu ~ 0.78MHz
PM ~ 82°
1
RESR  100m
C  10F
wz 
Ro _ pass  8.5
C  10F
w p1 
Roa  900k
C pa  1 pF
w p2 
1
 1.1M
RoaC pa
R par  400
C par  3 pF
w p3 
1
 833.33M
R parC par
o
o
RESRCo
1
Ro _ passCo
 1M
 11.8K
52
Cadence Simulation
•
ωz cancels ωp2 and the phase margin can be approximated to:
 GB 
  90  tan 1  2  0.78   89o
M  90  tan 

 833.33 
 w p3 
1
•
Which is close to the simulated value of 82o
•
The step response for this
case of ILmax is shown where
Vin varies from 0 to 3.5V and
accordingly Vo varies from 0
to 3.3V
•
For the case of ILmin of 250µA, the dominant pole becomes even smaller and
very far away from ωp3 and so the phase margin is almost 90o
53
Simulation Results From Simulink
Loop Gain and Phase
Fu ~ 5.4MHz
Loop Gain ~ 51.8dB
PM ~ 90°
54
Open Loop Gain and Phase For Different
wp3 Locations
PM  90°
wp3  100GBW
PM  45°
wp3  GBW
Notes:
1-Open Loop System
2- The location of wp3 was varied
3- The variation (wp3) was simulated in Matlab using a “for loop”
55
Current Limiters Architecture
Courtesy of Tuli Dake from TI
56
ILIM Op Amp
57
References
[1] G. A. Rincon-Mora, V. Gupta, “A 5mA 0.6mA CMOS miller-compensated LDO regulator
with -27dB worst-case power-supply rejection using 60pF of on-chip capacitance ,”
ISSCC, Feb. 2007.
[2] L.-G. Shen et al., “Design of low-voltage low-dropout regulator with wide-band high-PSR
characteristic,” International Conference on Solid-State and Integrated Circuit
Technology, ICSICT, Oct. 2006.
[3] R. J. Milliken, J. Silva-Martínez, and E. Sánchez-Sinencio, “Full on-chip CMOS lowdropout voltage regulator,” IEEE Trans. on Circuits and Systems – I, pp 1879-1890, vol.
54, Issue 9, Sept. 2007.
[4] C. K. Chava, and J. Silva-Martinez, “A frequency compensation scheme for LDO voltage
regulators,” IEEE Trans. on Circuits and Systems – I, vol. 51, No.6, pp. 1041-1050, June
2004.
[5] K. N. Leung, and P.K.T. Mok, “A capacitor-free CMOS low-dropout regulator with
damping-factor-control frequency compensation,” IEEE J. Solid-State Circuits, vol.38,
no.10, pp.1691-1702, Oct. 2003.
[6] K. C. Kwok, P. K. T. Mok. “Pole-zero tracking frequency compensation for low dropout
regulator,” 2002 IEEE International Symposium on Circuits and Systems, Vol. IV, pp.
735-738, May 2002.
[7] J. C. Teel, “Understanding noise in linear regulators” Analog Application Journal, 2Q
2005, www.ti.com/aaj
[8] K. N. Leung, P. K. T. Mok, and W. H. Ki, "A novel frequency compensation technique for
low-voltage low-dropout regulator," IEEE International Symposium on Circuits and
Systems, vol. 5, May 1999.
[9] G. A. Rincon-Mora and P. A. Allen, "A low-voltage, low quiescent current, low drop-out
regulator," IEEE J. Solid-State Circuits, vol.33, no.1, pp.36-44, Jan. 1998.
58