Idea Transcript
Linear Regulators: Fundamentals and Compensation Vahe Caliskan, Sc.D. Senior Technical Expert Motorola Automotive Government & Enterprise Mobility Solutions
February 15, 2012
Vahe Caliskan, Sc.D. (g17823)
Linear Regulators
February 15, 2012
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1
Introduction
2
Review of Linear Regulator Topologies
3
Transfer Functions
4
Poles & Zeros
5
Bode Magnitude & Phase Plots
Vahe Caliskan, Sc.D. (g17823)
Linear Regulators
February 15, 2012
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Outline
1
Introduction
2
Review of Linear Regulator Topologies
3
Transfer Functions
4
Poles & Zeros
5
Bode Magnitude & Phase Plots
Vahe Caliskan, Sc.D. (g17823)
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Introduction to Seminar Series
Goals of the Seminar Series Provide an overview of power conversion techniques Power supplies are common subsystems in most of our products Present follow-up seminars in related areas → switching regulator topologies/compensation, simulation Offer refresher seminars in fundamental areas → mathematical modeling, circuit analysis, control design
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Previous Seminars
Overview of Linear and Switching Power Supplies Two seminars were held on September 15 and October 17, 2005 a total of 83 people attended these seminars Follow-up seminars in linear and switching regulators were requested http://compass.mot.com/go/powerconversion
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Outline
1
Introduction
2
Review of Linear Regulator Topologies
3
Transfer Functions
4
Poles & Zeros
5
Bode Magnitude & Phase Plots
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Linear Regulator Basics Three-terminal devices – input, output, common (ground) Linear regulators may be classified by their series (pass) transistor − Series element may consist of bipolar of field-effect transistors
Bipolar outputs → Darlington NPN, PNP, NPN-PNP Majority of regulators use bipolars (FET-based regulators $) Series transistor structure determines Vdropout , Ibias , Iq , Pdiss Frequency compensation and protection circuity also important Vdropout minimum input-output voltage difference to stay in regulation Ibias bias current for the pass transistor Iq regulator quiescent current of which Ibias is one component Pdiss regulator power dissipation Vahe Caliskan, Sc.D. (g17823)
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Linear Regulator – Typical Usage TPS76433 Vin
IN
Vout
OUT
4.7µF 1µF
EN BYPASS GND
ESR 0.01µF
TPS76433 – 3.3V, 150mA, PMOS LDO linear regulator Low output voltage noise (50µV), Low power (Iq = 140µA) 0.01µF bypass capacitor filters reference voltage Capacitor ESR important for stability (not too high, not too low) Current limit (1A), thermal protection (165◦ C shutdown)
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NPN Regulator
NPN Regulator
Characteristics
Vin
Iload
Vout R1
−
Ibias
Vref
R2 + −
PNP driver Used in 78xx series Ibias ≈ Iload /β 3
Error Amp +
NPN Darlington pass
GND
Smallest chip area Small comp. capacitor Least expensive Vdo = 2VBE +Vsat ≈ 2.0V No reverse battery protection
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PNP Low Dropout (LDO) Regulator
Characteristics
PNP (LDO) Regulator Vin
Vout
Iload R1 −
R2
Ibias
Vref
+ −
NPN or EA direct drive Vdo = Vsat ≈ 600mV Inherent reverse battery protection
Error Amp +
PNP pass
GND
Ibias ≈ Iload /βpnp Large chip area Large comp. capacitor More expensive
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Composite (Quasi-LDO) Regulator
Composite Regulator Vin
Characteristics Vout
Iload
R1 −
Ibias
Vref
R2 + −
PNP driver Vdo = VBE + Vsat ≈ 1.3V Ibias ≈ Iload /β 2
Error Amp +
NPN pass
GND
Compromise between NPN and PNP Larger chip area than NPN Large comp. capacitor No reverse battery protection
Vahe Caliskan, Sc.D. (g17823)
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PMOS LDO Regulator
PMOS Regulator
Characteristics
Vin
Vout
Iload R1 +
R2
− Vahe Caliskan, Sc.D. (g17823)
Vref
+ −
NPN driver Very low Vdo (≈ 50mV) Vdo controlled by Rds,on
Error Amp
Ibias
PMOS pass
GND
Linear Regulators
Very low Ibias Can’t enhance FET for Vin < 3V
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NMOS LDO Regulator
NMOS Regulator
Characteristics
Vin
Vout
Iload R1 Vbias
Vahe Caliskan, Sc.D. (g17823)
Direct drive Very low Vdo Lower Rds,on than PMOS
−
Error Amp + Vref
NMOS pass
R2 + −
GND
Linear Regulators
Lower output impedance Smaller external caps Needs Vbias > Vout to enhance FET
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Summary of Linear Regulator Advantages/Disadvantages Topology NPN
PNP LDO
NPN/PNP PMOS LDO NMOS LDO
Advantages smallest die size fastest transient response smallest comp. capacitor low dropout voltage rev. battery protection moderate dropout voltage lower Iq than PNP very low Vdo and Ibias Vdo ∝ Rds,on very low Vdo , low Rout lower Rds,on than PMOS smaller external capacitors
Vahe Caliskan, Sc.D. (g17823)
Linear Regulators
Disadvantages large dropout voltage no rev. batt. protection high quiescent current large comp. capacitor large die size large comp. capacitor no rev. battery protection need Vin > 3V need Vbias > Vout
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Outline
1
Introduction
2
Review of Linear Regulator Topologies
3
Transfer Functions
4
Poles & Zeros
5
Bode Magnitude & Phase Plots
Vahe Caliskan, Sc.D. (g17823)
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Transfer Function Fundamentals response ) Transfer function is a ratio of response to excitation ( excitation
Use of ( output input ) for TFs is vague (E and R can be at same port) Expressed in frequency domain using Laplace or Fourier Transforms R
Voltage Gain (V/V), ωc =
vin + −
+ vout −
C
iin
= corner frequency
1 1 vout (s) 1 = sC 1 = = vin (s) 1 + sRC 1 + ωsc R + sC
Input Impedance (Ω)
R + vin −
A(s) =
1 RC
s
C
Vahe Caliskan, Sc.D. (g17823)
Zin (s) =
1+ vin (s) 1 1 + sRC = R+ =R = R s ωc iin (s) sC sRC ωc
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Poles & Zeros Transfer function is a ratio of two polynomials A(s) =
num(s) den(s)
Poles are values of s that make den(s) = 0 Also called roots or natural frequencies Response to initial conditions, independent of applied excitation Determine stability
Zeros are values of s that make num(s) = 0 Also called transmission zeros No impact on stability Determine undershoot, transient response (with poles)
Evaluate TF by letting s = jω and take complex magnitude and phase ω 1 1 −1 ∠ − tan A(jω) = ω = r 2 1 + j ωc ωc {z } | 1 + ωωc phase {z } | magnitude
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Bode Plots & Stability
Loop gain T (s) is the product of forward and feedback gains Closed-loop system can be unstable even if T (s), G (s) have no RHP poles Undesired ringing and overshoot can occur even in stable systems Crossover frequency ωc is where kT (jωc )k = 1 ⇒ 0dB Phase margin φm = 180◦ + ∠T (jωc ) If φm > 0◦ ⇒ feedback system stable (no RHP poles) Small φm ⇒ high-Q resonant poles near ωc ⇒ overshoot & ringing We normally need φm ≥ 45◦ in practical feedback systems If φm < 0◦ ⇒ feedback system unstable (at least one RHP pole)
Vahe Caliskan, Sc.D. (g17823)
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Outline
1
Introduction
2
Review of Linear Regulator Topologies
3
Transfer Functions
4
Poles & Zeros
5
Bode Magnitude & Phase Plots
Vahe Caliskan, Sc.D. (g17823)
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1st Order Poles and Zeros
1st Order Pole
1 1+s/ωc
1st Order Zero 1 + s/ωc 40dB
0dB 3dB
+20dB/dec
20dB
−20dB/dec
3dB
−20dB 0dB −40dB ω 0.1ωc
ωc
ωc
10ωc
10ωc 90◦
0◦ −45◦
ω 0.1ωc
ω 5.7◦ 5.7◦
45◦
−45◦/dec
−90◦
Vahe Caliskan, Sc.D. (g17823)
5.7
◦
+45◦/dec
0◦ 5.7◦
ω 0.1ωc
Linear Regulators
ωc
10ωc
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Outline
1
Introduction
2
Review of Linear Regulator Topologies
3
Transfer Functions
4
Poles & Zeros
5
Bode Magnitude & Phase Plots
Vahe Caliskan, Sc.D. (g17823)
Linear Regulators
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Bode Plot (magnitude & phase) 100 80 Magnitude (dB)
60 40
-20dB/dec
20 0 -20 -40 -60 180 135
Phase (deg)
90 45 0 -45 -90
-135 -180 -225-1 10
10 0
Vahe Caliskan, Sc.D. (g17823)
10 1
10 2 Frequency (rad/sec) Linear Regulators
10 3
10 4
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LDO System (3.3V/100mA) TPS76433
Vout
Iload
Co 10µF
Error Amp
+ −
+ −
Vin
R1 0.64R
Vref 1.192V
Vout = (1 +
R1 R2 )Vref
+ −
= (1 +
RC 2Ω
R2 0.36R
0.64R 0.36R ) 1.192V
Cb 0.5µF
RL
= 3.31V
RL = Vout /Iload = 3.3V/100mA = 33Ω Vahe Caliskan, Sc.D. (g17823)
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LDO System Model
rds
S Cgs
Vin
+ −
Error Amp +
G
Roa
Vahe Caliskan, Sc.D. (g17823)
R1 0.64R
gm vgs
−
vgs
Vout
D
Vref +− 1.192V
R2 0.36R
Linear Regulators
Co 10µF RC 2Ω
Cb RL 0.5µF 33Ω
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LDO System Model Simple rds
D
Zo (s) ≈ (Rc +
Gpmos vgs = − + (gm rds )vgs
R1 0.64R
S vs
G
Rc Cgs
R2 0.36R
+ G v − ea s
vout
Co 10µF
Roa
vgs
1 1 sCo )k sCb kRL
Cb
RL
0.5µF
33Ω
2Ω
S }| { z Gea (vs − Vref ) |{z} →0
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LDO System Loop Gain Goa (s)
−Gpmos
EA – PMOS Frequency Response
1 1+sRoa Cgs
PMOS Voltage Gain
vgs
G (s) Load & Filter Zo (s) rds +Zo (s)
−gm rds
vout
Gfb + vs
Gea Error Amp Gain
−
R2 R1 +R2
Feedback Divider
Vref = 0
Vahe Caliskan, Sc.D. (g17823)
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LDO System Loop Gain (redrawn) Goa (s) Error Amp Gain
EA – PMOS Frequency Response
Gea
1 1+sRoa Cgs
+ Vref = 0 − vs
Gpmos
G (s)
PMOS Voltage Gain
Load & Filter
vgs gm rds
Zo (s) rds +Zo (s)
vout
T (s)
R2 R1 +R2
Gfb Feedback Divider
Vahe Caliskan, Sc.D. (g17823)
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Loop Gain Calculation
G (s) ≈ G0
1 + s/ωz RL with G0 = (1 + s/ωo )(1 + s/ωb ) rds + RL
T (s) ≈ Gpmos G0 Gfb Gea
1 + s/ωz (1 + s/ωo )(1 + s/ωb )(1 + s/ωoa )
T0 = Gpmos G0 Gfb Gea ⇒ Low-frequency loop gain ωo ≈ 1/[Co (Rc + rds kRL )] ⇒ Load pole ωoa = 1/[Roa Cgs ] ⇒ Pole due to opamp-PMOS interaction ωb ≈ 1/[Cb Rc (rds kRL )/(Rc + (rds kRL ))] ⇒ Pole due to bypass cap ωz = 1/[Rc Co ] ⇒ Zero due to ESR
Vahe Caliskan, Sc.D. (g17823)
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Parameters, Gains, Pole/Zero Locations Vout RL Rc gm rds R1
3.3V 33Ω 2Ω 123mA/V 65Ω 64kΩ
Iload Roa Co Cb Cgs R2
100mA 300kΩ 10µF 0.5µF 200pF 36kΩ
Gpmos Gfb Go Gea T0
gm rds R1 /(R1 + R2 ) RL /(rds + RL ) N/A Gpmos G0 Gfb Gea
8 ⇒ 18.1dB 0.36 ⇒ −8.9dB 0.337 ⇒ −9.45dB 56.2 ⇒ 35dB 54.5 ⇒ 34.7dB
ωo ωoa ωb ωz
1/[Co (Rc + rds kRL )] 1/[Roa Cgs ] 1/[Cb Rc k(rds kRL )] 1/[Rc Co ]
4.2krad/s ⇒ 667Hz 16.7krad/s ⇒ 2.65kHz 1.1Mrad/s ⇒ 172kHz 50krad/s ⇒ 8kHz
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Conclusion
item 1 item 2 item 3 item 4 item 5
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References
Everett Rogers, “Stability Analysis of low-dropout linear regulators with a PMOS pass element” Texas Instruments Analog Applications Journal, Dallas, TX, August 1999. Bang S. Lee, “Understanding the stable range of equivalent series resistance of an LDO regulator” Texas Instruments Analog Applications Journal, Dallas, TX, November 1999. Chester Simpson, “Linear Regulators: Theory of Operation and Compensation” National Semiconductor Application Note AN–1188, Santa Clara, CA, May 2000. Kieran O’Malley, “Compensation for Linear Regulators” ON Semiconductor Application Note SR0003AN/D, Phoenix, AZ, April 2001. Kieran O’Malley, “Linear Regulator Output Structures” ON Semiconductor Application Note SR0004AN/D, Phoenix, AZ, April 2001. Todd Schiff, “Stability in High Speed Linear LDO Regulators” ON Semiconductor Application Note AND8037/D, Phoenix, AZ, October 2000.
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Sources of information on the web
http://www.analog.com —– Analog Devices http://www.infineon.com – Infineon Technologies http://www.linear.com —– Linear Technology http://www.maxim-ic.com – Maxim http://www.national.com – National Semiconductor http://www.onsemi.com —– ON Semiconductor http://www.ti.com ———– Texas Instruments
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