design of lc harmonic notch filter for ripple reduction in
TRANSCRIPT
DESIGN OF LC HARMONIC NOTCH FILTER FOR RIPPLE REDUCTION IN STEP-DOWN
DC-DC BUCK CONVERTER
MinhTri Tran*, Yasunori Kobori, Anna Kuwana, and Haruo Kobayashi
Gunma
KobayashiLaboratory
Gunma University, Japan
1. Research Background• Motivation, objectives and achievements• Characteristics of an adaptive feedback network
2. Analysis of Power-Stage of DC-DC Converter• Operating regions of 2nd-order systems• Phase margin of power-stage of DC-DC converter
3. Ripple Reduction for DC-DC Converters• Linear swept frequency modulation • Passive and active LC Harmonic Notch filters
4. Conclusions
Outline
2
1. Research BackgroundNoise in Electronic Systems
Common types of noise:• Electronic noise• Thermal noise,• Intermodulation noise,• Cross-talk,• Impulse noise,• Shot noise, and• Transit-time noise.
DC-DC converters• Overshoot,• Ringing• Ripple
Device noise:• Flicker noise,• Thermal noise,• White noise.
Signal to Noise Ratio:
Performance of a devicePerformance of a system
Figure of Merit:
Signal power
SNRNoise power
Output SNRInput SNR
F
3
1. Research BackgroundEffects of Ripple and Ringing on Electronic Systems
• Ringing is overshoot/undershoot voltage or current when it’s seen on time domain.
• Ripple is wasted power, and has many undesirable effects in a DC circuit.
Ringing does the followingthings:• Causes EMI noise,• Increases current flow,• Consumes the power,• Decreases the performance,• Damages the devices.
Ripple does the followingthings:• Heats components,• Increases noise,• Creates the distortion,• Causes digital circuits
to operate improperly.
4
• Ringing test for power-stage of DC-DC buck converters.
• Ripple reduction using linear swept frequency modulation and LC harmonic notch filters
• Proposed design of an active inductor for the harmonic notch filter for DC-DC buck converter using a general impedance converter
• Measurement of self-loop function in power-stage of DC-DC buck converter
1. Research BackgroundObjectives of Study
1. Research BackgroundAchievements of Study
Alternating current conservationfor deriving self-loop function
Incident current
Transmitted current
( ) inc
trans
VV
L
Derivation of self-loop function
Implemented circuit
Phase margin of power stage
LC notch filter
Stability test for power-stage
134o
Phase margin46 degrees
131o
Phase margin49 degrees
6
1. Research BackgroundApproaching Methods
Baluntransformer
input
output
Measurement set up
Simplified power-stage
Design of DC-DC buck converter
PWM CONTROL
BLOCK
7
1. Research BackgroundCharacteristics of Adaptive Feedback Network
Block diagram of a typical adaptive feedback system
Reference voltage
Adaptive feedback is used to control the output source along with the decision source (DC-DC Buck converter).
Transfer function of an adaptive feedback network is significantly different from transfer function of a linear negative feedback network. Loop gain is independent of frequency variable (referent voltage, feedback voltage, and error voltage are DC voltages).
DC voltage
DC voltage
DC voltage
DC voltage+ Ripple voltage
1. Research BackgroundSelf-loop Function in A Transfer Function
8
( ( )(( ) ))
)1
(out
in
H VV
AL
Transfer function
( )L
( )A ( )H
: Open loop function : Transfer function
: Self-loop function
Linear systemInput Output
( )H ( )inV ( )outV
0 1
0 1
( ) ... ( )(
)) ... (
()
nn n
nn n
Hb j b j ba j a j a
Model of a linear system
oMagnitude-frequency plotoAngular-frequency plot
oPolar chart Nyquist chart
oMagnitude-angular diagram Nichols diagram
Bode plots
Variable: angular frequency (ω)
9
1. Research BackgroundAlternating Current Conservation
( ) 1( ) 1
;(
( )
)
in
o
i
ut
in
o
ou
n
ut
tHZZ
Z
V
L
V
Z
Transfer function
Simplified linear system
Self-loop function
( )inc trans in
t
c
tra
in
i u nsn o t ou
V ZL
Z ZV
VZV
Incident current
Transmitted current
10 mHinductance
Derivation of self-loop function
10
1. Research Background Limitations of Conventional Methods
o Middlebrook’s measurement of loop gainApplying only in feedback systems (DC-DC converters).
o Replica measurement of loop gainUsing two identical networks (not real measurement).
o Nyquist’s stability condition Theoretical analysis for feedback systems (Lab tool).
o Nichols chart of loop gain Only used in feedback control theory (Lab tool).
1. Research Background• Motivation, objectives and achievements• Characteristics of an adaptive feedback network
2. Analysis of Power-Stage of DC-DC Converter• Operating regions of 2nd-order systems• Phase margin of power-stage of DC-DC converter
3. Ripple Reduction for DC-DC Converters• Linear swept frequency modulation • Passive and active LC Harmonic Notch filters
4. Conclusions
Outline
12
2. Analysis of Power-Stage of DC-DC ConverterSimulations of Second-order Transfer Function
21
2
3
2
2
1 ;1
1 ;1
1 ;
( )
( )
( )
2
3 1
j
j
j
j
j
j
H
H
H
•Under-damping:
•Critical damping:
•Over-damping:
Bode plot of transfer function
Nyquist chart of transfer function
0dB
-12dB
-6dB
-90o
13
2. Analysis of Power-Stage of DC-DC ConverterBehaviors of Second-order Transfer Function
Case Over-damping Critically damping Under-dampingDelta
Module
Angular
( )2
211 0
0 0
1 4 02
aa a
a a
2211 0
0 0
1 4 02
a a aa a
2211 0
0 0
1 4 02
a a aa a
( )H
0
2 22 2
2 21 1 1 1
0 0 0 0 0 0
1
1 12 2 2 2
a
a a a aa a a a a a
02
2 1
0
11 62
2
dBa
aa
0
2 22 2 2 2
1 1 1 1
0 0 0 0 0 0
1
1 12 2 2 2
a
a a a aa a a a a a
( ) 2 2
1 1 1 1
0 0 0 0 0 0
arctan arctan1 1
2 2 2 2
a a a aa a a a a a
0
1
22 arctan
aa
2 2
1 1
0 0 0 0
1 1
0 0
1 12 2
arctan arctan
2 2
a aa a a aa aa a
1
02 cut
aa
0
1
2( ) cut
aH
a( )
2
cut0
1
2( ) cut
aH
a ( )2
cut0
1
2( ) cut
aH
a ( )2
cut
20 1
1( )1 ( )
Ha j a j
Second-order transfer function:
14
2. Analysis of Power-Stage of DC-DC ConverterSimulations of Second-order Self-loop Function
21
2
3
2
2
( )
( ) ;2
;
( ) 3 ;
L
L
j
j
j
j
L j
j
•Under-damping:
•Critical damping:
•Over-damping:
Bode plot of self-loop function
Nyquist chart of self-loop function
92o
103.7o
128o
Phase margin52 degrees
15
2. Analysis of Power-Stage of DC-DC ConverterBehaviors of Second-order Self-loop Function
Case Over-damping Critical damping Under-damping
Delta ( ) 21 04 0 a a 2
1 04 0 a a 21 04 0 a a
( )L 2 20 1 a a 2 2
0 1 a a 2 20 1 a a
( ) 0
1arctan2
aa
0
1arctan2
aa
0
1arctan2
aa
11
0
5 22aa
1( ) 1 L 1( ) 76.3 o
1( ) 1 L 1( ) 76.3 o1( ) 1 L 1( ) 76.3 o
12
02aa
2( ) 5 L 2( ) 63.4 o
2( ) 5 L 2( ) 63.4 o2( ) 5 L 2( ) 63.4 o
13
0
aa
3( ) 4 2 L 3( ) 45 o3( ) 4 2 L 3( ) 45 o
3( ) 4 2 L 3( ) 45 o
0 1( ) L j a j aSecond-order self-loop function:
16
2. Analysis of Power-Stage of DC-DC ConverterSummary of Operating Regions of 2nd-Order System
Over-damping:Phase margin is 88 degrees.Critical damping:Phase margin is 76.3 degrees.Under-damping: Phase margin is 52 degrees.
98o
103.7o
128o
Nichols plot of self-loop functionBode plot of transfer function
Transient response
0dB
-12dB
-6dB
Phase margin52 degrees
17
2. Analysis of Power-Stage of DC-DC ConverterBehaviors of power-stage of DC-DC Converter
20 1
20 1
1( ) ;1
( ) ;
out
in
VHV a j a j
L a j a j
21 / 22
L CR Z Z R
LC L21 / 2
2
L CR Z Z R
LC L21 / 2
2
L CR Z Z R
LC L
Operating regions
•Over-damping:
•Critical damping:
•Under-damping:
Parallel RLC low-pass filter Transfer function & self-loop function:
0 1; ; La LC aRWhere:
0
0 0
1 ;; 1 ;
L C
LCZ L Z C
2L CZ Z R Balanced charging-
discharging time condition
18
2. Analysis of Power-Stage of DC-DC ConverterPhase Margin of Power-Stage of DC-DC ConverterSimplified power-stage
Implemented circuit
L1 = 220 uH, C1 = 100 uF, R1 = 5 Ω,
Bode plot of transfer function
Nichols plot ofself-loop function
Measured results
134o
Phase margin46 degrees
Under-damping region
1. Research Background• Motivation, objectives and achievements• Characteristics of an adaptive feedback network
2. Analysis of Power-Stage of DC-DC Converter• Operating regions of 2nd-order systems• Phase margin of power-stage of DC-DC converter
3. Ripple Reduction for DC-DC Converters• Linear swept frequency modulation • Passive and active LC Harmonic Notch filters
4. Conclusions
Outline
20
3. Ripple Reduction for DC-DC ConvertersRipple Reduction using Linear Swept Frequency Modulation
SAW VCO
Vm
Vb
PWM
Current conpensation
20
∆ISAW
ISAW
ModulationSignal
G
Modify
Modulate
Linear swept frequency modulation
Block diagram of DC-DC buck converter Withoutfrequency modulation
Withfrequency modulation
Withoutfrequency modulation
Withfrequency modulation
21
3. Ripple Reduction for DC-DC ConvertersRipple Reduction using LC Harmonic Notch Filter
Simplified model of power-stage
2
4 3 20 1 2 3
4 3 20 1 2 3
0 1
1
b jH
a j a j a j a j
L a j a j a j a j
0 2 2 0 1 1 2 2
1 2 2 11 2 1 1 2 2 1 2 3
; ;
; ; ;
L L
b L C a LC L CL L C La a LC L C LC aR R
Transfer function & self-loop function
Schematic diagram of DC-DC buck converter
Where,
22
3. Ripple Reduction for DC-DC ConvertersPassive and Active LC Harmonic Notch Filters
L1 = 220 uH, C1 = 100 uF, R1 = 4 kΩ, R2 = 2 kΩ, RL = 5 Ω, C2 = 65 nF, L2 = 12 uH, R3 = 15kΩ, C1 = 100 pF, R4 = 1 kΩ, R5 = 1 kΩ, and fn at 180 kHz.
3 2 32
1 1L out out
C
R R RRZ Z sCZR Z R
Approximated value of inductor
Passive component parameters
Schematic diagram of DC-DC converter Behaviors of LC harmonic notch filters
Passive notch filter
Active notch filter
Under-damping region
Under-damping region
23
3. Ripple Reduction for DC-DC ConvertersImplemented Circuit for DC-DC Converter
Input Voltage (Vin) 12 VOutput Voltage (Vo) 5.0 VOutput Current (Io) 1 A
Clock Frequency (Fck) 180 kHzOutput Ripple < 10 mVpp
Design parameters Measurement set up
Implemented circuit
24
3. Ripple Reduction for DC-DC ConvertersMeasurement Results of Proposed Design Circuit
Bode plot of transfer function Nichols plot of self-loop function
134o
Phase margin46 degrees
Under-damping region
131o
Phase margin49 degrees
o Reduce the cut-off frequency of the power-stage
Reduce the ripple caused by high-order harmonic signals
o Improvement of phase marginof the power-stage
Reduce the overshoot caused by the passive components
25
3. Ripple Reduction for DC-DC ConvertersRipple Reduction using Harmonic Notch Filter
PWM CONTROL
BLOCK
Schematic diagram of DC-DC Buck converter Implemented circuit
Withoutnotch filter
Withnotch filter
Output spectrum
Output spectrum
Ripple Reduction 5 mVpp
11 mVpp
Spectrum reduction -35 dBV -38 dBV
at 180 kHz
Output spectrum
1. Research Background• Motivation, objectives and achievements• Characteristics of an adaptive feedback network
2. Analysis of Power-Stage of DC-DC Converter• Operating regions of power-stage of DC-DC converter• Passive parallel RLC network
3. Ripple Reduction for DC-DC Converters• Linear swept frequency modulation • Passive and active LC Harmonic Notch filters
4. Conclusions
Outline
4. Comparison
Features This work Replicameasurement
Middlebrook’smethod
Main objective Self-loop function Loop gain Loop gain
Transfer function accuracy Yes No No
Ringing Test Yes Yes Yes
Operating region accuracy Yes No No
Phase margin accuracy Yes No No
Passive networks Yes No No
4. Discussions• Loop gain is independent of frequency variable.Loop gain in adaptive feedback network is significantly
different from self-loop function in linear negative feedback network.
https://www.mathworks.com/help/control/ref/nichols.html
Network Analyzer
Nichols chart is only used in MATLAB simulation.
Nichols chart isn’t used widely in practical measurements
(only used in control theory).
(Technology limitations)
This work:• Investigation of behaviors of power-stage in DC-DC
converters based on alternating current conservation
• Proposed designs of passive and active LC harmonic notch filters for ripple reduction Phase margin improvement from 46 degreesinto 49 degrees Ripple reduction from 11 mVpp into 5 mVpp
Future of work:• Stability test for dynamic loads, and parasitic
components in printed circuit boards
4. Conclusions
[1] H. Kobayashi, T. Nabeshima, Handbook of Power Management Circuits, Pan Stanford Publisher (2016).[2] M. Tran, N. Miki, Y. Sun, Y. Kobori, H. Kobayashi, "EMI Reduction and Output Ripple Improvement of Switching DC-DC Converters with Linear Swept Frequency Modulation" IEEE Int. Conf. ICSICT2018, 2018.[3] M. Tran, Y. Sun, N. Oiwa, Y. Kobori, A. Kuwana, H. Kobayashi, "Mathematical Analysis and Design of Parallel RLC Network in Step-down Switching Power Conversion System", J. Mechanical and Electrical Intelligent System, May 2020.[4] M. Tran, Y. Sun, Y. Kobori, A. Kuwana, H. Kobayashi, "Design Proposal for Inductor Type Buck Converter in Bluetooth Receiver Chip with Overshoot Cancellation and Ripple Reduction Technique", J. Applied Mechanics and Materials (accepted).[5] M. Tran, Y. Sun, N. Oiwa, Y. Kobori, A. Kuwana, H. Kobayashi, "Fast Response, Small Ripple, Low Noise Switching Converter with Digital Charge Time Control and EMI Harmonic Filter", J. Mechanical and Electrical Intelligent System, Dec. 2019.[6] M. Tran, Y. Sun, Y. Kobori, A. Kuwana, H. Kobayashi, "Minimum Output Ripple and Fixed Operating Frequency Based on Modulation Injection for COT Ripple Control Converter", IEEE Int. Conf. ASIC, 2019.[7] M. Tran, Yifei Sun, Y. Kobori, A. Kuwana, H. Kobayashi, "Overshoot Cancelation Based on Balanced Charge-Discharge Time Condition for Buck Converter in Mobile Applications", IEEE Int. Conf. ASIC, 2019.[8] M. Tran, A. Kuwana, H. Kobayashi, "Design of Active Inductor and Stability Test for Passive RLC Low Pass Filter", Int. Conf. Signal and Image Processing, London, UK, July, 2020.[9] M. Tran, A. Kuwana, H. Kobayashi, "Design of Active Inductor and Stability Test for Ladder RLC Low Pass Filter Based on Widened Superposition and Voltage Injection", IIAE Int. Conf. Industrial Application Engineering, Shimane, Japan, March, 2020.
References
Thank you very much!谢谢
Gunma
KobayashiLaboratory