DESIGN OF LC HARMONIC NOTCH FILTER FOR RIPPLE REDUCTION IN

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


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).




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:


•Over-damping:

Bode plot of self-loop function

Nyquist chart of self-loop function

92o

103.7o

128o


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


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:


•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


Under-damping region




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



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



131o


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


2. Analysis of Power-Stage of DC-DC Converter• Operating regions of power-stage of DC-DC converter• Passive parallel RLC network


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

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DESIGN OF LC HARMONIC NOTCH FILTER FOR RIPPLE REDUCTION IN