transient response improvement of dc-dc buck …...transient response improvement of dc-dc buck...

Transient Response Improvement of DC-DC Buck Converter by Adjustable Triangular Wave Generator

Shu Wu, Yasunori Kobori, Haruo Kobayashi

Gunma University, Japan

2014/7/10 1

電子情報通信学会電子通信エネルギー技術研究会広島工業大学（2014年7月10日(木)－7月11日(金)）

Outline

• Research Objective • Proposed Triangular Wave Generator

• Duty Cycle Modulation • Slope Adjustable Triangular Wave Generator • Improvement of Transient Response

• Stability Analysis

• Simulation Results • Line Transient Response • Load Transient Response

• Conclusion

2014/7/10 2

Outline





• Conclusion

2014/7/10 3

Transient Response •Three disturbance sources •Output reference signal • Input voltage • Load

Band-gap reference

Line feed-forward control

Trouble

Fast dynamic current slew rate presents challenge in load transient response of power supplies

2014/7/10 4

Previous Control Schemes •Feedback • Voltage-Mode Control (VMC)

• Easy to design and analyze • Limited bandwidth: slow response

• Current-Mode Control (CMC) • Inherent line feed-forward control • Wide band • Slope compensation • Current sensor

•Feed-forward Complicated non-linear calculation 2014/7/10 5

Research Objective • Design a slope adjustable triangular wave generator to

improve transient response of DC-DC buck converter • Based on VMC: compared to CMC

---Not require current sensor and slope compensation

• The slope is regulated by input and output voltage: compared to conventional VMC

---Provide line feed-forward control and higher band-width

• Simple: compared to previous feed-forward control

---Not require complicated calculation

2014/7/10 6

Outline





• Conclusion

2014/7/10 7

t Reference

+

- +

-

Error Amplifier Comparator

Output 𝑉𝐸

Triangular wave

PWM

V PWM

Triangular Wave 𝑉𝐸

𝑰𝑳𝑹𝒊

+

- +

-

Error Amplifier Comparator

Output 𝑉𝐸

PWM

Reference

PWM 𝑉𝐸 𝑰𝑳𝑹𝒊

t

V

Voltage-Mode Control Current-Mode Control

Triangular wave: constant ramp Triangular wave: proportional to inductor current

Duty cycle modulation:

∆𝑑 =𝐺𝑐

𝑉𝑝∆𝑣

Duty cycle modulation:

∆𝑑 =𝐿𝑅𝑖𝑓𝑠𝐺𝑐

𝑉𝑖𝑛−𝑉𝑜𝑢𝑡∆𝑣

Duty Cycle Modulation (1)

2014/7/10 8

•During load transient response, slope of triangular wave always keep constant (conventional VMC and CMC).

•Duty cycle modulation by slope (proposed).


∆𝑑 =𝑡𝑜𝑛2−𝑡𝑜𝑛1

𝑇𝑠

=𝑉𝐸

𝑇𝑠

1

𝑀2−

1

𝑀1

=𝑉𝐸

𝑇𝑠∆

1

𝑀

Duty cycle variation is inversely proportional to slope.

2014/7/10 9


Deviation Duty cycle

∆𝑣 = 𝑉𝑟𝑒𝑓 − 𝑉𝑜𝑢𝑡 ∆𝑑

Slope of triangular wave

∆𝑀

Error signal modulation proportional

Slope modulation inversely proportional inversely proportional

Slope modulation proportional

2014/7/10 10

System Configuration

Op-amp1: • generate error signal • Type 3 compensation

Op-amp2: • Amplify deviation • Control variable of TWG

TWG: slope adjustable • 𝑉𝑖𝑛 ∝ 𝑀

• 𝐺𝑘∆𝑣 ∝ 1

𝑀

2014/7/10 11

Triangular Wave Generator (1)

VCR: Voltage Controlled Resistor VCCS: Voltage Controlled Current Source 2014/7/10 12

•VCR


S

G D

𝑽𝒄𝒐𝒏

𝑉𝐷𝑆2

𝑉𝑡ℎ

+ + +

Voltage Summer

𝑀1

VCR--𝑅𝐷𝑆

𝑽𝒊𝒏

𝑉𝐷𝑆 Voltage Divider

Triode region

𝐼𝐷 = 𝐾𝑛 𝑉𝐺𝑆 − 𝑉𝑡ℎ 𝑉𝐷𝑆 −𝑉𝐷𝑆

2

2 where 𝐾𝑛 = 𝜇𝑛𝐶𝑜𝑥𝑊 𝐿

1

𝑅𝐷𝑆=

𝐼𝐷

𝑉𝐷𝑆= 𝐾𝑛 𝑉𝐺𝑆 − 𝑉𝑡ℎ −

𝑉𝐷𝑆

2

Set 𝑉𝐺𝑆 = 𝑉𝑡ℎ +𝑉𝐷𝑆

2+ 𝑉𝑐𝑜𝑛 by voltage summer,

get a voltage controlled resistor

𝑅𝐷𝑆 =1

𝐾𝑛𝑉𝑐𝑜𝑛 ……(1)

𝑅𝐵

If 𝑅𝐵 ≫ 𝑅𝐷𝑆

𝑽𝑫𝑺 =𝟏

𝑲𝒏𝑹𝑩

𝑽𝒊𝒏

𝑽𝒄𝒐𝒏 ……(2)

𝑽𝑫𝑺 is controlled by input voltage and control variable 2014/7/10 13

• VCCS & TWG


𝑉𝐷𝐷

+ amp1

𝑀2 𝑀3

𝑽𝑻

CLK

VCCS

𝐶𝑇

𝑅𝑐𝑠

𝑉𝑎

𝑉𝑏

𝑖𝑇

𝑖𝑐𝑠

𝑄1

𝑉𝐷𝑆

𝑖𝑇 = 𝑖𝐶𝑆 =𝑉𝑎−𝑉𝑏

𝑅𝐶𝑆=

𝑉𝐷𝑆

𝑅𝐶𝑆

-

amp2 -

+

𝑉𝑇 =𝑖𝑇

𝐶𝑇𝑡

Substitute Eq. (2)

𝑽𝑻 =𝑽𝒊𝒏

𝑲𝒏𝑹𝑩𝑹𝑪𝑺𝑪𝑻𝑽𝒄𝒐𝒏𝒕 = 𝑴

𝟏

𝑽𝒄𝒐𝒏, 𝑽𝒊𝒏 𝒕 ……(3)

2014/7/10 14

𝑉𝑜𝑢𝑡 =1

𝐿𝐶𝑠2 +𝐿𝑅𝑠 + 1

𝑉𝑖𝑛𝑉𝑃

𝑉𝐸

Improve Line Transient Response ------ Line feed-forward Control

Transfer function from error signal to output voltage (VMC buck converter)

Since 𝑉𝑝 = 𝑀𝑇𝑠, where M depend on 𝑉𝑖𝑛 (proportional) and 𝑉𝑐𝑜𝑛

Input voltage change effects are reduced.

2014/7/10 15

Improve Load Transient Response ------ Additional duty cycle modulation

∆𝑑1 is caused by slope modulation

∆𝑑1=𝑉𝐸

𝑇𝑠

1

𝑀1−

1

𝑀2=

𝑉𝐸

𝑇𝑠∆

1

𝑀

∆𝑑2 =𝐺𝑐∆𝑣

𝑇𝑠

1

𝑀1− ∆

1

𝑀=

𝐺𝑐∆𝑣

𝑇𝑠𝑀1−

𝐺𝑐∆𝑣

𝑇𝑠∆

1

𝑀

∆𝑑2 is caused by slope modulation and error signal modulation

∆𝒅 = ∆𝒅𝟏 + ∆𝒅𝟐=𝑽𝑬

𝑻𝒔−

𝑮𝒄∆𝒗

𝑻𝒔∆

𝟏

𝑴+

𝑮𝒄∆𝒗

𝑻𝒔𝑴𝟏 ……(4)

Conventional VMC Additional duty cycle modulation by proposed TWG 2014/7/10 16

Outline





• Conclusion

2014/7/10 17

System Block Diagram

∆𝒅 = ∆𝒅𝟏 + ∆𝒅𝟐≈ 𝑨∆𝒗 +𝑮𝒄

𝑽𝒑_𝒔𝒕𝒂𝒕𝒊𝒄∆𝒗

Ignore non-linear terms

𝐴 =𝐾𝑛𝑅𝐵𝑅𝐶𝑆𝐶𝑇𝑉𝐸𝐺𝑘

𝑇𝑠𝑉𝑖𝑛

𝑉𝑝_𝑠𝑡𝑎𝑡𝑖𝑐 = 𝑇𝑠𝑀1

Open-loop transfer function: T = 𝐴 +𝐺𝑐

𝑉𝑝_𝑠𝑡𝑎𝑡𝑖𝑐𝐺𝑣𝑑𝐻

2014/7/10 18

Example

Power Stage • 𝑉𝑖𝑛 = 5𝑉 • 𝑉𝑜𝑢𝑡 = 3.5𝑉 • 𝑉𝑝_𝑠𝑡𝑎𝑡𝑖𝑐 = 3𝑉

• 𝐿 = 10𝜇𝐻 (𝐸𝑆𝑅 = 10𝑚𝛺) • 𝐶 = 50𝜇𝐹(𝐸𝑆𝑅 = 10𝑚𝛺) • 𝑅 = 35𝛺 • 𝑓𝑠𝑤𝑖𝑡𝑐ℎ = 1𝑀𝐻

Phase Compensation • Type 3 compensation

• 𝑓𝑐 =𝑓𝑠𝑤𝑖𝑡𝑐ℎ

20= 50𝑘𝐻𝑧

• PM = 40° Design for conventional VMC

TWG • 𝐺𝑘 = 10 • 𝑅𝐵 = 1𝑘𝛺 • 𝐾𝑛 ≈ 3 • 𝑅𝑐𝑠 = 100𝛺 • 𝐶𝑇 = 50𝑝𝐹

𝑨 ≈ 𝟑𝟎

2014/7/10 19

Bode Plot

Compare to conventional VMC --- (𝐺𝑐𝐺𝑣𝑑/𝑉𝑝)

• Bandwidth is increased 50kHz 109kHz • Phase margin is decreased 40° 10 °

2014/7/10 20

Nyquist Plot

2014/7/10 21

Increase Phase Margin

Add a high frequency zero point to A: A A∗ 𝑠 + 𝜔ℎ

• Bandwidth 109kHz 130kHz • Phase Margin 10° 30 °

2014/7/10 22

Outline





• Conclusion

2014/7/10 23

Line Transient Response (1)

𝑉𝑖𝑛

𝑉𝑜𝑢𝑡

Without proposed TWG

With proposed TWG

𝑉𝑖𝑛: 5V ↔ 8V

( Simulation conditions is shown in P19) 2014/7/10 24

Line Transient Response (2) 𝑉 𝑜

𝑢𝑡

𝑉 𝐸 &

TW

P

WM

55mV 5mV

Without proposed TWG With proposed TWG 2014/7/10 25

Load Transient Response (1)

𝐼𝑜𝑢𝑡

𝑉𝑜𝑢𝑡

Without proposed TWG

With proposed TWG

320mA

𝐼𝑜𝑢𝑡: 100mA ↔ 420mA

2014/7/10 26

Load Transient Response (2) --- step up 𝑉 𝑜

𝑢𝑡

𝑉 𝐸 &

TW

P

WM

𝐼 𝐿 &

𝐼𝑜𝑢𝑡

14mV, 15𝜇𝑠 9mV, 6𝜇𝑠


Load Transient Response (3) --- step down 𝑉 𝑜

𝑢𝑡

𝑉 𝐸 &

TW

P

WM

𝐼 𝐿 &

𝐼𝑜𝑢𝑡

16mV, 22𝜇𝑠 10mV, 12𝜇𝑠


Outline





• Conclusion

2014/7/10 29

Conclusion

•Design a slope adjustable triangular wave generator for DC-DC converter. • Improve line and load transient response • Simple - Not require current sensor and slope compensation

•Next Step circuit implementation

2014/7/10 30

The End

Thanks for your attention

2014/7/10 31

Q&A

• Normally, we increased the feedback gain to improve transient response. So that, what is the advantage of your method, comparing to the normal method?

A: with a larger feedback gain, we can get higher bandwidth, but it is limited by the gain-bandwidth product of op-amp, especially, VMC need Type 3 compensation. The proposed method increase the open-loop bandwidth by a novel way. Although it also limited by op-amp, but not so much as conventional method.

• During line transient response, which parameter is changed?

A: Since the triangular wave slope is controlled by input voltage, it means the peak value of triangular wave --Vp also be controlled by input. During line transient response, the variation in Vin is eliminated by the changed Vp. 2014/7/10 32

transient response improvement of dc-dc buck …...transient response improvement of dc-dc buck...

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