dynamic performance improvement of dc-dc buck …...•design a slope adjustable triangular wave...

Voltage Mode Control Using Triangular Wave Slope Modulationfor DC-DC Buck Converter

Shu WU, Yasunori KOBORI, Nobukazu Tsukiji , Haruo KOBAYASHI

Division of Electronics and Informatics

Gunma University

November 10, 2014

1

第57回自動制御連合講演会10th ~11th November, Gunma

OUTLINE

• Research Objective• Proposed Triangular Wave Generator

• Slope Adjustable Triangular Wave Generator• Improvement of Transient Response • Stability Analysis

• Simulation Results• Line Transient Response• Load Transient Response

• Conclusion

2

OUTLINE




• Conclusion

3

Transient Response

• 3 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

4

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

• Easy to design and analyze• Without line feed-forward control• Limited bandwidth: slow response

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

•Feed-forward Complicated non-linear calculation 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 or slope compensation

• Slope is regulated by input and output voltages:compared to conventional VMC

---Provide line feed-forward control and wideband• Simple:

compared to previous feed-forward control ---Not require complicated calculation

6

OUTLINE




• Conclusion

7

System Configuration

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

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

TWG (Triangular Wave Generator):Slope adjustable• Controlled by 𝑉𝑖𝑛 and 𝑉𝑐𝑜𝑛

8

Triangular Wave Generator (1)

VCR: Voltage Controlled ResistorVCCS: Voltage Controlled Current Source 9

𝑅𝐵

𝑽𝒄𝒐𝒏

𝑉𝐷𝑆2𝑉𝑡ℎ

+ ++

Voltage Summer

𝑀1

𝑉𝐷𝐷

Voltage Divider

VCR--𝑅𝐷𝑆

𝑽𝒊𝒏

+

-

+

-

𝑀3 𝑀4

𝑽𝒕𝒓𝒊

CLK

VCCS𝑉𝐷𝑆1

𝐶𝑇

𝑅𝑐𝑠

𝑉𝑎

𝑉𝑏

𝑖𝑇

𝑖𝑐𝑠

𝑄1

𝑅𝐵

𝑉𝐷𝑆2

𝑀2

𝑉𝑐_𝑚𝑎𝑥

+

-Op-amp3

𝐺3∆𝑉𝐷𝑆

Part 1 Part 2

Op-amp4

Op-amp5

•VCR

Triangular Wave Generator (2)---Part 1

NMOS 𝑀1 operates in triode regionEquivalent resistor:1

𝑅𝐷𝑆=

𝐼𝐷

𝑉𝐷𝑆= 𝐾𝑛 𝑉𝐺𝑆 − 𝑉𝑡ℎ −

𝑉𝐷𝑆

2

𝑅𝐷𝑆 =1

𝐾𝑛𝑉𝑐𝑜𝑛

If 𝑅𝐵 ≫ 𝑅𝐷𝑆

𝑉𝐷𝑆 ≈1

𝐾𝑛𝑅𝐵

𝑉𝑖𝑛

𝑉𝑐𝑜𝑛

10

Set 𝑉𝐺𝑆 = 𝑉𝑡ℎ +𝑉𝐷𝑆

2+ 𝑉𝑐𝑜𝑛

𝑅𝐵

𝑽𝒄𝒐𝒏

𝑉𝐷𝑆2𝑉𝑡ℎ

+ ++

Voltage Summer

𝑀1

Voltage Divider

VCR--𝑅𝐷𝑆

𝑽𝒊𝒏

𝑉𝐷𝑆1

𝑅𝐵

𝑉𝐷𝑆2

𝑀2

𝑉𝑐_𝑚𝑎𝑥

+

-


※ 𝑲𝒏 = 𝝁𝒏𝑪𝒐𝒙𝑾 𝑳

𝑽𝒄_𝒎𝒂𝒙 = 𝑽𝒕𝒉 +𝑽𝑫𝑺

𝟐+ 𝑽𝒄𝒐𝒏_𝒎𝒂𝒙

𝑮𝟑∆𝑽𝑫𝑺 =𝑮𝟑𝑽𝒊𝒏

𝑲𝒏𝑹𝑩

𝟏

𝑽𝒄𝒐𝒏−

𝟏

𝑽𝒄𝒐𝒏_𝒎𝒂𝒙

Op-amp3

• VCCS & TWG

Triangular Wave Generator (3)---Part 2

𝑉𝐷𝐷

+

𝑀2 𝑀3

𝑽𝒕𝒓𝒊

CLK

VCCS

𝐶𝑇

𝑅𝑐𝑠

𝑉𝑎

𝑉𝑏

𝑖𝑇

𝑖𝑐𝑠

𝑄1

𝑖𝑇 = 𝑖𝐶𝑆 =𝑉𝑎−𝑉𝑏

𝑅𝐶𝑆=


𝑅𝐶𝑆

-

-

+

𝑉𝑡𝑟𝑖 =𝑖𝑇

𝐶𝑇𝑡

𝑉𝑡𝑟𝑖 = 𝑉𝑖𝑛 𝑎1

𝑉𝑐𝑜𝑛− 𝑏 𝑡 = 𝑀 𝑉𝑖𝑛, 𝑉𝑐𝑜𝑛 𝑡

11


𝑎 =𝐺3

𝐾𝑛𝑅𝐵𝑅𝐶𝑆𝐶𝑇𝑏 =

𝑎

𝑉𝑐𝑜𝑛_𝑚𝑎𝑥Where

𝑀 ∝ 𝑉𝑖𝑛 , 𝑀 ∝1

𝑉𝑐𝑜𝑛

,

Op-amp4

Op-amp5

𝑉𝑜𝑢𝑡 =1

𝐿𝐶𝑠2 +𝐿𝑅𝑠 + 1

𝑉𝑖𝑛𝑉𝑃

𝑉𝐸

Line Transient Response Improvement------ Line feed-forward control

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

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

Input voltage change effects are reduced.

12𝑉𝑃 --- the peak of triangular wave

Load Transient Response Improvement (1)------ Additional duty cycle modulation

∆𝑑1 is caused by slope modulation

∆𝑑1=𝑉𝐸

𝑇𝑠

1

𝑀2−

1

𝑀1=

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 and error modulations

∆𝒅 = ∆𝒅𝟏 + ∆𝒅𝟐=𝑽𝑬

𝑻𝒔+

𝑮𝒄∆𝒗

𝑻𝒔∆

𝟏

𝑴+

𝑮𝒄∆𝒗

𝑻𝒔𝑴𝟏

Conventional VMC--∆𝑑𝑒Additional duty cycle modulation by proposed TWG--∆𝑑𝑠 13

𝑽𝒑_𝒔𝒕𝒂𝒕𝒊𝒄 = 𝑻𝒔𝑴𝟏

14

∆𝑑 =𝑉𝐸𝑇𝑠

+𝐺𝑐∆𝑣

𝑇𝑠

𝑉𝑟𝑒𝑓 + 𝐺𝑘∆𝑣

𝑉𝑖𝑛 𝑎 − 𝑏 𝑉𝑟𝑒𝑓 + 𝐺𝑘∆𝑣−

𝑉𝑟𝑒𝑓

𝑉𝑖𝑛 𝑎 − 𝑏𝑉𝑟𝑒𝑓+

𝐺𝑐∆𝑣

𝑉𝑝_𝑠𝑡𝑎𝑡𝑖𝑐

∆𝑑 = 𝐴∆𝑣 +𝐺𝑐∆𝑣

𝑉𝑝_𝑠𝑡𝑎𝑡𝑖𝑐

𝐴 ∆𝑣 =𝑎𝐺𝑘 𝑉𝐸 + 𝐺𝑐∆𝑣

𝑇𝑠𝑉𝑖𝑛 𝑎 − 𝑏𝑉𝑟𝑒𝑓 𝑎 − 𝑏𝑉𝑟𝑒𝑓 − 𝑏𝐺𝑘∆𝑣

∆𝑣

Large Large

approach to 0

𝐴

approach to a constant

Non-linearly change

Enable fast transient response

To ensure the loop stability

Load Transient Response Improvement (2)------ Non-linear control features

System Block Diagram

Supposing ∆𝑣 is enough small, and A is approximated as constant

Open-loop transfer function: T = 𝐴 +𝐺𝑐

𝑉𝑝_𝑠𝑡𝑎𝑡𝑖𝑐𝐺𝑣𝑑𝐻

2014/7/10 15

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 16

Bode Plot

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

• Bandwidth is increased50kHz 109kHz

• Phase margin is decreased40° 10 °

2014/7/10 17

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 18

OUTLINE




• Conclusion

19

Line Transient Response (1)

𝑉𝑖𝑛

𝑉𝑜𝑢𝑡

Without proposed TWG

With proposed TWG

𝑉𝑖𝑛: 5V ↔ 8V

( Simulation conditions are shown in P16) 20

Simulation Tools: SIMetrix 6.2

Line Transient Response (2)𝑉 𝑜

𝑢𝑡

𝑉 𝐸&

TW

PW

M

55mV 5mV

Without proposed TWG With proposed TWG 21

Load Transient Response (1)

𝐼𝑜𝑢𝑡

𝑉𝑜𝑢𝑡

Without proposed TWG

With proposed TWG

320mA

𝐼𝑜𝑢𝑡: 100mA ↔ 420mA

22

Load Transient Response (2) --- step up𝑉 𝑜

𝑢𝑡

𝑉 𝐸&

TW

PW

M𝐼 𝐿

& 𝐼𝑜𝑢𝑡

14mV, 15𝜇𝑠 9mV, 6𝜇𝑠

Without proposed TWG With proposed TWG 23

Load Transient Response (3) --- step down𝑉 𝑜

𝑢𝑡

𝑉 𝐸&

TW

PW

M𝐼 𝐿

& 𝐼𝑜𝑢𝑡

16mV, 22𝜇𝑠 10mV, 12𝜇𝑠

Without proposed TWG With proposed TWG24

OUTLINE




• Conclusion

25

Conclusion

•Design a slope adjustable triangular wave generatorfor DC-DC converter.• Line and load transient response improvement• Simple

- Not require current sensor or slope compensation

•Next StepCircuit implementation

2014/7/10 26

The End

Thanks for your attention

27

Q&A

• The proposed method causes the phase margin decrease. How do you deal with this problem?

A: the reason of phase margin decrease is the phase of additional feedback loop (A*Gvd) is too low. Therefore I try to increase the phase of A*Gvd at high frequency. We can add a high-frequency zero point in A. This can be realized through insert a appropriate capacitor in op-amp2 (Page 8) or op-amp3 (Page 9). By this way, the phase of A*Gvd is increased at the crossover frequency, the phase margin also increase.

28

dynamic performance improvement of dc-dc buck …...•design a slope adjustable triangular wave...

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