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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
• 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
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
• 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
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
+
-
𝐺3∆𝑉𝐷𝑆
※ 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=
𝐺3∆𝑉𝐷𝑆
𝑅𝐶𝑆
-
-
+
𝑉𝑡𝑟𝑖 =𝑖𝑇
𝐶𝑇𝑡
𝑉𝑡𝑟𝑖 = 𝑉𝑖𝑛 𝑎1
𝑉𝑐𝑜𝑛− 𝑏 𝑡 = 𝑀 𝑉𝑖𝑛, 𝑉𝑐𝑜𝑛 𝑡
11
𝐺3∆𝑉𝐷𝑆
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
• 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
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
• 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
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
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