A Novel Tri riangular Wave Slo lope Modulation for Im Improving - PowerPoint PPT Presentation

59 th System LSI Joint Seminar A Novel Tri riangular Wave Slo lope Modulation for Im Improving Dynamic Perf rformance of f DC-DC Buck Converter Shu Wu Division of Electronics and Informatics School of Science and Technology Gunma University 1

Outline • Background • Control schemes of buck converter • Triangular wave slope modulation • Circuit and principle • Stability analysis • Simulation • Conclusion 2

Outline • Background • Control schemes of buck converter • Triangular wave slope modulation • Circuit and principle • Stability analysis • Simulation • Conclusion 3

Background • Switching converter as a part of power supplies system is very impotent for various electronic devices (DC-DC converter, AC-DC rectifier, DC-AC inversion, AC-AC cycloconversion ) • Two concerned issues – Efficiency  Save energy  Control temperature (cost and stability) – Reliability  Stability  Dynamic performance 4

Motivation • 3 disturbance sources • Output reference signal  Band-gap reference • Input voltage  Line feed-forward control • Load  Trouble • Continuous advancement of integrated circuits • Faster and faster dynamic current slew rate (120A/us) • Lower and lower voltage (0.8V for subthreshold operated circuit) Dynamic performance improvement of power supplies 5

Outline • Background • Control schemes of buck converter • Triangular wave slope modulation • Circuit and principle • Stability analysis • Simulation • Conclusion 6

Feedback control scheme ------ Voltage-Mode Control 7

Feedback control scheme ------ Current-Mode Control 8

Feedback control scheme ------ Hysteretic Control 9

Phase compensation for VMC and CMC Type 2 compensator • Not be required in Hysteretic control • Realize by the error Type 3 compensator amplifier • Type 2 for CMC • Type 3 for VMC 10

GBP constraint for Type 3 compensator (GBP---the Gain Bandwidth Product of op-amp) Type 3 : • Large gain at high frequency • Increase phase margin Severe GBP constraint VMC cannot has wider band 11

Advantages and Disadvantages VMC CMC Hysteretic control • Easy loop analysis • Inherent line feed-forward • Simple • Fixed switching frequency • Wider band • Fast transient • Fixed switching frequency • No line feed-forward • Current sensor • Variable switching • Low bandwidth • Slope compensation frequency • Blanking time • Large output ripple (GBP of op-amp) The slowest The fastest This research is based on VMC 12

Objective of this research • Triangular wave slope modulation  Based on VMC Fixed switching frequency No require current sensor, slope compensation, and blanking time  The slope depends on input and output voltage Line feed-forward control Wider band Non-linearly changed loop gain The line and load transient response both are improved 13

Outline • Background • Control schemes of buck converter • Triangular wave slope modulation • Circuit and principle • Stability analysis • Simulation • Conclusion 14

System configuration Op-amp1 : • Generate control variable 𝑊 𝑑 • Type 3 compensation Op-amp2 : • Amplify deviation • Control variable of TWG TWG (Triangular Wave Generator) : Slope adjustable Controlled by 𝑊 𝑕 and 𝑊 • 𝑑𝑝𝑜 15

Triangular Wave Generator (1) Part 1 Part 2 VCCS VCR-- 𝑆 𝐸𝑇 VCR: Voltage Controlled Resistor 16 VCCS: Voltage Controlled Current Source

Triangular Wave Generator (2)---Part 1 • VCR NMOS 𝑁 1 operates in triode region Equivalent resistor: 𝑾 𝒉 𝑾 𝒅𝒑𝒐 1 𝐽 𝐸 𝑊 𝐸𝑇 𝑆 𝐸𝑇 = 𝑊 𝐸𝑇 = 𝐿 𝑜 𝑊 𝐻𝑇 − 𝑊 𝑢ℎ − 𝑆 𝑐 𝑆 𝑐 2 Op-amp3 𝑊 𝑊 𝑢ℎ 𝐻 3 ∆𝑊 𝐸𝑇1 𝐸𝑇 + 𝑊 𝐸𝑇 Set 𝑊 𝐻𝑇 = 𝑊 𝑢ℎ + 2 + 𝑊 𝑊 𝑑𝑝𝑜 𝐸𝑇2 - + + + Voltage 𝟐 𝑺 𝑬𝑻 = Summer 𝑳 𝒐 𝑾 𝒅𝒑𝒐 𝑊 𝑑_𝑛𝑏𝑦 If 𝑆 𝑐 ≫ 𝑆 𝐸𝑇 𝑁 1 𝑁 2 𝑊 1 𝑕 𝑊 𝐸𝑇 ≈ VCR-- 𝑆 𝐸𝑇 𝐿 𝑜 𝑆 𝑐 𝑊 𝑑𝑝𝑜 𝑯 𝟒 𝑾 𝒉 𝟐 𝟐 ※ 𝑳 𝒐 = 𝝂 𝒐 𝑫 𝒑𝒚 𝑿 𝑴 𝑯 𝟒 ∆𝑾 𝑬𝑻 = − 𝑳 𝒐 𝑺 𝒄 𝑾 𝒅𝒑𝒐 𝑾 𝒅𝒑𝒐_𝒏𝒃𝒚 𝑾 𝑬𝑻 𝑾 𝒅_𝒏𝒃𝒚 = 𝑾 𝒖𝒊 + 𝟑 + 𝑾 𝒅𝒑𝒐_𝒏𝒃𝒚 17

Triangular Wave Generator (3)---Part 2 • VCCS & TWG 𝑊 𝑏 −𝑊 𝑐 𝐻 3 ∆𝑊 𝐸𝑇 𝑊 𝑗 𝐷 = 𝑗 𝐷𝑇 = 𝑆 𝐷𝑇 = 𝐸𝐸 𝑆 𝐷𝑇 𝑗 𝑑 𝑊 𝑢𝑠𝑗 = 𝐷 𝑑 𝑢 VCCS 𝑁 3 𝑁 4 𝐻 3 ∆𝑊 Op-amp4 𝐸𝑇 𝑗 𝑑 𝑾 𝒖𝒔𝒋 + 1 𝑊 𝑢𝑠𝑗 = 𝑏 ∙ 𝑊 𝑕 ∙ 𝑑𝑝𝑜 − 𝑐 𝑢 = 𝑁 𝑊 𝑕 , 𝑊 𝑑𝑝𝑜 ∙ 𝑢 Q 𝑊 - 𝑊 𝑏 𝐷 𝑑 1 𝐻 3 𝑐 = 𝑏 = 𝑆 𝑑𝑡 𝑗 𝑑𝑡 Where 𝑊 𝐿 𝑜 𝑆 𝐶 𝑆 𝐷𝑇 𝐷 𝑑 𝑑𝑝𝑜_𝑛𝑏𝑦 + CLK 𝑊 𝑐 - 1 𝑁 ∝ 𝑊 𝑕 , 𝑁 ∝ Op-amp5 𝑊 𝑑𝑝𝑜 18

Line feed-forward control (1) Transfer function from control variable to output voltage (VMC buck converter) 𝑊 1 𝑕 𝑊 𝑝𝑣𝑢 = 𝑊 𝑑 𝑀𝐷𝑡 2 + 𝑀 𝑊 𝑆 𝑡 + 1 𝑄 𝑊 𝑊 𝑊 𝑊 𝑝𝑣𝑢 Conventional VMC: 𝑑 𝑝𝑣𝑢 𝑕 Output voltage return to the reference 𝑊 𝑄 --- the peak of triangular wave 19

Line feed-forward control (2) 𝑊 𝑊 Line feed-forward: 𝑄 𝑕 1 1 𝑑𝑝𝑜 − 𝑑𝑝𝑜_𝑛𝑏𝑦 𝐻 3 𝑈 𝑡 𝑊 𝑊 𝑊 𝑞 = 𝑁 𝑊 𝑕 , 𝑊 𝑑𝑝𝑜 ∙ 𝑈 𝑡 = ∙ 𝑊 𝑕 𝐷 𝐷 𝑆 𝐷𝑇 𝑆 𝑐 𝐿 𝑜 The input variation is eliminated by the proportional variation in 𝑊 𝑄 Nothing to do with 𝑊 𝑝𝑣𝑢 and 𝑊 𝑑 *The changed 𝑊 𝑕 cause the ripple of inductor current is changed During line transient response, 𝑱 𝑴 ≠ 𝑱 𝒑𝒗𝒖 . Similar to load transient response Line feed-forward only consider the input voltage variation 20

Non-linear duty cycle modulation(1) Once output voltage deviate from the reference, whatever the reason ∆𝑒 1 is caused by slope modulation ∆𝑒 1 = 𝑊 1 − 1 = 𝑊 ∙ ∆ 1 𝐷 𝐷 ∙ 𝑈 𝑛 2 𝑛 1 𝑈 𝑛 𝑡 𝑡 ∆𝑒 2 is caused by slope and 𝑾 𝒅 modulations ∆𝑒 2 = 𝐻 𝑑 ∆𝑤 ∙ 1 = 𝐻 𝑑 ∆𝑤 1 + ∆ 1 ∙ 𝑈 𝑛 2 𝑈 𝑛 1 𝑛 𝑡 𝑡 ∆𝒆 = ∆𝒆 𝟐 + ∆𝒆 𝟑 = 𝑾 𝑫 + 𝑯 𝒅 ∆𝒘 ∙ ∆ 𝟐 𝒏 + 𝑯 𝒅 ∆𝒘 𝑼 𝒕 𝑾 𝒒_𝒕𝒕 Additional duty cycle modulation Conventional VMC by proposed TWG 21 𝑊 𝑞_𝑡𝑡 = 𝑛 1 𝑈 𝑡

Non-linear duty cycle modulation(2) ∆𝑒 ∆𝑤 = A ∆𝑤 ∙ ∆𝑤 + 𝐻 𝑑 ∆𝑤 𝑊 𝑞_𝑡𝑡 𝑊 𝐷 + 𝐻 𝑑 ∆𝑤 𝐻 𝑙 A ∆𝑤 = 𝑈 𝑡 ∙ 𝑏 ∙ 𝑊 𝑕 𝑐 𝑊 𝑠𝑓𝑔 − 𝐻 𝑙 ∆𝑤 − 1 ∙ 𝑐𝑊 𝑠𝑓𝑔 − 1 Enable fast transient response Large Large A ∆𝑤 ∆𝑤 Non-linearly change To ensure the loop stability approach to 0 approach to a constant 𝑊 𝐷 𝐻 𝑙 A 0 = 2 𝑈 𝑡 ∙ 𝑏 ∙ 𝑐𝑊 𝑠𝑓𝑔 − 1 22

Outline • Background • Control schemes of buck converter • Triangular wave slope modulation • Circuit and principle • Stability analysis • Simulation • Conclusion 23

System block diagram 𝑊 𝐷 𝐻 𝑙 A 0 = 2 𝑈 𝑡 ∙ 𝑏 ∙ 𝑐𝑊 𝑠𝑓𝑔 − 1 Conventional VMC 𝑈 𝑡 = 𝐵 0 ∙ 𝐼 𝑡 ∙ 𝐻 𝑤𝑒 𝑡 + 𝐼 𝑡 𝐻 𝑑 𝑡 𝐻 𝑤𝑒 𝑡 𝐵 0 + 𝐻 𝑑 𝑡 𝑈 𝑡 = ∙ 𝐼 𝑡 ∙ 𝐻 𝑤𝑒 𝑡 𝑊 𝑊 𝑞_𝑡𝑡 𝑞_𝑡𝑡 24

Bode plot Buck converter with conventional VMC: TWG: 𝑔 𝑑 = 𝑔 𝑡 20 = 50𝑙𝐼𝑨 , 𝜒 𝑛 = 40° 𝐵 0 ≈ 6.65 Compared to conventional VMC --- ( 𝐻 𝑑 𝐻 𝑤𝑒 /𝑊 𝑞 ) • Bandwidth increase 50kHz  68kHz • Phase margin decrease 40 °  17 ° Oscillation, even unstable 25

Nyquist plot In order to get enough phase margin Method 1: Increase the high-frequency phase of 𝐻 𝑑 𝑡 𝐻 𝑤𝑒 𝑡 𝑊 𝑞_𝑡𝑡 Method 2: Increase the high-frequency phase of 𝐵 0 𝐻 𝑤𝑒 𝑡 26

Two methods for enough phase margin Method 1 Method 2 TWG phase compensation • Crossover frequency decrease  • Crossover frequency increase  • Impossible (GBP of op-amp1)  • Easy  Add a high-frequency zero in TWG 27

TWG phase compensation 𝐻 6 𝑡 = 𝑆 2 𝐷 1 𝑆 1 𝑡 + 1 𝑆 1 𝒈 𝒅 = 𝟗𝟓𝒍𝑰𝒜 𝝌 𝒏 = 𝟒𝟗° 28

Outline • Background • Control schemes of buck converter • Triangular wave slope modulation • Circuit and principle • Stability analysis • Simulation • Conclusion 29