ISPACS2017 Paper 2017 ID 21 Nov. 9 NQ-L5 Paper ID 21, Estimation of Circuit Component Values in Buck Converter using Efficiency Curve S. Sakurai, N. Tsukiji, Y. Kobori, H. Kobayashi Gunma University 1/36
Outline 2/33 1. Purpose of this work 2. Background 3. Estimation principle 4. Estimation result 5. Summary
Outline 3/33 1. Purpose of this work 2. Background 3. Estimation principle 4. Estimation result 5. Summary
Purpose of this work 4/33 Development of an estimation method for component values in DC-DC converter from its measured efficiency curve Validation of its transfer function estimation for phase compensation design with estimated component values
Outline 5/33 1. Purpose of this work 2. Background 3. Estimation principle 4. Estimation result 5. Summary
Background 6/33 Electronic Devices Switching converter IoT Device Information Device rds1 L ESR rl Vout Demands Vin PWM Gate Drivers PWM Generator rds2 SAW ESR rc C Error Amplifier Rload Smaller Lighter Higher efficiency
Negative Feedback Circuit 7/33 Switching converter use negative feedback control When loop gain Aβ = 1, circuit oscillates. Need suitable phase compensation. v o v in = A 1 + Aβ 0 db Amplifier Feedback gain -180
Phase Compensation Design 8/33 rds1 L ESR rl Vout Phase Compensation Network Vin Gate Drivers rds2 ESR rc C Rload PWM PWM Generator SAW Error Amplifier エラーアンプ Error Amplifier Vin rds1 L rds2 ESR rl ESR rc C Vout G dv s ቚ Vi =0 I o =0 = ΔV o D 2 ω n s 2 2 + 2ζω n s + ω n Transfer function of power stage Power stage is necessity
Gain [db] Phase [deg] Power-Stage Transfer Function and Component Values 9/33 G dv s ቚ Vi =0 I o =0 = ΔV o D = ζ = r L + r C + r ds 2 2 ω n s 2 2 + 2ζω n s + ω n V i ω n 2 s 2 + 2ζω n s + ω n 2 1 + s ω esr C L,ω n = 1 LC,ω esr = 1 Cr c Damping factor ζ 60 40 20 Solid line: Gain Dashed line: Phase ζ:small ζ:large 180 120 60 0 0 1,000 10K 100K -20-60 ζ Gain Phase Larger Peak Looser -40-120 Smaller No peak Steeper -60 Frequency [Hz] -180
Gain [db] Phase [deg] Importance of Component Values 10/33 ζ depends on circuit component values ζ = r L + r ds + r C 2 C L 60 40 Solid line: Gain Dashed line: Phase ζ:small 180 120 20 60 rds1 L ESR rl Vout ζ:large Vin rds2 ESR rc C 0 0 1,000 10K 100K -20-60 Necessary for phase compensation design -40-60 Frequency [Hz] -120-180
Problems 11/33 Implemented power supply Component values rds1 L ESR rl Vout Vin rds2 ESR rc C Difficult to measure
Efficiency η[%] Proposed method 12/33 Implemented power supply Component values rds1 L ESR rl Vout Vin rds2 ESR rc C Easy Measure efficiency curve Estimate Our proposal Not directly measure. Output current[a] Estimation from measured efficiency curve.
Outline 13/33 1. Purpose of this work 2. Background 3. Estimation principle 4. Estimation result 5. Summary
Efficiency η[%] Efficiency η[%] Estimation Principle 14/33 Measured efficiency Theoretical formula of losses P sw loss = 1 6 V ii o ΔT ON + ΔT OFF f sw P L = R L I o 2 P C = R C I C 2 η = V out I o V out I o + P loss Output current[a] Fitted efficiency curve Fitting Component values rds1 L ESR rl Vout Vin rds2 ESR rc C Output current[a]
15/33 Loss Classification of Switching Regulator Rds1 loss position Vi L ESR RL Vo Rds2 ESR RC C Rload 1. Proportional to the load current :P 1 [W] Switching loss 2. Proportional to square of the load current :P 2 [W] Conduction loss 3. Constant loss :P const [W]
Switching Loss (P 1 ) 16/33 First loss Vi Io ΔTon Io ΔToff Vi 0V 0A P sw loss = f sw න 0 ΔT onvtr ΔT offvtr t i tr t dt + න t i tr t dt 0 = 1 6 V i I o ΔT ON + ΔT OFF f sw V i :Drain-source voltage [V] I o :Load current [A]
Conduction Loss of L, C (P 2 ) 17/33 Second loss ESR (Equivalent Series Resistance) Rds1 L ESR RL Vo I 2 R drop by lead, metal coating Vi ION Rds2 IOFF ESR RC C Rload Caused by resistances of cable, metal Inductor loss P L = R L I o 2 Capacitor loss P C = R C I c 2 I C I o R L :Inductor ESR I o :Load current R C :Capacitor ESR I c :Ripple current
MOSFET Conduction Loss (P 2 ) 18/33 Second loss MOSFET Conduction loss i ON t on t off t on t off Rds1 I t I o I b i OFF I Vi ION L Rds2 ESR RL IOFF ESR RC C Vo Rload I t I o I b I V o V in 1 V o V in P cond1 I o 2 + ΔI2 12 R ds1 P cond2 I o 2 + ΔI2 12 R ds2 P cond = I o 2 V o V in R ds1 R ds2 + R ds2 I o :Load current ΔI: Ripple current R DS1 :High-side MOS resistance R DS2 :Low-side MOS resistance
Loss Equations 19/33 First loss:p 1 P sw loss = 1 6 V ii o ΔT ON + ΔT OFF f sw Second losses:p 2 P L = R L I o 2 P C = R C I c 2 I C I o P cond = I o 2 V o V in R ds1 on R ds2 on + R ds2 on Constant loss:p const Control stage Error amp Comparator Gate driver Quiescent current Given as constant
Loss Equations - Highlight 20/33 Most important! Second order losses:p 2 2 2 P L = R L I o P C = R C I c I C I o P cond = I o 2 V o V in R ds1 on R ds2 on + R ds2 on Component values rds1 L ESR rl Vout Vin rds2 ESR rc C
Efficiency η Losses and Efficiency 21/33 P 2 = P MOS + P L + P C = K 2 I o 2 100% P 1 = P sw = K 1 I o P const 90% P loss = P 2 + P 1 + P const 80% Efficiency 70% point:measured line:calculated η = V out I o V out I o + P loss 60% 0 0.5 1 1.5 2 2.5 3 Load current[a] Fitting between calculation and measurement
Efficiency η[%] Effect of Each Loss to Efficiency 22/33 For load current increase Constant loss First loss First loss constant Second loss decrease Efficiency Second loss Constant loss log increase Load current Io[A]
Outline 23/33 1. Purpose of this work 2. Background 3. Estimation principle 4. Estimation result 5. Summary
Experiment Conditions 24/33 Synchronous step-down DC/DC converter (TPS54317 Texas Instruments) Only measured efficiency curve used Inductor ESR High side MOS DC resistance MOSFET Turn on time Constant loss Input Voltage V i 3.0V/4.0V/5.0V/6.0V Output Voltage V o 1.8V Switching frequency f sw Inductor L Capacitor C Estimation parameters Setting parameter Capacitor ESR Low side MOS DC resistance MOSFET Turn off time 550kHz 1μH 200μF(100uF*2+1.0nF)
Efficiency [%] Fitting Result 25/33 0.95 Second loss 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 3VFit 4VFit 5VFit 6VFit 3V 4V 5V 6V Slope is coincide. Line :calculated value Point :measured value 0 0.5 1 1.5 2 Load Current [A]
Differential Error [%] Fitting Result Error 26/33 0.80 0.60 0.40 0.20 0.00-0.20-0.40-0.60-0.80-1.00 Constant slope Second loss matched Second loss 0 0.5 1 1.5 2 Load Current [A] 3V 4V 5V 6V
Efficiency [%] Component Value Estimation Result 27/33 Estimation result Inductor ESR 10mΩ Capacitor ESR 1mΩ Load Current [A] Turn-on time of MOSFET T on Turn-off time of MOSFET T off 2nsec 4nsec High side ON resistor of MOSFET R ds1 Low side ON resistor of MOSFET R ds2 Quiescent current of IC I IC. 30mΩ at 3V 20mΩ at 4V 15mΩ at 5V 10mΩ at 6V 45mΩ at 3V 30mΩ at 4V 24mΩ at 5V 20mΩ at 6V 4.8mA at 3V 5.1mA at 4V 5.2mA at 5V 5.3mA at 6V
Transfer Function Calculation 28/33 Transfer function of power stage is necessary for phase compensation Possible to use estimated values Parameters of G dv at 3.0V Switching Frequency f sw 550kHz Input Voltage V i 3.0V Inductor L 0.8μH Capacitor C 160μF Inductor ESR r L 10mΩ Capacitor ESR r C 1mΩ High side MOSFET DC resistance r ds1 30mΩ Low side MOSFET DC resistance r ds2 45mΩ
Gain [db] Phase [deg] Transfer Function Comparison 29/33 40 20 0 90 45 0-20 -40-60 -80 Estimated Gain Measured Gain Estimated Phase Measured Phase -100 100 1K 10K 100K Frequency [Hz] -45-90 -135-180 -225
Gain [db] Phase [deg] Transfer Function Comparison 30/33 40 20 0 Almost match 90 45 0-20 -40-60 -80 Estimated Gain Measured Gain Estimated Phase Measured Phase -100 100 1K 10K 100K Frequency [Hz] Estimation result can be used for phase compensation -45-90 -135-180 -225
Outline 31/33 1. Purpose of this work 2. Background 3. Estimation principle 4. Estimation result 5. Summary
Summary 32/33 Proposed a method to derive DC-DC converter component values from measured efficiency curve. Calculated the transfer function of power stage using estimation result. Measured and estimated results are well matched.
Future Research 33/33 More experiment for validation Design of phase compensation using estimation result. More accurate fitting incorporate losses not considered.
Back Up 34/33
Power stage transfer function 35/33 Power stage transfer function at open loop G dv s ቚ Vi =0 I o =0 = ΔV o D = = 2 V i ω n s 2 2 + 2ζω n s + ω 1 + s n ω esr V i 1 + jωcr c 1 ω 2 LC + jωc(r L + r c + r ds ) ζ = r L + r C + r ds 2 C L,ω n = 1 LC,ω esr = 1 Cr c Parameter of G dv at 3.0V Switching Frequency f sw 550kHz Input Voltage V i 3.0V Inductor L 0.8μH Capacitor C 160μF Inductor ESR r L 10mΩ Capacitor ESR r C 1mΩ High side MOSFET DC resistance r ds1 30mΩ Low side MOSFET DC resistance r ds2 45mΩ