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- 1. 1 Steady-state Equivalent CircuitModeling Dr. Edgar Sánchez-Sinencio ECEN 489 Power Management Circuits and Systems Spring 2018 Equivalent Circuit Modeling: Efficiency and feedback control
- 2. 2 Steady-state Equivalent CircuitModeling • The dc transformer model – Inclusion of inductor copper loss – Construction of equivalent circuit model – Efficiency analysis • SPICE simulation of dc-dc converters – Switched Spice model – Averaged switch model • dc-dc converter control Outline
- 3. 3 Steady-state Equivalent CircuitModeling The dc transformer model Ideally, the converter performs with η = 100% 𝑃𝑖𝑛 = 𝑃𝑜𝑢𝑡 𝑉 𝑔𝐼𝑔 = 𝑉𝐼 𝑉 = 𝑀 𝐷 𝑉 𝑔 𝐼𝑔 = 𝑀 𝐷 𝐼 (ideal conversion ratio) These equations are valid only under equilibrium (dc) conditions. During transients, energy storage within filter elements may cause 𝑃𝑖𝑛 ≠ 𝑃𝑜𝑢𝑡
- 4. 4 Steady-state Equivalent CircuitModeling Corresponding equivalent circuits 𝑃𝑖𝑛 = 𝑃𝑜𝑢𝑡 𝑉 𝑔𝐼𝑔 = 𝑉𝐼 𝑉 = 𝑀 𝐷 𝑉 𝑔 𝐼𝑔 = 𝑀 𝐷 𝐼
- 5. 5 Steady-state Equivalent CircuitModeling Example: use of the DC transformer model
- 6. 6 Steady-state Equivalent CircuitModeling Inclusion of inductor copper loss
- 7. 7 Steady-state Equivalent CircuitModeling Analysis of non-ideal boost converter
- 8. 8 Steady-state Equivalent CircuitModeling Switch in position 1
- 9. 9 Steady-state Equivalent CircuitModeling Switch in position 2
- 10. 10 Steady-state Equivalent CircuitModeling Inductor voltage and capacitor current waveforms
- 11. 11 Steady-state Equivalent CircuitModeling Solution for output voltage RL limits the maximum output voltage the converter can produce. What is the solution and what are the trade- offs?
- 12. 12 Steady-state Equivalent CircuitModeling Construction of equivalent circuit model
- 13. 13 Steady-state Equivalent CircuitModeling Inductor voltage equation
- 14. 14 Steady-state Equivalent CircuitModeling Capacitor current equation
- 15. 15 Steady-state Equivalent CircuitModeling Complete equivalent circuit
- 16. 16 Steady-state Equivalent CircuitModeling Solution of equivalent circuit
- 17. 17 Steady-state Equivalent CircuitModeling Solution for input (inductor) current
- 18. 18 Steady-state Equivalent CircuitModeling Solution for converter efficiency
- 19. 19 Steady-state Equivalent CircuitModeling Efficiency for different values of RL
- 20. 20 Steady-state Equivalent CircuitModeling Switched SPICE Model
- 21. 21 Steady-state Equivalent CircuitModeling Transient Start-up
- 22. 22 Steady-state Equivalent CircuitModeling Averaged Circuit Model
- 23. 23 Steady-state Equivalent CircuitModeling Averaged Circuit Model Simulation
- 24. 24 Steady-state Equivalent CircuitModeling Switched vs Averaged Simulation
- 25. 25 Steady-state Equivalent CircuitModeling Averaged Switch Model in dc-dc Converters Buck Converter Boost Converter Buck-Boost Converter
- 26. 26 Steady-state Equivalent CircuitModeling Small-Signal Analysis Control loop analysis is based on dynamic behavior of voltages, currents, and switching. This can be described in terms of small-signal variations around a steady-state operating point. Steady-state (dc) term Small-signal (ac) perturbation
- 27. 27 Steady-state Equivalent CircuitModeling Switch Transfer Function Switch and diode Model for transformation of average voltage and current Model that separates steady-state and small signal components
- 28. 28 Steady-state Equivalent CircuitModeling PWM (Averaged) Buck Converter Simulation a c d p U2 PWMVM Fs = 50k L = 100u Vs 6Vdc 0 Vin Vctrl 1Vac 0.55Vdc 0 0 L1 100uH RL 0.1 Resr 0.4 C1 75u 0 RLoad 2 0 Vout U3 TCLOSE = 3m 1 2 0 RLoad2 4 V
- 29. 29 Steady-state Equivalent CircuitModeling Steady-state (dc) Analysis
- 30. 30 Steady-state Equivalent CircuitModeling Transient Analysis
- 31. 31 Steady-state Equivalent CircuitModeling AC Analysis
- 32. 32 Steady-state Equivalent CircuitModeling Synchronous buck converter with a voltage-mode error-amplifier
- 33. 33 Steady-state Equivalent CircuitModeling Block diagram model of the synchronous buck converter Switches, drivers and output filter F(s) Error amplifier and compensation network
- 34. 34 Steady-state Equivalent CircuitModeling Filter Transfer Function GP(s) GP(s) Zero
- 35. 35 Steady-state Equivalent CircuitModeling Pulse-Width Modulation Transfer Function The PWM circuit converts the output from the compensated error amplifier to a duty ratio. The error amplifier output voltage is compared to a sawtooth waveform with amplitude VP. Ve Ve(s)
- 36. 36 Steady-state Equivalent CircuitModeling Bode plot of the power stage
- 37. 37 Steady-state Equivalent CircuitModeling Loop Gain of the System Crossover frequency • Typically, F0 ≈ 1/10 to 1/5 of fsw. • Speed of the system response to load transients is determined by F0. • F0 should be low enough to allow attenuation of switching noise. • Slope at F0 ≈ -20dB and phase margin > 45° for stability.
- 38. 38 Steady-state Equivalent CircuitModeling Type 2 Error Amplifier with Compensation Resistor to ground for k
- 39. 39 Steady-state Equivalent CircuitModeling Type 3 Error Amplifier with Compensation
- 40. 40 Steady-state Equivalent CircuitModeling Control Circuit Design 1. The design of the circuit begins by selection of various operating parameters and component values, largely determined by the basic operating requirements, namely: • Input voltage range • Output voltage • Output current range • Operating frequency
- 41. 41 Steady-state Equivalent CircuitModeling Control Circuit Design (2) 2. By using these design requirements, the values of the filter components are determined, and the power switches are selected. 3. After selecting the main circuit components, the error amplifier and voltage reference must be added to provide output voltage regulation.
- 42. 42 Steady-state Equivalent CircuitModeling LTSpice Simulation of Loop
- 43. 43 Steady-state Equivalent CircuitModeling LTSpice Simulation of Loop
- 44. 44 Steady-state Equivalent CircuitModeling Thanks! Questions?
- 45. 45 Steady-state Equivalent CircuitModeling DC-DC Converter Control Buck converter with feedback Control representation