Chapter 7 DC-DC Switch-Mode Converters dc-dc converters for switch-mode dc power supplies and dc-motor drives 7-1
Block Diagram of DC-DC Converters Functional block diagram 7-2
Stepping Down a DC Voltage A simple approach that shows the evolution 7-3
Pulse-Width Modulation in DC-DC Converters Role of PWM 7-4
Duty cycle Switching frequency given by the sawtooth Control voltage u control is the diffence between reference and measured voltages amplified by the controller u control gives the on-time of the switch t on Relative on time, duty cycle t u D on T Uˆ s ohj st 7-5
Step-Down DC-DC Converter Pulsating input to the low-pass filter 7-6
Output voltage In continuous conduction mode (CCM) V o = 1 T s Output depends linearly from the Duty cycle 0 And therefore also from control voltage u control Discontinuous conduction mode (DCM) Will be discussed in next slides Ts v o t dt = t on T s V d = DV d Also output current (power) has an effect on voltage average Nonlinear dependence on the duty cycle 7-7
Step-Down DC-DC Converter: Waveforms Steady state; inductor current flows continuously 7-8
Continuous Conduction Mode, CCM Voltage integral over the inductor must be zero at steady state V d V o t on = V o T s t on => V o V d = t on T s = D If there are no losses in the converter V d I d = V o I o => I o Id = V d V o = 1 D 7-9
Transformer In CCM operates like transformer without galvanic isolation Duty cycle D acts like a portabless turns ratio in a transformer, changes from 0 to 1 Input current i d changes also as the switch operates In many cases filtering needed in the input side too, depends on the supplying voltage source 7-10
FilteringYtytt Filter inductance ensures that output is current source as input normally is voltage source Filter corner frequency ƒ C Selected to be much smaller than ƒ s Attenuation of harmonics is high Output voltage can be assumed to be constant in many cases 7-11
Step-Down DC-DC Converter: Waveforms at the boundary of Cont./Discont. Conduction Critical current below which inductor current becomes discontinuous ilpeak Ud Uo DT I t s U U I 2 2L 2L LB on d o ob Chapter 7 DC-DC Switch-ModeConverters 7-12
Step-Down DC-DC Converter: Discontinuous Conduction Mode Steady state; inductor current discontinuous 7-13
DCM with constant Ud Typical in motor drives Replacing U o = DU d we end up to DUdT I s LB 1 D I 2L ob Highest output current for CCM needed at D = 0,5 I LB = I ob UdVis d = constant vakio 0.5 1.0 I LB,max = T sv d 8L D 7-14
U o /U d in DCM with constant Ud Voltage integral over the inductor U U 0 o d Uo DTs Uo Ts U 1 Average of output current Replacing we obtain D U D U T I i T D 2 L 2 2L 1 I 1= o 4 I D 1 o 1 d s o Lpeak 1 s 1 LB max U U o d D 2 d D 1 4 2 I D D I o LB max 1 7-15
Step-Down DC-DC Converter: Limits of Cont./Discont. Conduction The duty-ratio of 0.5 has the highest value of the critical current 7-16
DCM with constant U o Typical in power supplies Replacing U d = U o /D ilpeak Ud Uo TsU I o LB ton 1 D 2 2L 2L Maximum required current for CCM when D = 0 I LB max TU s 2L o 7-17
Duty cycle in DCM with constant U o Using previous equations U D D D U U I D D Ud D 1 2LIo Uo I D D o Ud Ud ILB max U DT U D I o o 2 o o 2 Duty cycle is d s d LB max D U I I U 1 U U o o LB max d o d Ratio of voltages is nonlinear 2 2 Uo D D D 4 Io I U 2 I I d o LB max LB max 7-18
Step-Down DC-DC Converter: Limits of Cont./Discont. Conduction Output voltage is kept constant 7-19
Step-Down Conv.: Output Voltage Ripple ESR is assumed to be zero 7-20
Ripple (sykkeisyys in Finnish) Peak-to-peak Q 1 IL Ts U Uo o Uo U I t T t o 1 DT C 2C 2 2 L L L 2 π 2 o s c Ripple reduces when ƒ C «ƒ s Compare to Fig 7-4 In CCM doesn t depend on output power Allowed ripple often < 1 % L off s on s U 1 T f 1 1 D 1 D jossa fc Uo 8 LC 2 fs 2π LC u o (t) = U o can be assumed to be constant 2 7-21
Step-Up DC-DC Converter (Boost) Output voltage must be greater than the input 7-22
Step-Up DC-DC Converter Waveforms U 1 0 o T U s dton Ud Uo toff U t 1 D d off Io U U d d Id UoIo 1 D I U d o Continuous current conduction mode 7-23
Step-Up DC-DC Converter: Limits of Cont./Discont. Conduction, constant Uo ilpeak Ud TsU I o LB ton D1 D 2 2L 2L Note I L I o TU IoB ILB D D D 2L 2 TU I s o ob max 27 L 1 s o 1 2 7-24
Step-Up DC-DC Converter: DCM, constant Uo U D Ud DTs Ud Uo 1T s U 1 0 o d 1 I I o d 1 D 1 U D T U I DT I D d 1 jolloin s d U d s o 1 o 4 U 1 1 o U o I D and 1 o 2L 1 2L U d 27 U d U d I ob max 7-25
Step-Up DC-DC Converter: Limits of Cont./Discont. Conduction The output voltage is held constant 7-26
Step-Up DC-DC Converter: Effect of Parasitics The duty-ratio is generally limited before the parasitic effects become significant 7-27
Effect of Parasitics Especially nonidealities, i.e. resistive losses in L and C At large D, peak value of current is large when compared to the average value Major part of input voltage is needed to overcome the voltage drop of parasitics Losses are increasing too Output voltage ripple and capacitor current increase too 7-28
Effect of Parasitics, U o /U d Losses of inductor and capacitor, r L, r c Resistors are percentages of load resistor R It can be shown that 2 2 2 o 1 1D R Rr 1, jossa C R D 1 1 where R rl D d R C C U U D R r R r Analysis of transfer functions in Chapter 10 gives this 7-29
U o /U d when parasitics are 1 % 10 9 8 7 1 1 D U U o d 6 5 4 r L r C 0 3 2 1 r r 0,01R L 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 C D 7-30
Effect of Parasitics, U o /U d Up to D 0,6 ideal and practical curve match well Maximum increase is about 4,7 with 1 % resistors In practice always less than 10, i.e. infinite gain impossible E.g. operating at D 0,88 Supply voltage reduces Feedback increases D in order to increas U o Because of parasitics U o actually drops and finally D = 1 and short circuit D needs to be limited to some practical value 7-31
Efficiency with parasitics For simplicity parasitics of L considered only R r R1 D 2 Uo 1D 1D R 2 2, Ud R r D D rl L 1 1 L U U o d 1 1 D 7-32
Efficiency with parasitics Only inductor losses 2 Po Uo R 1 R, 2 2 2 o rl Uo R ILrL 1 1 D L P P r The higher D the smaller efficiency is 1 D 1 7-33
Step-Up DC-DC Converter Output Ripple ESR is assumed to be zero Inductance has no effect as it is in the input side Q I DT U DT U DT DT Uo C C R C U RC o s o s o s s o 7-34
Step-Down/Up DC-DC Converter, Buck-Boost How to derive Buck-Boost Series connection of Buck and Boost K1 I D2 + L + V d D1 K2 C V o Buck, K2 is always open Boost, K1 is always closed 7-35
Common current source Same current source, Boost turned around D1 needs to be removed, it only shortcircuits the current source laskeva Buck katkoja ylösalaisin käännetty nos Boost tava turned katkojaaround K1 D2 K1 D2 + V d D1 I I K2 C + V o + V d I K2 C + V o 7-36
Buck-Boost K2 can be removed too, it is only shortcircuiting current source K1 D2 + i L + + V I C V o d K2 V V d v L L o C - + i d i o V o + R 7-37
Step-Down/Up DC-DC Converter, Buck- Boost The output voltage can be higher or lower than the input voltage 7-38
Step-Up DC-DC Converter: Waveforms U t d on U t o off 0 U DT U 1 D T 0 d s o s Uo D I 1 ja o D U 1 D I D d d CCM, Continuous conduction mode Chapter 7 DC-DC Switch-Mode Converters 7-39
Step-Up DC-DC Converter: Limits of Cont./Discont. Conduction, Vo constant ilpeak Ud TsU I o LB DTs 1 D 2 2L 2L TU Io IL Id ja IoB ILB IdB 1 D ILB 1 D 2L TU I s o ob max 2L s o 2 7-40
Step-Up DC-DC Converter: Discontinuous Conduction Mode, Vo constant U 1 0 o D I ja o Ud DTs Uo Ts U I D d 1 d 1 I L Ud D DTs 2L 1 1 U T 2L U U I I I T I D 1 d o o 1 s s 1 o eli o 1 o o 2L Ts UoTs Ud Ud IoB max 7-41
Step-Up DC-DC Converter: Limits of Cont./Discont. Conduction The output voltage is held constant 7-42
Buck-Boost: Effect of Parasitics The duty ratio is limited to avoid these parasitic effects from becoming significant, same as boost 7-43
Step-Up DC-DC Converter: Output Voltage Ripple ESR is assumed to be zero Inductance not part of ripple equation Note I L I o I o Q I DT U DT U DT DT Uo C C R C U RC o s o s o s s o 7-44
Cuk DC-DC Converter Name is based on the family name of the invertor The output voltage can be higher or lower than the input voltage, dualism with buck-boost Capacitor C1 acts as intermediate energy storage 7-45
Cuk DC-DC Converter: Waveforms The capacitor voltage is assumed constant U U 11 0 d d DTs Ud UC D Ts UC1 1 D U U 1 1 0 o C Uo DTs U o D Ts UC1 D Uo D Io Ud 1 D U 1 D I U D d d o 7-46
Sepic Converter Single-Ended Primary Inductance Converter L 1 :n correspons to Boost L 2 :n correspons to Buck-Boost L 1 i L 1 u C 1 + D + + u L 1 C 1 i L 2 + U d T L 2 u L 2 + C R U o 7-47
Sepic comparison Advantages Continuous input current as in boost Step up is possible L1 and L2 can be connected magnetically, possible to compensate ripple in one of the inductors Reduces start and short-circuit currents Galvanic isolation by adding a second winding to L2 Disadvantage Switch and diode current and voltage higher than in Boost 7-48
Similar to Cúk Sepic, voltages 1 L U D D U U U 1 d o C1 d 1 D L U D 1 DU 0 U U D 2 C1 o C1 o 1 D U 1 o D Ud D DUo Uo Ud D U 1 D d 7-49
Sepic, currents In steady state average current of C1 needs to be zero i i i C1 L2 i C1 L1 L2 L1 d L2 d o I L1 = I d and I L2 = I o kytkimen Switch conducts johtaessa kun Switch kytkimen is not ei conducting johda 1 D I D 1 D I 1 D I I I I D 7-50
Full-bridge dc-dc converter Converter for UPS and DC-Motor Drives Either dc or ac output depending on modulation Four quadrant operation is possible 7-51
Bi-polar voltage switching Switches TA+ and TB TA and TB+ Are controlled simultaneously Output changes between +U d :n and U d :n 7-52
Control of output Triangle ˆ t u utri Utri 0 t Ts 4 control T t1 s T 4 Uˆ 4 s tri On time of T A+ and T B T t 1 u ton 2 t D 1 s on control 1 1 2 T 2 ˆ s Utri On time of T A and T B+ D =1 D 2 1 2 1 U U U D D U D U o AN BN 1 2 d 1 d U d u ˆ control Const. vakio u U tri control 7-53
Uni-polar voltage switching Two control voltages with opposite signs D 1 ton 1 u 1 T 2 ˆ s U control tri U U D U u vakio u o 2 1 1 d ˆ d control control Utri 7-54
RMS of output voltage Bipolar 1 s T 2 o, rms 0 o d T s U u dt U Unipolar 2 r, rms o 2, rms o 2 d 1 2 1 1 2 d 1 1 2 U U U U D U D D 1 4t u U u dt U U U 2D 1 Ts 2 1 2 control o, rms 0 o d d ˆ d 1 T s Ts Utri 2 2 2 2 r, rms o, rms o d 1 1 d 1 1 U U U U 2D 1 2D 1 U 6D 4D 2 7-55
Output Ripple in Converters for DC- Motor Drives bi-polar and uni-polar voltage switching 7-56
Switch Utilization in DC-DC Converters Ratio U T = maximum voltage over switch I T = maximum current P P o T U I U I o o T T It varies significantly in various converters 7-57
Equivalent Circuits in DC-DC Converters replacing inductors and capacitors by current and voltage sources, respectively 7-58
Reversing the Power Flow in DC-DC Conv. For power flow from right to left, the input current direction should also reverse 7-59
Efficiency and losses of power semiconductor devices Losses of power semiconductor devices Conduction losses Switching losses, turn-on and turn-off For simplicity following investigation is on Buck converter Can be generalized to other converters 7-60
Conduction losses On-state voltage drop Assumed to be the same in the switch and diode Losses t t on off P P P U I U I U I, t t T T T DC Q D on o on o on o on off s s s Efficiency Example Po UoIo U o P P U I U I U U o DC o o on o o on U o = 3 V, U on = 0,5 V => = 85,7% 7-61
Switching losses Infinite rise and fall time when switches are turning on and off An ideal switch would Conduct full load current immeadiately without voltage drop Current and voltage are assumed to changing linearly during turn-on and -off 7-62
Switching inductive current 7-63
Turning off and on T- conducts I o and it is turned off Voltage over it increases and when it is U d diode D+ starts to conduct Because of parasitic inductances voltage exceeds U d D+ conducts I o and T- is turned on Current inceares and exceeds I o because of diode reverse recovery current After recovery of the diode voltage over T- drops to nearly zero 7-64
Switching losses, best case It is assumed that voltage and current are changing simultaneously P P on off t t U I T on ton on d o uidt 0 s Ts 6 t t U I off toff off uidt d o T 0 s Ts 6 V d I Switch voltage o Turning off Turning on Switch current t on T s t off 7-65
Conduction and switching losses, best case It is assumed that t on = t off Efficiency including conduction and switching losses Example (cont.) Lets assume U d = 48 V, U o = 3 V, U on = 0,5 V, f s = 50 khz and t on = t off = 0,3 µs and T s = 20 µs With these numbers P P P AC on off t T on s U I 3 Po UoIo U o P P P U I U I U I t 3T U U U t 3T d o o DC AC o o on o d o on s o on d on s 3 100% 80, 2% 3 0,5 480,3 320 7-66
Conduction and switching losses, worst case Current reaches final value before voltage drops V d Switch voltage P P on off t U I t U I T 2 T 2 Ri d o FU d o s t U I t U I T 2 T 2 RU d o Fi d o s Turning off Turning on s s Switch current T s t Ri t Fu t Ru 7-67
Conduction and switching losses, worst case t Ri = t FU = t RU = t Fi P P P U I 2 Ri AC on off d o Ts Uo Po P P P U U 2U t T o DC AC o on d Ri s Other values same as before, additionally, t Ri = 0,3 µs 3 100% 60, 7% 3 0,5 2480,3 20 Corresponding linear power supply U 3 o 100% 100% 6, 25% U 48 d t 7-68