EE 545 POWER EECTRONICS I ecture #4: Chapter 4 Non-Isolated DC-DC Converters PWM Converters DCM Analysis (DCM)
Objectives Overview of Discontinuous Conduction Mode Buck Converter Analysis (DCM) Simulation of Buck in DCM Boost and Buck Boost Converter Analysis (DCM) Voltage Conversion Ratio (M=Gain) Average Input and Output Currents Output Voltage Ripple via Charge approximation Boundary Between CCM and DCM Examples of Analysis and Design for Boost and Buck Boost Converters in CCM/DCM PSPICE Simulation Verification
DCM Buck Converter i min = 0 Means inductor current starts at zero (i (0)=0), and ends at zero (i (T)=0) For a certain inductor value, DCM occurs as load is low,, Io is small. Io<Io,critical - In DCM, Vo/Vin= M= f(d,t,r,) Vo/Vin= M= f(d,d ) and D = f(d,t,r,)
Intuitive Concepts (All other variables are constant) Smaller Smaller Io arger T arger inductor current slope arger inductor current ripple More likely to go to DCM Smaller inductor average current (DC value) More likely to go to DCM Extended switching period allows more time for I to reach zero arger inductor current ripple More likely to go to DCM 3
DCM Buck Analysis S Mode : S on, D off Inductor charges from zero Mode : S off, D on Inductor discharges to zero 0 DT DT D T D T T V = Vin Vo I (0)=0 Vin Vo Vo I() t t I() t ( tdt) I( DT) Mode 3: S off, D off Inductor current =0 V = -Vo V = 0 I() t 0 oad is supplied by output capacitance4
I (0) 0 I( DT ) Vin Vo DT Volt Second balance: (Vin-Vo)*DT - Vo*(D -D)T = 0 Vo D M Vin D I max -I o c -I o o Vin-Vo -Vo o DT D T T t 5
I avg, Vo Io R I ( DT ) DT T Vo ( ) D RDT Vin Vo M RDT M Area under curve T Vin Vo DDT o 6
Solve for M D M D RD T M M M RD T M RD T M M M M RD T RD T M 0 Find roots of M b b 4ac a DRT 8 M 4 D RT 7
8 n R T RT 8 4 n n D M D Power Electronics often uses gain curves for design. It is easier to use normalized (Unit less) parameters, such as:
Book corrections - Eq. 4.9 must be corrected to: I D 8 D Eq.4.9 n 3 n nmax 4 n D - The y-axis in fig. 4.44 must be labeled I nmax instead of M 9
DCM buck Output voltage ripple I max -I o I max Imax Io DT t t ( I max Io) DT t t I Q ( t t )( Imax Io ) ( Imax Io) DT Vc C I V c max max Vo ( ) D RDT Vin Vo ( Imax Io) Vo CRD I ( Vin Vo) max Triangles similarity i c -I o v o, where t t DT D T T Vin Vo I max DT 0 t
CCM Boost Converter Mode : S on Mode : Mode : Switch and diode voltage stress= Vo Mode : S off
Voltage gain (from mode ) (from mode ) Using the above two equations, or using volt-second balance
Min & Max inductor current min Critical inductor Converter enters DCM when inductor current reaches zero I I max I in I in I I find critical Io?
CCM Boost Output voltage ripple Use capacitor charge Q DTI V o c V V c find v c (t)? o DTV CR D RCf o
DCM Boost Converter () Vin i t t 0 DT Vin Vo i () t ( tdt) I ( DT) DT D T i () 0 t D T T
( ) Vin I DT DT Using the above two equations, or using volt-second balance Vin DT ( Vin Vo)( D D) T 0 Vo D Vin D D from mode Vin Vo I( DT ) 0 ( DD) T I( DT) from mode i I v i D i c 0 V in (V o V in ) I (DT) I max I o DT D T I o T t t t I o
Solve for M I Davg, I ( DT ) ( D D ) T VinD( D ) Vo I o R T Vo R DD ( DT ) () Vin M D D ( D D) M D D D ( M ) DM D DM ( M ) () Substitute eq. in eq. M D n n RT D T
DCM boost output voltage ripple I I I ( D D) T t DT t max max o DT ( I max Io)( D D) T I max Q ( tdt )( Imax Io ) ( I max Io) ( D D) T Vc C I D I max DM ( M ) Vin DT max Triangles similarity I max i c I o I o v c V o t t
CCM Buck-Boost Converter Mode : S on Mode : Mode : Mode : S off 0 DT DT T Note that buck-boost is an inverting converter (output is negative) Switch and diode voltage stress= Vin + Vo
3
(from mode ) (from mode ) Using the above two equations, or using volt-second balance M> M< M= 3 M( D) 0 3 0 0 0. 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 D 4
- D : D 5
Min & Max inductor current Critical inductor Converter enters DCM when inductor current reaches zero find critical Io? 6
CCM Buck-Boost Output voltage ripple Use capacitor charge Q DTI V o c V V c find v c (t)? o DTV CR D RCf o 7
DCM Buck-Boost Converter Mode : S off Mode : 0 DT Mode : Mode 3: i () t 0 i () t I c o Mode : S on Mode 3: S & D off DT D T D T T Switch and diode voltage stress= Vin + Vo 8
( ) Vin I DT DT from mode Vo I( DT ) 0 ( DD) T I( DT) from mode Using the above two equations, or using volt-second balance Vin DT Vo( D D) T 0 Vo D Vin D D 9
Solve for M I Davg, I ( DT ) ( D D ) T VinD( D ) Vo I o R T Vo R DD ( DT ) () Vin D M D D ( D D) M D DM D( M) D D( ) () M Substitute eq. in eq. M D n n RT D T 0
DCM Buck-Boost output voltage ripple I I I ( D D) T t DT t max max o DT ( I max Io)( D D) T I max Q ( tdt )( Imax Io ) ( I max Io) ( D D) T Vc C I D I max D( ) M Vin DT max Triangles similarity I max i c I o I o v c V o t t
Buck Converter Analysis: ipes Examples for Buck DCM DC/DC-Converter Basic Topologies Buck-Converter - () Buck-Converter - () Buck-Converter - (3) Buck-Converter: Start-Up with Constant Duty Cycle
Buck Converter Analysis: Simulation Verification Example-Buck DCM
Buck Converter Analysis: Simulation Verification Example-Buck DCM
Buck Converter Analysis: Simulation Verification Example-Buck DCM
Buck Converter Analysis: Simulation Verification Example-Buck DCM
Buck Converter Analysis: Simulation Verification Example-Buck DCM
Buck Converter Analysis: Simulation Verification Example-Buck DCM 0V.0V 0V.0V -0V 5.0A V(:,:) 9.880m,6.4896u) SE>> 0V.0A V(Gate).5A (9.894m,5.685m) 0A SE>> -.0A (9.890m,3.006) 9.8875ms 9.9000ms 9.95ms I() Time -.0A 9.89ms 9.90ms 9.9ms 9.9ms 9.93ms I(Cf) Time
Buck Converter Analysis: Simulation Verification Example-Buck DCM 6V 5V 4V 0V (0.000,4.048) 5V SE>> V.50A V(Road:) SE>> 0V.0A V(Road:).5A.0A.00A 9.89ms 9.90ms 9.9ms 9.9ms 9.93ms I(Road) Time 0A 0Hz 40KHz 80KHz 8KHz I(Road) Frequency
Example 4.-BuckBoost Consider a buck-boost converter with the following values: Vo=V, Pout=5W, Vin=0V and ƒ=00khz. (a) Design the above converter so that it will operate in ccm (b) Repeat part (a) for dcm, (c) Find the maximum inductor current under both ccm and dcm (d) If the load resistance increases by 50% (i.e. the load current changes.08a to.39a) determine the mode of operation for the two converters and then the maximum inductor current (e) Sketch the new inductor currents derived from part (e.)
Example 4.-BuckBoost V o := V in := 0 P o := 5 f := 00 0 3 T s := f (a) For CCM R := V o P o R = 5.76 crit := R T s ( D) 0 D D D :=.375 T s = 0 5 D T s = 3.75 0 6 solve, D.375 float, 3 crit =.5 0 5 Chose higher than crit for CCM :=. 0 3 Note-This is an arbitrary assignment that puts us into CCM mode. Since in CCM M is independent of, we do not effect the conversion ratio so long as >crit. The value of chosen does effect ripple current in the inductor though.
Example 4.-BuckBoost (b) For DCM Chose to less than crit := 5 0 6 τ n := R T s M D τ n τ n = 0.087 D := 0 τ n D = 0.5 M D D D solve, D 3
Example 4.-BuckBoost (c) For CCM :=. 0 3 D :=.375 i max D V in V in D T s D V in := R ( D) + i min := R ( D) V in D T s i max = 3.708 i min =.958 (c) For DCM := 5 0 6 D :=.5 i max := V in i max = 0 D T s
Example 4.-BuckBoost (d) Assume load resistance increase by 50% Assume Vo remains at V and Po Changes R := 5.76 +.5 5.76 D :=.375 R = 8.64 crit := R T s ( D) crit =.688 0 5 P := V o R P = 6.667 With at.mh, we are still in CCM for our original CCM design :=. 0 3 D :=.375 i max D V in V in D T s D V in := R ( D) + i min := R ( D) V in D T s i max =.597 i min =.847
Example 4.-BuckBoost For our original DCM design, reducing the load current moves us deeper into DCM (b) For DCM Chose to less than crit := 5 0 6 D R M τ n := T τ s n τ n = 0.058 D := 0 τ n M D D D D = 0.04 solve, D.5443305395873555 i max := V in i max = 8.65 D T s
Example 4.-BuckBoost Simulation CCM Original (R=5.76)
Example 4.-BuckBoost Simulation CCM Original (R=5.76) 0V 4.0A -5V 3.6A -0V 3.A -5V -0V 0s 5ms 0ms 5ms V(Output) Time 4.0.8A 4.980ms 4.985ms 4.990ms 4.995ms -I() Time 3.0.0.0 0 4.980ms 4.985ms 4.990ms 4.995ms V(Gate) -I() Time
Example 4.-BuckBoost Simulation DCM Original (R=5.76)
Example 4.-BuckBoost Simulation DCM Original (R=5.76) 0V -5V 8 4-0V 0-5V 0s 5ms 0ms 5ms V(Output) Time -4 4.980ms 4.985ms 4.990ms 4.995ms -I() V(Gate) Time
Example 4.-BuckBoost Simulation CCM New (R=8.64)
Example 4.-BuckBoost Simulation CCM New (R=8.64) 0V.6A -5V.4A -0V.A -5V.0A -0V 0s 5ms 0ms 5ms V(Output) Time.8A 4.980ms 4.985ms 4.990ms 4.995ms -I() Time
Example 4.-BuckBoost Simulation DCM New (R=8.64)
Example 4.-BuckBoost Simulation DCM New (R=8.64) 5V 0A 0V 5A -5V -0V 0A -5V 0s 5ms 0ms 5ms V(Output) Time -5A 4.980ms 4.985ms 4.990ms 4.995ms -I() Time