TSTE25 Power Electronics Lecture 6 Tomas Jonsson ISY/EKS
2016-11-15 2 Outline DC power supplies DC-DC Converter Step-down (buck) Step-up (boost) Other converter topologies (overview) Exercises 7-1, 7-2, 7-7, 7-8
2016-11-15 3 Basic use of DC-DC converter Unregulated DC input, controlled DC output Regulated DC may be larger or smaller than the unregulated DC voltage Input to DC-DC converter may vary a lot
2016-11-15 4 DC Power supplies Regulated output Defined tolerance of output voltages Isolation No direct electric connection to supply voltage Multiple outputs Both positive and negative possible Various current and voltage ratings
2016-11-15 5 Linear power supply Bulky transformer Low frequency Poor efficiency 30 60 % Low EMI
2016-11-15 6 Switch-mode dc power supply schematic Small size High efficiency EMI protection
2016-11-15 7 Multiple voltages Linear control may be applied if multiple controlled voltages are required High efficiency (70 90 %)
2016-11-15 8 Step down converter principle V d > V o T s constant, t on and t off changing Large ripple on V d
2016-11-15 9 DC/DC-converter control Pulse width modulation, PWM, to control switching Switching frequency f s
2016-11-15 10 PWM waveform, duty cycle Switch duty cycle (duty ratio) D = t on = v control T s V st 0 < D < 1
2016-11-15 11 Step-down (buck) converter Add filter to reduce ripple voltage Diode added to protect switch V L -> infinity if no diode and instantaneous switching! Parasitic capacitances C x would be charged by the inductor current C x
2016-11-15 12 Step-down converter waveforms T s = t on + t off Average output voltage V o = t on T s V d = D V d
2016-11-15 13 Input voltage before low-pass filter V oi = V d when switch on When switch off V oi = 0 if i L > 0 V oi = V o if i L = 0 LP filter BW(f c ) << f s
2016-11-15 14 Current Conduction modes Average i L equals i o Two current conduction modes (i L ) Continuous current conduction Non-continuous current conduction Converter characteristics different depending on mode Both modes can be supported by a converter Mode applicable is depending on load
2016-11-15 15 Continuous Conduction mode Switch on (diode off) Switch off (diode on)
2016-11-15 16 Continuous conduction mode, cont. i L never zero Steady state => A = B Average v oi output voltage, average v L zero in steady state V d t on + 0 t off T s t on V d V o = V o Ideal conditions: No power loss in converter = V o T s t on => V o V d = t on T s = D P d = P o V d I d = V o I o I o = V d = 1 I d V o D DC transformer with turns ratio equal to D i d still slanted square wave
i L reach zero at end of period Average I o I LB = 1 2 i L,peak = t on 2L V d Vo 2016-11-15 17 Discontinuous/Continuous Conduction mode boundary I LB = DT s 2L V d V o I LB = DT s 2L V d 1 D < T sv d 8L For fixed input voltage V d I LB,max at 50% duty cycle I LB,max = T sv d 8L
Discontinuous conduction mode Equal area: V d V o DT s + V o Δ 1 T s = 0 V o D = V d D + Δ 1 i L,peak = V o L Δ 1T s I o = i L,peak D + Δ 1 2 I o = V ot s 2L D + Δ 1 Δ 1 = V dt s 2L DΔ 1 I o Δ 1 = 4I LB,max D V o V d = D 2 D 2 + 1 4 I o/i LB,max v oi v L,i L v d 2016-11-15 18 v o
2016-11-15 19 Constant V d step-down characteristic Very low load result in increased output voltage! I LB,max = T sv d 8L
2016-11-15 20 Discontinuous conduction mode with constant V o I LB,max = T sv o 2L Control ratio for constant V o
2016-11-15 21 Output voltage ripple Assuming: ripple current in C Average current in R ΔV o = ΔQ C = 1 C 1 ΔI L T s 2 2 2 I L = V o L 1 D T s ΔV o = 1 T 2 s 1 D = V o 8 LC = π2 2 1 D f c f s 2
2016-11-15 22 Step-down (buck) converter summary Output vs input V o V d = D I o I d = 1 D High ripple current I Lpeak = 2I o Practical for D not lower than 0.2
Lecture 6 Exercises, buck-converter
2016-11-15 24 7-1 In a step-down converter, consider all components to be ideal. Let v o V o be held constant at 5 V by controlling the switch duty ratio D. Calculate the minimum inductance L required to keep the converter operation in a continuous-conduction mode under all conditions if: V d is 10-40 V, P o 5 W, and f s = 50 khz.
2016-11-15 25 7-2 Consider all components to be ideal. Assume V o = 5 V, f s = 20 khz, L = 1 mh, and C = 470 µf. Calculate V o (peak-peak) if V d = 12.6 V, and I 0 = 200 ma.
Lecture 6 Step-up, boost-converter
2016-11-15 27 Step-up (boost) converter Output must be larger than input voltage Otherwise is V d driving V o directly => V o = V d Load energy into inductor, then output energy into load while still consuming energy from source C large enough to give low ripple, v o (t) V o
2016-11-15 28 Step-up converter waveform, continuous conduction mode Switch on, diode off Switch off, diode on
2016-11-15 29 Step-up converter, continuous mode V d t on + V d V o t off = 0 V o /V d = T s = 1 t off 1 D Lossless circuit: V d I d = V o I o I o I d = 1 D
Boundary between continuous and discontinuous mode 2016-11-15 30 I LB = 1 2 i L,peak = 1 2 V d L t on I LB = T sv o 2L I ob = T sv o 2L D 1 D D 1 D 2 L = T sv o 2I ob D 1 D 2
2016-11-15 31 Boundary between continuous and discontinuous mode V o constant I LB max when D = 0.5 I LB,max = T sv o 8L I ob max when D = 1/3 I ob,max = 2 T s V o 27 L = 0.074 T sv o L I LB = 4D 1 D I LB,max I ob = 27 4 D 1 D 2 I ob,max
2016-11-15 32 Step-up, discontinuous mode V d DT s + V d V o Δ 1 T s = 0 V o = Δ 1 + D V d Δ 1 I o = Δ 1 I d Δ 1 + D D = 4 V o 27 V d I d = V d 2L DT s D + Δ 1 I o = T sv d 2L DΔ 1 Controller V o V d 1 I o I ob,max 1/2
2016-11-15 33 Step up converter characteristics, V o constant I ob,max = 0.074 T sv o L
2016-11-15 34 Effects of parasitics Losses in L, diode, switch, C Limited also by acceptable D ratio
2016-11-15 35 Output voltage ripple ΔV o = ΔQ C = I odt s C ΔV o = DT s V o RC = D T s τ where τ = RCtime constant
Lecture 6 Exercises on boost converter
2016-11-15 37 7-7 In a step-up converter, consider all components to be ideal. Let V d be 8-16 V, V o = 24 V (regulated), f s = 20 khz, and C = 470 µf. Calculate L min that will keep the converter operating in a continuous-conduction mode if Po 5 W.
2016-11-15 38 7-8 In a step-up converter, V d =12 V, V o = 24 V, I 0 = 0.5 A, L = 150 µh, C = 470 µf, and f s =20 khz. Calculate V o (peak-peak).
Equivalent Circuits in DC-DC Converters a) Buck, b) Boost, c) Buck-Boost, d) Cúk
Lecture 6 Other converter topologies
2016-11-15 41 Flyback converter Derived from buck-boost structure Second winding gives electric isolation Only flux flow in one direction Never negative currents in the transformer
2016-11-15 42 Flyback converter circuit states Switch on and switch off Continuous conduction mode Incomplete demagnetization L m size important Ideal transformer have inifinite L m
2016-11-15 43 Flyback converter waveforms Same control equation as for buck-boost converter D = t on T s V o = N 2 D V d N 1 1 D
2016-11-15 44 Alternative flyback converter topologies Two transistor flyback Both turn on and off simultaneously Voltage rating half compared to single transistor No snubber necessary because of diodes
2016-11-15 45 Alternative flyback converter topologies Paralleling flyback converter Same frequency of switching Phase-shifting switches π Allow higher power Redundancy Increased effective switching frequency
2016-11-15 46 Forward converter Derived from step-down converter Ideal transformer assumed Transformer magnetizing current not included Converter failure if not taken care of V o V d = N 2 N 1 D
2016-11-15 47 Practical forward converter Feed magnetic current back to source Requires a third winding
2016-11-15 48 Practical forward converter waveforms To guarantee demagnitized transformer max t m T s = 1 D 1 D max = N 3 N 1 D max D max = 1 1 + N 3 /N 1
2016-11-15 49 Other forward converter topologies Two-switch forward converter Commonly used Voltage rating half of single transistor case No snubbers necessary
2016-11-15 50 Other forward converter topologies Parallelled forward converter Same advantages as parallelled flyback converter
2016-11-15 51 Push-pull converter Derived from step-down converter Diodes due to leakage inductances PWM control V o V d = 2 N 2 N 1 D 0 < D < 0.5
2016-11-15 52 Half-bridge converter Derived from step-down converter Additional diodes for switch protection V o V d = N 2 N 1 D 0 < D < 0.5
Full-bridge converter 2016-11-15 53 Derived from step-down converter Switches carry half the current compared to the half bridge converter V o V d = 2 N 2 N 1 D 0 < D < 0.5
2016-11-15 54 Current-source dc-dc converter L d and D > 0.5 gives current source input One or both switches always on Operates like a step-up converter V o V d = N 2 N 1 1 2 1 D D > 0.5
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