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TSTE25 Power Electronics Lecture 6 Tomas Jonsson ISY/EKS TSTE25/Tomas Jonsson 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 2 TSTE25/Tomas Jonsson 2016-11-15 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 3 TSTE25/Tomas Jonsson 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 4 TSTE25/Tomas Jonsson Linear power supply Bulky transformer Low frequency Poor efficiency 30 – 60 % Low EMI 2016-11-15 5 TSTE25/Tomas Jonsson 2016-11-15 Switch-mode dc power supply schematic Small size High efficiency EMI protection 6 TSTE25/Tomas Jonsson Multiple voltages Linear control may be applied if multiple controlled voltages are required High efficiency (70 – 90 %) 2016-11-15 7 TSTE25/Tomas Jonsson Step down converter principle Vd > Vo Ts constant, ton and toff changing Large ripple on Vd 2016-11-15 8 TSTE25/Tomas Jonsson DC/DC-converter control • Pulse width modulation, PWM, to control switching • Switching frequency fs 2016-11-15 9 TSTE25/Tomas Jonsson PWM waveform, duty cycle Switch duty cycle (duty ratio) 𝐷= 𝑡𝑜𝑛 𝑣𝑐𝑜𝑛𝑡𝑟𝑜𝑙 = 𝑇𝑠 𝑉𝑠𝑡 0<𝐷<1 2016-11-15 10 2016-11-15 TSTE25/Tomas Jonsson 11 Step-down (buck) converter Add filter to reduce ripple voltage Diode added to protect switch VL -> infinity if no diode and instantaneous switching! Parasitic capacitances Cx would be charged by the inductor current Cx 2016-11-15 TSTE25/Tomas Jonsson Step-down converter waveforms Ts = ton + toff Average output voltage 𝑉𝑜 = 𝑡𝑜𝑛 𝑉 = 𝐷 ∙ 𝑉𝑑 𝑇𝑠 𝑑 12 TSTE25/Tomas Jonsson Input voltage before low-pass filter Voi = Vd when switch on When switch off Voi = 0 if iL > 0 Voi = Vo if iL = 0 LP filter BW(fc) << fs 2016-11-15 13 TSTE25/Tomas Jonsson Current Conduction modes Average iL equals io Two current conduction modes (iL) 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 14 TSTE25/Tomas Jonsson Continuous Conduction mode Switch on (diode off) Switch off (diode on) 2016-11-15 15 2016-11-15 TSTE25/Tomas Jonsson 16 Continuous conduction mode, cont. iL never zero Steady state => A = B 𝑡𝑜𝑛 𝑉𝑑 − 𝑉𝑜 = 𝑉𝑜 𝑇𝑠 − 𝑡𝑜𝑛 => Average voi output voltage, average vL zero in steady state 𝑉𝑑 𝑡𝑜𝑛 + 0 ∙ 𝑡𝑜𝑓𝑓 = 𝑉𝑜 𝑇𝑠 Ideal conditions: No power loss in converter 𝑃𝑑 = 𝑃𝑜 ⇒ 𝑉𝑑 𝐼𝑑 = 𝑉𝑜 𝐼𝑜 𝐼𝑜 𝑉𝑑 1 = = 𝐼𝑑 𝑉𝑜 𝐷 DC transformer with turns ratio equal to D id still slanted square wave 𝑉𝑜 𝑡𝑜𝑛 = =𝐷 𝑉𝑑 𝑇𝑠 2016-11-15 TSTE25/Tomas Jonsson Discontinuous/Continuous Conduction mode boundary iL reach zero at end of period Average Io 1 𝑡𝑜𝑛 𝑖𝐿,𝑝𝑒𝑎𝑘 = 𝑉 − 𝑉𝑜 2 2𝐿 𝑑 𝐷𝑇𝑠 𝐼𝐿𝐵 = 𝑉 − 𝑉𝑜 2𝐿 𝑑 𝐷𝑇𝑠 𝑇𝑠 𝑉𝑑 = 𝑉 1−𝐷 < 2𝐿 𝑑 8𝐿 𝐼𝐿𝐵 = 𝐼𝐿𝐵 For fixed input voltage Vd ILB,max at 50% duty cycle 𝐼𝐿𝐵,𝑚𝑎𝑥 = 𝑇𝑠 𝑉𝑑 8𝐿 17 2016-11-15 TSTE25/Tomas Jonsson Discontinuous conduction mode 𝐸𝑞𝑢𝑎𝑙 𝑎𝑟𝑒𝑎: 𝑉𝑑 − 𝑉𝑜 𝐷𝑇𝑠 + −𝑉𝑜 Δ1 𝑇𝑠 = 0 voi 𝑉𝑜 𝐷 = 𝑉𝑑 𝐷 + Δ1 𝑉𝑜 𝑖𝐿,𝑝𝑒𝑎𝑘 = Δ1 𝑇𝑠 𝐿 vL,iL 𝐷 + Δ1 𝐼𝑜 = 𝑖𝐿,𝑝𝑒𝑎𝑘 2 𝑉𝑜 𝑇𝑠 𝑉𝑑 𝑇𝑠 𝐼𝑜 = 𝐷 + Δ1 Δ1 = 𝐷Δ1 2𝐿 2𝐿 𝐼𝑜 Δ1 = 4𝐼𝐿𝐵,𝑚𝑎𝑥 𝐷 𝑉𝑜 𝐷2 = 𝑉𝑑 𝐷2 + 1 𝐼 /𝐼 4 𝑜 𝐿𝐵,𝑚𝑎𝑥 vd vo 18 TSTE25/Tomas Jonsson 2016-11-15 Constant Vd step-down characteristic Very low load result in increased output voltage! 𝐼𝐿𝐵,𝑚𝑎𝑥 = 𝑇𝑠 𝑉𝑑 8𝐿 19 TSTE25/Tomas Jonsson Discontinuous conduction mode with constant Vo 𝐼𝐿𝐵,𝑚𝑎𝑥 𝑇𝑠 𝑉𝑜 = 2𝐿 Control ratio for constant Vo 2016-11-15 20 2016-11-15 TSTE25/Tomas Jonsson Output voltage ripple Assuming: ripple current in C Average current in R Δ𝑄 1 1 Δ𝐼𝐿 𝑇𝑠 Δ𝑉𝑜 = = 𝐶 𝐶2 2 2 𝑉𝑜 ∆𝐼𝐿 = 1 − 𝐷 𝑇𝑠 𝐿 Δ𝑉𝑜 1 𝑇𝑠2 1 − 𝐷 = = 𝑉𝑜 8 𝐿𝐶 π2 = 1−𝐷 2 𝑓𝑐 𝑓𝑠 2 21 TSTE25/Tomas Jonsson 2016-11-15 Step-down (buck) converter summary • Output vs input 𝑉𝑜 =𝐷 𝑉𝑑 𝐼𝑜 1 = 𝐼𝑑 𝐷 • High ripple current 𝐼𝐿𝑝𝑒𝑎𝑘 = 2𝐼𝑜 • Practical for D not lower than 0.2 22 Lecture 6 Exercises, buck-converter TSTE25/Tomas Jonsson 2016-11-15 24 7-1 • In a step-down converter, consider all components to be ideal. Let vo Vo 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: Vd is 10-40 V , Po 5 W, and fs = 50 kHz. TSTE25/Tomas Jonsson 2016-11-15 7-2 • Consider all components to be ideal. Assume Vo = 5 V, fs = 20 kHz, L = 1 mH, and C = 470 µF. • Calculate Vo (peak-peak) if Vd = 12.6 V, and I0 = 200 mA. 25 Lecture 6 Step-up, boost-converter TSTE25/Tomas Jonsson 2016-11-15 Step-up (boost) converter Output must be larger than input voltage Otherwise is Vd driving Vo directly => Vo = Vd Load energy into inductor, then output energy into load while still consuming energy from source C large enough to give low ripple, vo(t) Vo 27 TSTE25/Tomas Jonsson 2016-11-15 Step-up converter waveform, continuous conduction mode Switch on, diode off Switch off, diode on 28 TSTE25/Tomas Jonsson 2016-11-15 Step-up converter, continuous mode 𝑉𝑑 𝑡𝑜𝑛 + 𝑉𝑑 − 𝑉𝑜 𝑡𝑜𝑓𝑓 = 0 𝑇𝑠 1 𝑉𝑜 /𝑉𝑑 = = 𝑡𝑜𝑓𝑓 1 − 𝐷 Lossless circuit: 𝑉𝑑 𝐼𝑑 = 𝑉𝑜 𝐼𝑜 𝐼𝑜 ⇒ = 1−𝐷 𝐼𝑑 29 TSTE25/Tomas Jonsson Boundary between continuous and discontinuous mode 1 1 𝑉𝑑 𝑖𝐿,𝑝𝑒𝑎𝑘 = 𝑡 2 2 𝐿 𝑜𝑛 𝑇𝑠 𝑉𝑜 𝐼𝐿𝐵 = 𝐷 1−𝐷 2𝐿 𝑇𝑠 𝑉𝑜 𝐼𝑜𝐵 = 𝐷 1−𝐷 2 2𝐿 𝑇𝑠 𝑉𝑜 𝐿= 𝐷 1−𝐷 2 2𝐼𝑜𝐵 𝐼𝐿𝐵 = 2016-11-15 30 2016-11-15 TSTE25/Tomas Jonsson Boundary between continuous and discontinuous mode 𝑉𝑜 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝐼𝐿𝐵 max when D = 0.5 𝑇𝑠 𝑉𝑜 𝐼𝐿𝐵,𝑚𝑎𝑥 = 8𝐿 𝐼𝑜𝐵 max when D = 1/3 2 𝑇𝑠 𝑉𝑜 𝑇𝑠 𝑉𝑜 𝐼𝑜𝐵,𝑚𝑎𝑥 = = 0.074 27 𝐿 𝐿 𝐼𝐿𝐵 = 4D 1 − 𝐷 𝐼𝐿𝐵,𝑚𝑎𝑥 27 𝐼𝑜𝐵 = 𝐷 1 − 𝐷 2 𝐼𝑜𝐵,𝑚𝑎𝑥 4 31 2016-11-15 TSTE25/Tomas Jonsson Step-up, discontinuous mode 𝑉𝑑 𝐷𝑇𝑠 + 𝑉𝑑 − 𝑉𝑜 Δ1 𝑇𝑠 = 0 𝑉𝑜 Δ1 + 𝐷 = 𝑉𝑑 Δ1 𝐼𝑜 Δ1 = 𝐼𝑑 Δ1 + 𝐷 𝑉𝑑 𝐼𝑑 = 𝐷𝑇 𝐷 + Δ1 2𝐿 𝑠 𝑇𝑠 𝑉𝑑 𝐼𝑜 = 𝐷Δ1 2𝐿 Controller 4 𝑉𝑜 𝑉𝑜 𝐼𝑜 𝐷= −1 27 𝑉𝑑 𝑉𝑑 𝐼𝑜𝐵,𝑚𝑎𝑥 1/2 32 TSTE25/Tomas Jonsson 2016-11-15 33 Step up converter characteristics, Vo constant 𝐼𝑜𝐵,𝑚𝑎𝑥 = 0.074 𝑇𝑠 𝑉𝑜 𝐿 TSTE25/Tomas Jonsson Effects of parasitics Losses in L, diode, switch, C Limited also by acceptable D ratio 2016-11-15 34 TSTE25/Tomas Jonsson Output voltage ripple Δ𝑄 𝐼𝑜 𝐷𝑇𝑠 = 𝐶 𝐶 Δ𝑉𝑜 𝐷𝑇𝑠 𝑇𝑠 = =𝐷 𝑉𝑜 𝑅𝐶 τ Δ𝑉𝑜 = where τ = 𝑅𝐶time constant 2016-11-15 35 Lecture 6 Exercises on boost converter TSTE25/Tomas Jonsson 2016-11-15 7-7 • In a step-up converter, consider all components to be ideal. Let Vd be 8-16 V, Vo = 24 V (regulated), fs = 20 kHz, and C = 470 µF. • Calculate Lmin that will keep the converter operating in a continuous-conduction mode if Po 5 W. 37 TSTE25/Tomas Jonsson 2016-11-15 7-8 • In a step-up converter, Vd =12 V, Vo = 24 V, I0 = 0.5 A, L = 150 µH, C = 470 µF, and fs =20 kHz. • Calculate Vo (peak-peak). 38 Equivalent Circuits in DC-DC Converters a) Buck, b) Boost, c) Buck-Boost, d) Cúk Lecture 6 Other converter topologies TSTE25/Tomas Jonsson 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 41 TSTE25/Tomas Jonsson Flyback converter circuit states Switch on and switch off Continuous conduction mode Incomplete demagnetization Lm size important Ideal transformer have inifinite Lm 2016-11-15 42 TSTE25/Tomas Jonsson Flyback converter waveforms Same control equation as for buck-boost converter 𝑡𝑜𝑛 𝑇𝑠 𝑉𝑜 𝑁2 𝐷 = 𝑉𝑑 𝑁1 1 − 𝐷 𝐷= 2016-11-15 43 TSTE25/Tomas Jonsson 2016-11-15 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 44 TSTE25/Tomas Jonsson 2016-11-15 Alternative flyback converter topologies Paralleling flyback converter Same frequency of switching Phase-shifting switches π Allow higher power Redundancy Increased effective switching frequency 45 2016-11-15 TSTE25/Tomas Jonsson Forward converter Derived from step-down converter Ideal transformer assumed Transformer magnetizing current not included Converter failure if not taken care of 𝑉𝑜 𝑁2 = 𝐷 𝑉𝑑 𝑁1 46 TSTE25/Tomas Jonsson Practical forward converter Feed magnetic current back to source Requires a third winding 2016-11-15 47 TSTE25/Tomas Jonsson 2016-11-15 Practical forward converter waveforms To guarantee demagnitized transformer 𝑡𝑚 𝑚𝑎𝑥 =1−𝐷 𝑇𝑠 𝑁3 1 − 𝐷𝑚𝑎𝑥 = 𝐷 𝑁1 𝑚𝑎𝑥 1 𝐷𝑚𝑎𝑥 = 1 + 𝑁3 /𝑁1 48 TSTE25/Tomas Jonsson 2016-11-15 Other forward converter topologies Two-switch forward converter Commonly used Voltage rating half of single transistor case No snubbers necessary 49 TSTE25/Tomas Jonsson 2016-11-15 Other forward converter topologies Parallelled forward converter Same advantages as parallelled flyback converter 50 TSTE25/Tomas Jonsson Push-pull converter Derived from step-down converter Diodes due to leakage inductances PWM control 𝑉𝑜 𝑁2 =2 𝐷 𝑉𝑑 𝑁1 0 < 𝐷 < 0.5 2016-11-15 51 TSTE25/Tomas Jonsson Half-bridge converter Derived from step-down converter Additional diodes for switch protection 𝑉𝑜 𝑁2 = 𝐷 𝑉𝑑 𝑁1 0 < 𝐷 < 0.5 2016-11-15 52 TSTE25/Tomas Jonsson Full-bridge converter Derived from step-down converter Switches carry half the current compared to the half bridge converter 𝑉𝑜 𝑁2 =2 𝐷 𝑉𝑑 𝑁1 0 < 𝐷 < 0.5 2016-11-15 53 TSTE25/Tomas Jonsson 2016-11-15 54 Current-source dc-dc converter Ld and D > 0.5 gives current source input One or both switches always on Operates like a step-up converter 𝑉𝑜 𝑁2 1 = 𝑉𝑑 𝑁1 2 1 − 𝐷 𝐷 > 0.5 www.liu.se