ECE1750, Spring 2018 Week Buck Converter

Transcription

1 ECE1750, Sprg 018 Week 5 Buck Converter 1

2 Objective to efficiently reduce DC voltage The DC equivalent of an AC transformer I I + + DC DC Buck Converter ossless objective: P = P, which means that I = I and I I

3 Here is an example of an efficient DC DC converter R 1 The load + R + R R R R R 1 R 1 R If = 39, and = 13, efficiency η is only 0.33 Unacceptable except very low power applications 3

4 + 39dc Another method lossless conversion of 39dc to average 13dc Rstereo Stereo voltage 39 0 Switch closed Switch open Switch state, Stereo voltage Closed, 39dc Open, 0dc DT T If the duty cycle D of the switch is 0.33, then the average voltage to the expensive car stereo is = 13dc. This is lossless conversion, but is it acceptable? 4

5 Convert 39dc to 13dc, cont. + 39dc C Rstereo Try addg a large C parallel with the load to control ripple. But if the C has 13dc, then when the switch closes, the source current spikes to a huge value and burns the switch. + 39dc C Rstereo Try addg an to prevent the huge current spike. But now, if the has current when the switch attempts to open, the ductor s current momentum and resultg di/dt burns the switch. + 39dc lossless C ADCDC DC-DC Buck Converter Rstereo By addg a free wheelg diode, the switch can open and the ductor current can contue to flow. With highfrequency switchg, the load voltage ripple can be reduced to a small value. 5

6 Capacitors and Inductors In capacitors: i( t) C dv( t) dt The voltage cannot change stantaneously Capacitors tend to keep the voltage constant t (voltage ertia ). An ideal capacitor with fite capacitance acts as a constant voltage source. Thus, a capacitor cannot be connected parallel with a voltage source or a switch (otherwise K would be violated, i.e. there will be a short-circuit) In ductors: v ( t ) di( t) dt The current cannot change stantaneously Inductors tend to keep the current constant (current ertia ). An ideal ductor with fite ductance acts as a constant current source. Thus, an ductor cannot be connected series with a current source or a switch (otherwise KC would be violated) 6

7 Buck converter + v i I i + C i C Assume large C so that t has very low ripple Sce has very low ripple, then assume I has very low ripple What do we learn from ductor voltage and capacitor current the average sense? i + 0 I I I + C 0A 7

8 The put/put equation for DC-DC converters usually comes by examg ductor voltages i + ( ) i i I Switch closed for DT seconds + C (i I ) Reverse biased, thus the diode d is open v di dt, v for DT seconds, di dt, di dt Note if the switch stays closed, then = 8

9 Switch open for (1 D)T seconds + i I + C (i I ) i contues to flow, thus the diode is closed. This is the assumption of contuous conduction the ductor which is the normal operatg condition. v di dt, v for (1 D)T seconds, di dt, di dt 9

10 Sce cethe eaverage eagevoltage otageacoss across is zero eo avg D 1 D 0 D D D The put/put p equation becomes D From power balance, I I, so I I D Note even though i is not constant (i.e., i has harmonics), the put power is still simply I because has no harmonics 10

11 Exame the ductor current Switch closed, v, di dt Switch open, v, di dt From geometry, I avg = I is halfway I max i A/ sec between I max and I m I avg = I I m A/ sec I Periodic fishes a period where it started DT (1 D)T T The state variables (ductor currents and capacitor voltages) transition from 11 a transient state to another transient state but average they reach steady state

12 Effect of raisg and lowerg I while holdg,, f, and constant i Raise I I I ower I I I is unchanged owerg I (and, therefore, P ) moves the circuit toward discontuous operation (when the current the ductor is zero for part of the period) 1

13 Effect of raisg and lowerg f while holdg,, I, and constant i ower f Raise f Slopes of i are unchanged owerg f creases I and moves the circuit toward discontuous operation 13

14 Effect of raisg and lowerg while holdg,, I and f constant i ower Raise owerg creases I and moves the circuit toward discontuous operation 14

15 Inductor current ratg I rms 1 1 I I I I avg 1 pp 1 Max impact of I on the rms current occurs at the boundary of contuous/discontuous conduction,, where I =I I i I avg = I 0 I I 1 4 rms I I I rms I 3 1 I Use max 3 15

16 Capacitor current and current ratg i I C (i I ) I i C = (i I ) Note raisg f or, which lowers I, reduces the capacitor current 0 I I Max rms current occurs at the boundary of contuous/discontuous conduction, where I =I Use max I Crms I avg I 0 I I Crms I 3 16

17 MOSFET and diode currents and current ratgs i i I C (i I ) I I 0 I I 0 Take worst case D for each Use max I rms I 3 17

18 Worst-case ostcase load ripple voltage Now, consider that the assumption that the put voltage is perfectly constant is no longer valid so you have some put voltage ripple i C = (i I ) I 0 T/ I C chargg Durg the chargg period, the C voltage moves from the m to the max. The area of the triangle shown above gives the peak-to-peak ripple voltage. Q C 1 T I T I C 4C I 4Cf Raisg f or reduces the load voltage ripple 18

19 Buck converter waveforms Consider a Buck converter with f = 0 khz, = 50, D = 0.4, R= ohms, =100 μh, C=0 μf (horizontal axis is time seconds). 19

20 Buck converter waveforms Consider a Buck converter with f = 0 khz, = 50, D = 0.4, R= ohms, =100 μh, C=0 μf (horizontal axis is time seconds). 0

21 Buck converter waveforms Consider a Buck converter with f = 0 khz, = 50, D = 0.4, R= ohms, =100 μh, H C=0 μf F (horizontal axis is time seconds). I,max T T T I,m i I ( I I ),max ( I I ),m From the circuit: Assume put i ic i I i ( I,max I ) ( I I,m ) current is constant C i,max,m ( I I ) T ( I I ) T From the circuit, when the switch is open: i (1 DT ) T T T 1 i 1 T (1 DT ) T Q (1 D) C C C 8Cf From the blue triangle 1

22 oltage ratgs Switch Closed i i I + C i C C sees Diode sees MOSFET sees i I Switch Open + C i C Diode and MOSFET, use Capacitor, use 1.5

23 There is a another mode of operation: discontuous MOSFET I DIODE C I + Occurs for light loads, or low operatg frequencies, where the ductor current eventually hits zero durg the switchopen state The diode d opens to prevent backward current flow The small capacitances of the MOSFET and diode, actg parallel with each other as a net parasitic capacitance, teract with to produce an oscillation The put C is series with the net parasitic capacitance, but C is so large that it can be ignored the oscillation phenomenon 3

24 Onset of the discontuous state I I avg =I i A/ sec I 0 onset onset (1 D)T 1 D T 1 D I f 1 D f onset Then, considerg the worst case (i.e., D 0), I f use max guarantees contuous conduction use m 4