Components. Magnetics. Capacitors. Power semiconductors. Core and copper losses Core materials

Transcription

1 Compoets Magetics Core ad copper losses Core materials Capacitors Equivalet series resistace ad iductace Capacitor types Power semicoductors Diodes MOSFETs IGBTs Power Electroics Laboratory Uiversity of Colorado, Boulder R W Erickso

2 Magetic devices Core loss Eergy per cycle W flowig ito - tur widig of a iductor, excited by periodic waveforms of frequecy f: W = v(t)i(t)dt + v(t) i(t) turs Φ core core area A c core permeability µ oe cycle Relate widig voltage ad curret to core B ad H via Faraday s law ad Ampere s law: db(t) v(t)=a c dt H(t) l m = i(t) Substitute ito itegral: W = oe cycle db(t) A c dt = A c l m HdB oe cycle H(t)l m dt

3 Core loss: Hysteresis loss B W = A c l m oe cycle HdB Area oe cycle HdB The term A c l m is the volume of the core, while the itegral is the area of the B-H loop. H (eergy lost per cycle) = (core volume) (area of B-H loop) P H = f A c l m HdB oe cycle Hysteresis loss is directly proportioal to applied frequecy

4 Modelig hysteresis loss Hysteresis loss varies directly with applied frequecy Depedece o maximum flux desity: how does area of B-H loop deped o maximum flux desity (ad o applied waveforms)? Emperical equatio (Steimetz equatio): P H = K H fb α max (core volume) The parameters K H ad α are determied experimetally. Depedece of P H o B max is predicted by the theory of magetic domais.

5 Core loss: eddy curret loss Magetic core materials are reasoably good coductors of electric curret. Hece, accordig to Lez s law, magetic fields withi the core iduce currets ( eddy currets ) to flow withi the core. The eddy currets flow such that they ted to geerate a flux which opposes chages i the core flux Φ(t). The eddy currets ted to prevet flux from peetratig the core. flux Φ(t) eddy curret i(t) core Eddy curret loss i 2 (t)r

6 Modelig eddy curret loss Ac flux Φ(t) iduces voltage v(t) i core, accordig to Faraday s law. Iduced voltage is proportioal to derivative of Φ(t). I cosequece, magitude of iduced voltage is directly proportioal to excitatio frequecy f. If core material impedace Z is purely resistive ad idepedet of frequecy, Z = R, the eddy curret magitude is proportioal to voltage: i(t) = v(t)/r. Hece magitude of i(t) is directly proportioal to excitatio frequecy f. Eddy curret power loss i 2 (t)r the varies with square of excitatio frequecy f. Classical Steimetz equatio for eddy curret loss: P E = K E f 2 2 B max (core volume) Ferrite core material impedace is capacitive. This causes eddy curret power loss to icrease as f 4.

7 Total core loss: maufacturer s data Ferrite core material 1 1MHz 500kHz 200kHz Empirical equatio, at a fixed frequecy: Power loss desity, Watts / cm kHz 50kHz 20kHz β P fe = K fe B max A c l m B max, Tesla

8 Core materials Core type B sat Relative core loss Applicatios Lamiatios iro, silico steel Powdered cores powdered iro, molypermalloy Ferrite Magaese-zic, Nickel-zic T high Hz trasformers, iductors T medium 1 khz trasformers, 100 khz filter iductors T low 20 khz - 1 MHz trasformers, ac iductors

9 Low-frequecy copper loss DC resistace of wire R = ρ l b A w where A w is the wire bare cross-sectioal area, ad l b is the legth of the wire. The resistivity ρ is equal to Ω cm for soft-aealed copper at room temperature. This resistivity icreases to Ω cm at 100 C. The wire resistace leads to a power loss of i(t) R 2 P cu = I rms R

10 Eddy currets i widig coductors The ski effect wire Φ(t) curret desity eddy currets wire i(t) i(t) eddy currets

11 Peetratio depth δ For siusoidal currets: curret desity is a expoetially decayig fuctio of distace ito the coductor, with characteristic legth δ kow as the peetratio depth or ski depth. ρ δ = π µ f peetratio depth δ, cm 0.1 Wire diameter #20AWG 100 C #30AWG For copper at room temperature: C #40AWG δ = 7.5 f cm kHz 100kHz 1MHz frequecy

12 The proximity effect Ac curret i a coductor iduces eddy currets i adjacet coductors by a process called the proximity effect. This causes sigificat power loss i the widigs of high-frequecy trasformers ad ac iductors. A multi-layer foil widig, with d >> δ. Each layer carries et curret i(t). layer 3 layer 2 layer 1 3i 2i 2i i i d 2Φ Φ curret desity J

13 Estimatig proximity loss: high-frequecy limit Let P 1 be power loss i layer 1: 2 P 1 = I rms R dc d δ Power loss P 2 i layer 2 is: 2 P 2 = I rms =5P 1 R dc d δ + 2I rms 2 R dc d δ layer 3 layer 2 3i 2i 2i i 2Φ Power loss P 3 i layer 3 is: P 3 = 2I rms 2 =13P 1 R dc d δ + 3I rms 2 R dc d δ layer 1 i d Φ Power loss P m i layer m is: P m = ((m 1) 2 + m 2 ) P 1 curret desity J

14 Capacitors Equivalet circuit Equivalet series iductace ESL Equivalet series resistace ESR Capacitace C ESL depeds o coductor geometry ESR depeds o: dielectric loss, termiatio resistace, foil resistace. Power loss i ESR typically limits rms curret that capacitor ca hadle. C depeds o: dielectric costat, foil area, dielectric thickess. Materials havig high dielectric costat typically exhibit: high dielectric loss, high depedece of dielectric costat o temperature.

15 Capacitors Sources of ESR Coductor Termiatio (coectig lead) Dielectric (isulator) Termiatio (coectig lead) Coductor Dielectric loss (the dual of hysteresis loss i magetic materials) Resistace of foil coductors Cotact betwee foil ad termiatios Ski effect is usually sigificat

16 Types of capacitors Electrolytic All exhibit: High C, high esr, rms curret limited by power loss i esr, substatial depedece of C ad esr o temperature, required dc voltage bias Alumium electrolytic Covetioal big capacitor i big ca. Low cost. Beware of rms curret ratig. Example: 1000 µf, 400 V, 3 A rms, 0.1 Ω esr. Tatalum Tear-shaped, or cylidrical with radial leads. High esr. Example: 22 µf, 35 V, 0.5 Ω esr. Orgaic Very low voltage, high C, with fractal geometry. Now popular i lowvoltage microprocessor power supplies. Example: 470 µf, 3.3V.

17 Types of capacitors Nopolarized Plastic dielectric Low C, very low esr, high rms curret. Mylar, polypropylee, polystyree, etc. Curret is limited by temperature rise. Caot tolerate high ambiet temperatures. Example: polypropylee 10 µf, 100 V, 10 A rms, 3 mω esr. Silver mica Low C, very low esr, high rms curret. Ofte used i RF applicatios. Example: 1 F, 400 V, rms curret ot specified.

18 Types of capacitors Nopolarized ceramic All ceramic capacitors exhibit low esr, high rms curret, ad low capacitace. Dielectric materials vary widely: Z5U (high dielectric costat, high temperature depedece, relatively high esr). Ceramic disk Low cost. Capacitace limited to sub-µf levels. Example: 0.01 µf, 100 V. Ceramic Capacitace limited to several µf. Good high-curret high frequecy capacitor. Multilayer ceramic Very high cost; costructed usig exotic materials (lots of platium). High µf, high curret (depedig o dielectric material), low esr. Example: 22 µf, 100 V, 5 mω esr, $100.

19 Types of power diodes Stadard recovery Reverse recovery time ot specified, iteded for 50/60Hz Fast recovery ad ultra-fast recovery Reverse recovery time ad recovered charge specified Iteded for coverter applicatios Schottky diode A majority carrier device Essetially o recovered charge Model with equilibrium i-v characteristic, i parallel with depletio regio capacitace Restricted to low voltage (few devices ca block 100V or more)

20 Characteristics of several commercial power rectifier diodes Part umber Rated max voltage Rated avg curret V F (typical) t r (max) Fast recovery rectifiers 1N V 30A 1.1V 400s SD453N25S20PC 2500V 400A 2.2V 2µs Ultra-fast recovery rectifiers MUR V 8A 0.975V 35s MUR V 15A 1.2V 60s RHRU V 100A 2.6V 60s Schottky rectifiers MBR6030L 30V 60A 0.48V 444CNQ045 45V 440A 0.69V 30CPQ V 30A 1.19V

21 The Power MOSFET Gate Source Gate legths approachig oe micro p - p Cosists of may small ehacemetmode parallelcoected MOSFET cells, coverig the surface of the silico wafer Vertical curret flow -chael device is show Drai

22 MOSFET: o state source p- - juctio is slightly reversebiased p p positive gate voltage iduces coductig chael chael - drai curret flows through - regio ad coductig chael drai drai curret o resistace = total resistaces of - regio, coductig chael, source ad drai cotacts, etc.

23 MOSFET body diode source p- - juctio forms a effective diode, i parallel with the chael p Body diode p egative drai-tosource voltage ca forward-bias the body diode drai - diode ca coduct the full MOSFET rated curret diode switchig speed ot optimized body diode is slow, Q r is large

24 Sychroous rectifiers Replacemet of diode with a backwards-coected MOSFET, to obtai reduced coductio loss + v 1 i + v 1 i C 1 i + v off i o (reverse coductio) v o ideal switch covetioal diode rectifier MOSFET as sychroous rectifier istataeous i-v characteristic

25 Buck coverter with sychroous rectifier V g + i A Q 1 v A + C C Q 2 i B v B + L i L (t) MOSFET Q 2 is cotrolled to tur o whe diode would ormally coduct Semicoductor coductio loss ca be made arbitrarily small, by reductio of MOSFET oresistaces Useful i lowvoltage high-curret applicatios

26 Characteristics of several commercial power MOSFETs Part um ber R ated m ax voltage R ated avg curret R o Q g (typical) IRFZ48 60V 50A 0.018Ω 110C IRF V 5.6A 0.54Ω 8.3C IRF V 28A 0.077Ω 72C APT10M25BNR 100V 75A 0.025Ω 171C IRF V 10A 0.55Ω 63C MTM15N40E 400V 15A 0.3Ω 110C APT5025BN 500V 23A 0.25Ω 83C APT1001RBNR 1000V 11A 1.0Ω 150C

27 The Isulated Gate Bipolar Trasistor (IGBT) Emitter A four-layer device Gate Similar i costructio to MOSFET, except extra p regio p - p Collector p miority carrier ijectio O-state: miority carriers are ijected ito - regio, leadig to coductivity modulatio compared with MOSFET: slower switchig times, lower o-resistace, useful at higher voltages (up to 3300V)

28 The IGBT Symbol collector gate Locatio of equivalet devices emitter Equivalet circuit C p i 2 i 1 p G - i 1 i 2 p E

29 Curret tailig i IGBTs C IGBT waveforms i L v A (t) i A (t) curret tail V g diode waveforms } 0 0 i L t G i B (t) 0 0 v B (t) t i 1 i 2 V g E p A (t) = v A i A V g i L area W off t 0 t 1 t 2 t 3 t

30 Characteristics of several commercial devices Part umber R ated m ax voltage R ated avg curret V F (typical) t f (typical) Sigle-chip devices HGTG32N60E2 600V 32A 2.4V 0.62µs HGTG30N120D2 1200V 30A 3.2A 0.58µs Multiple-chip power modules CM400HA-12E 600V 400A 2.7V 0.3µs CM300HA-24E 1200V 300A 2.7V 0.3µs