6.334 Power Electronics Spring 2007


 Jasper Mathews
 1 years ago
 Views:
Transcription
1 MI OpenCourseWare hp://ocw.mi.edu Power Elecronics Spring 2007 For informaion abou ciing hese maerials or our erms of Use, visi: hp://ocw.mi.edu/erms.
2 Chaper 5 Inroducion o DC/DC Converers Analysis echniques: Average KVL, KCL, P.S.S. Condiions. KCL in i2 Figure 5.1: KCL i j = 0 (5.1) 34
3 35 Average over ime: 1 ij = 0 1 i j = 0 < ij > = 0 (5.2) KCL applies o average curren as well as insananeous currens. (Derives from conservaion of charge). KVL Vn Figure 5.2: KVL V k = 0 (5.3) Average over ime: 1 Vk = 0 1 V k = 0 < V k > = 0 (5.4)
4 36 CHAPER 5. INRODUCION O DC/DC CONVERERS KVL applies o averaged variables. P.S.S. o analyze converers in Periodic Seady Sae (P.S.S.): Average KCL < i j > = 0 (5.5) Average KVL < V k > = 0 (5.6) di L from < V L > = L < > d di L in P.S.S. < > = 0 d Inducor in P.S.S. < V L > = 0 (5.7) dv L from < i C > = C < > d dv L in P.S.S. < > = 0 d Capacior in P.S.S. < i C > = 0 (5.8) If Circui is Lossless: P in = P ou (5.9) Consider he DC/DC converer from before (see Figure 5.3): q() (>0) C1 il q() = 1 I2 1 q() = 0 VL Vx C2 Vx() Pulse Widh Modulaion (PWM) d d 2 Duy Raio d d d 2 <Vx> = d Figure 5.3: DC/DC Converer
5 37 Assume L s and C s are very big, herefore: Analyze (using average relaions) in P.S.S.: < V L > = 0 v C () V C (5.10) i L () I L (5.11) < V L > = d (V 1 V 2 ) (1 d) (V 2 ) dv 1 V 2 = 0 (Since < V L >= 0, < V 2 >=< V x >= dv 1.) Consider currens: Combining: < i C2 > = 0 V 2 = dv 1 (5.12) I 1 = I 2 (5.13) < i C1 > = 0 I C1 = (I 1 I 2 d ) I 1 (1 d) = 0 I 1 = di 2 (5.14) I 1 = di 2 dv 1 = V 2 dv 1 I 1 = di 2 V 2 V 1 I 1 = I 2 V 2 (5.15)
6 38 CHAPER 5. INRODUCION O DC/DC CONVERERS herefore, power is (ideally) conserved. Noe: rick in his ype of average analysis is o be careful when one can use an average value and when one mus consider insananeous quaniies Wih he following ype of exernal nework and V 1,V 2 > 0, power flows from Swich implemenaion: buck or down converer (see Figure 5.4). C1 C2 Figure 5.4: Buck (down) Converer ype of direc converer because a DC pah exiss beween inpu and oupu in one swich sae. Suppose we change he locaion of source and load: Refine swiching funcion so q() = 1 when swich is in down posiion (see Figure 5.5). Similar analysis: By conservaion of power: < V L > = 0 (V 1 V 2 )(1 d) V 1 d = 0 1 V 2 = V 1 (5.16) 1 d I 2 = (1 d)i 1 (5.17)
7 39 q() 1 il q() = 0 I2 d d 2 Vx()  q() = 1 VL C1 Vx C2   d d 2  VL  d Figure 5.5: Change he Locaion of Source and Load In his case, energy flows from 2 1 and he P.S.S. oupu volage (V 2 ) is higher han inpu volage (V 1 ). Wih he following swich implemenaion: boos or up converer. Anoher ype of direc converer (see Figure 5.6). C1 C2 Figure 5.6: Boos (up) Converer In general power flows direcion depends on: 1. Exernal nework 2. Swich implemenaion
8 40 CHAPER 5. INRODUCION O DC/DC CONVERERS 3. Conrol We may need o know all of hese o deermine behavior. he boos converer is ofen drawn wih power flowing lef o righ. However, here is nohing fundamenal abou his (see Figure 5.7). C2 C1 Figure 5.7: Boos (up) Converer Drawn Lef o Righ Boos: Swich urns on and incremenally sores energy from V 1 in L. Swich runs off and his energy and addiional energy from inpu is ransferred o oupu. herefore, L used as a emporary sorage elemen. Eiher he buck or boos can be seen as he appropriae connecion of a canonical cell (see Figure 5.8). A C B Figure 5.8: Direc Canonical Cell he direc connecion has B as he common node. he res of operaion is deermined by exernal nework, swich implemenaion and conrol. Swich implemenaion: Differen swiches can carry curren and block volage only in cerain direcions.
9 41 MOSFE can block posiive V and can carry posiive or negaive i (see Figure 5.9). D G D i V Body Diode S G Figure 5.9: MOSFE S BJ (or darlingon) is similar, bu negaive V blows up device (see Figure 5.10). i i Same for V V IGB Figure 5.10: BJ Combine elemens: 1. Block posiive V and carry posiive and negaive i (see Figure 5.11). i V Figure 5.11: Combine Elemens 1 2. Block posiive and negaive V and carry posiive i (see Figure 5.12).
10 42 CHAPER 5. INRODUCION O DC/DC CONVERERS i V Figure 5.12: Combine Elemens 2 3. Block posiive and negaive V and carry posiive and negaive i (see Figure 5.13). i V Figure 5.13: Combine Elemens 3 We can also consruc indirec DC/DC converers. Sore energy from inpu, ransfer energy o oupu, never a DC pah from inpu o oupu (see Figure 5.14). A B C Figure 5.14: Canonical Cell Spli capacior (see Figure 5.15):
11 43 q() = 1 q() = 0 1 q() d d 2 q() = 0 q() = 1 VL C1 C2 d Spli Capacior Figure 5.15: Indirec DC/DC Converer < V L > = 0 < V L > = V 1 d (1 d)v 2 d V 2 = V 1 (5.18) 1 d V 2 for 0 < d < 1 < < 0 (5.19) V 1 Sore energy in L(d ) from V 1. Discharge i (he oher way) in V 2. (mus have volage inversion). Buck/Boos or up/down converer (see Figure 5.16):
12 44 CHAPER 5. INRODUCION O DC/DC CONVERERS I2 Figure 5.16: Buck/Boos or up/down converer V 1 > 0 I 1 > 0 V 2 < 0 I 2 > 0 Oher indirec converers include CUK and SEPIC varians. Given conversion range < V 2 < 0, why no always use indirec vs. direc? V 1 1. Sign inversion (can fix) 2. Device and componen sresses Look a averaged circui variables (see Figure 5.17): Assume C, L are very large. I L = I 1 I 2 I L = I 1 I 2 (5.20) By averaged KCL ino doed box: Maybe couner inuiive: I 1 = average ransisor curren. I 1 I 2 = peak ransisor curren.
13 45 VC I2 iq iq IL I2 d Figure 5.17: Averaged Circui Variables By averaged KVL around loop: V C = V 1 V 2 V C = V 1 V 2 (5.21) herefore, for big L, C (see Figure 5.18): I2 Q D I2 Figure 5.18: Big L, C Indirec converer: So Q, D, L see peak curren I = I 1 I 2, Q, D, C block peak volage V = V 1 V 2. Consider direc converers (see Figure 5.19):
14 46 CHAPER 5. INRODUCION O DC/DC CONVERERS Buck Vq I2 Boos D C Q D Vd Q Vq C Figure 5.19: Direc Converers Buck: V C = V q,max = V d,max = V 1 (5.22) I L = i q,max = i d,max = I 2 (5.23) Boos: V C = V q,max = V d,max = V 2 (5.24) I L = i q,max = i d,max = I 1 (5.25) Direc converers (eiher ype): V C = V q,max = V d,max = max(v 1,V 2 ) (5.26) I L = i q,max = i d,max = max(i 1,I 2 ) (5.27) Device volage and curren sresses are higher for indirec converers han for direc converers wih same power. Inducor curren and capacior volage are also higher. Summary: For indirec converers (neglecing ripple) (see Figure 5.20):
15 47 VC I2 iq il I2 d Figure 5.20: Indirec Converers (neglecing ripple) I L = i sw,pk = i d,pk = I 1 I 2 (5.28) V C = V sw,pk = V d,pk = V 1 V 2 (5.29) For direc converers (neglecing ripple) (see Figure 5.21): Buck Vq IL Boos IL Vd Vq Figure 5.21: Direc Converers (neglecing ripple) I L = i sw,pk = i d,pk = max(i 1,I 2 ) (5.30) V C = V sw,pk = V d,pk = max(v 1,V 2 ) (5.31) Based on device sresses we would no choose an indirec converer unless we needed o, since direc converers have lower sress.
16 48 CHAPER 5. INRODUCION O DC/DC CONVERERS 5.1 Ripple Componens and Filer Sizing Now, selecing filer componen sizes does depend on ripple, which we have previously negleced. Les see how o approximaely calculae ripple componens. o eliminae 2 nd order effecs on capacior volage ripple: 1. Assume inducor is (Δi pp 0). 2. Assume all ripple curren goes ino capacior. Similarly, o eliminae 2 nd order effecs in inducor curren ripple: 1. Assume capaciors are (ΔV C,pp 0). 2. Assume all ripple volage is across he inducor. We can verify assumpions aferwards. Example: Boos Converer Ripple (see Figure 5.22) id id Figure 5.22: Boos Converer Ripple Find capacior (oupu) volage ripple (see Figure 5.23): Assume L, herefore, i 1 () I 1. So a ripple model for he oupu volage is (see Figure 5.24):
17 5.1. RIPPLE COMPONENS AND FILER SIZING 49 id Acual Waveform i D Including Ripple Id=<id>=(1D) D Figure 5.23: Capacior Volage Ripple ~ id D D ~ id C R ~ V (1D) ΔVCpp 2 ΔVCpp 2 ~ VC D o V 2. Figure 5.24: Ripple Model wih Capacior If we assume all ripple curren ino capacior 1 2πf sw C R or Ṽ2 is small recpec Le us calculae he ripple: herefore, o limi ripple: i = C dv C d D 1 D ΔV C,pp = I 1 d 0 C (1 D)D = I 1 (5.32) C
18 50 CHAPER 5. INRODUCION O DC/DC CONVERERS (1 D)D C I 1 (5.33) ΔV C,pp Now le us find he capacior volage ripple (see Figure 5.25): Zi Source Impedance Vx C1 Vx Acual Vx Including Ripple D <Vx>=(1D) Figure 5.25: Ripple Replace V x wih equivalen source and eliminae DC quaniies (see Figure 5.26). ~ Vx D D ~ ~ i1 Vx (1D) ~ i1 Δ ipp 2 D Δ ipp 2 Figure 5.26: Ripple Model wih Inducor Neglecing he drop on any source impedance ( Z i 2πf sw L). 1 D Δi L,pp = (1 D)V 2 d L 0 D(1 D) = V 2 (5.34) L
19 5.1. RIPPLE COMPONENS AND FILER SIZING 51 herefore, we need: L D(1 D) (5.35) Δi pp Energy sorage is one meric for sizing L s and C s. Physical size may acually be deermined by one or more of: energy sorage, losses, packing consrains, maerial properies. o deermine peak energy sorage requiremens we mus consider he ripple in he waveforms. Define ripple raios (see Figure 5.27): ΔV C,pp R C = (5.36) 2V C Δi L,pp R L = (5.37) 2I L his is essenially % ripple: peak ripple magniude normalized o DC value. Xpk X Δ Xpp 2 Δ Xpp 2 Figure 5.27: Ripple Raios Specificaion of allowed ripple and converer operaing parameers deermines capacior and inducor size requiremens. herefore: V C,pk = V C (1 R C ) (5.38) i L,pk = I L (1 R L ) (5.39)
20 52 CHAPER 5. INRODUCION O DC/DC CONVERERS So from our previous resuls (boos converer): C L (1 D)D 2R C V C (5.40) D(1 D) 2R L I 1 (5.41) he ripple raios also deermine passive componen energy sorage requiremens and semiconducor device sresses. So les calculae he required energy sorage for he capacior: 1 CV 2 E C = 2 C,pk 1 (1 D)D V 2 = 2 2RC V C (1 R C ) 2 C = DI 2 V 2 (1 R C ) 2 4f sw R C DP o (1 R C ) 2 = (5.42) 4f sw R C So required capacior energy sorage increases wih: 1. Conversion raio 2. Power level and decreases wih swiching frequency. Similar resul for inducor energy sorage: (1 D)P o (1 R L ) 2 E L = (5.43) 4f sw I can be shown ha direc converers always require lower energy sorage han indirec converers. R L
21 5.2. DISCONINUOUS CONDUCION MODE 53 able 5.1: Effec of Allowed Ripple on Swiches Converer ype Value L, C Finie L, C Direc Indirec i sw,pk, i d,pk V sw,pk, V d,pk i sw,pk, i d,pk V sw,pk, V d,pk max( I 1, I 2 ) max( V 1, V 2 ) I 1, I 2 V 1, V 2 max( I 1, I 2 )(1 R L ) max( V 1, V 2 )(1 R C ) ( I 1, I 2 )(1 R L ) ( V 1, V 2 )(1 R C ) Consider effec of allowed ripple on swiches (see able 5.1): Define a meric for swich sizing (qualiaive only): For a boos converer:. Swich Sress P arameer(ssp ) = V sw,pk i sw,pk (5.44) SSP = max(v 1,V 2 )(1 R C )max(i 1,I 2 )(1 R L ) herefore, SSP ges worse for: = V 2 (1 R C )I 1 (1 R L ) P o = (1 R C )(1 R L ) 1 D V 2 = P o (1 R C )(1 R L ) (5.45) V 1 Large power Large conversion raio Large ripple 5.2 Disconinuous Conducion Mode Consider he waveform of he boos converer (see Figure 5.28):
22 54 CHAPER 5. INRODUCION O DC/DC CONVERERS q() Swiching Funcion for Diode qd() VL D L q() C R D il D Figure 5.28: Boos Converer Waveforms V 1 D Δi L,pp = (5.46) L V 2 = R(1 D) (5.47) Δi L,pp 2 R L = I 1 = V 1 D(1 D)R 2V 2 L = D(1 D) 2 R 2L (5.48) R L as R,L (5.49) (see Figure 5.29 for an illusraion) Evenually peak ripple becomes greaer han DC curren: boh swich and diode off for par of cycle. his is known as Disconinuous Condiion Mode (DCM). I
23 5.2. DISCONINUOUS CONDUCION MODE 55 il As R Increases il As L Decreases D D Figure 5.29: Changing R and L happens when R L > 1. R L = R L > R D(1 D) 2 R 2L 1 2L D(1 D) 2 (5.50) A ligh load (big R and low power) we ge DCM. Ligher load can be reached in CCM for larger L. DCM occurs for: L D(1 D)2 R 2 (5.51) he minimum inducance for CCM operaion is someimes called he criical inducance. D(1 D) 2 R L CRI,BOOS = (5.52) 2 For some cases (e.g. we need o operae down o almos no load), his may be unreasonably large. Because of he new swich sae, operaing condiions are differen (see Figure 5.30).
24 56 CHAPER 5. INRODUCION O DC/DC CONVERERS DCM q(), q D () VL D (DD2)  D (DD2) il Mus Be Zero in Remaining ime D (DD2) Figure 5.30: Differen Operaing Condiions Volage conversion raio: < V L > = 0 in P.S.S. V 1 D (V 1 V 2 )D 2 = 0 where D 2 < 1 D. V 1 (D D 2 ) = V 2 D 2 How does his compare o CCM? In CCM: V 2 1 = 1 D V 1 V 2 D D 2 = V 1 D 2 D = 1 (5.53) D 2
25 5.2. DISCONINUOUS CONDUCION MODE 57 1 D D = 1 D D = 1 (5.54) 1 D Since V 2 = 1 D and D 2 < 1 D, V 2 is bigger in DCM. V 1 D 2 V 1 Eliminaing D 2 from equaions, can be shown for boos: V D 2 R = 1 (5.55) V L herefore, conversion raio depends on R, f sw, L,... unlike CCM. his makes conrol ricky, as all of our characerisics change for par of he load range. How do we model DCM operaion? Consider diode curren (see Figure 5.31). IL id id() ipk id I2 D (DD2) Figure 5.31: DCM Operaion Model V 1 D i pk = L D 2 = Δ
26 58 CHAPER 5. INRODUCION O DC/DC CONVERERS Δi = L V D L = L V 2 V 1 V 1 D D 2 = (5.56) V 2 V 1 < i ou > = < i d > 1 1 = (D 2 )(i pk ) 2 1 V 1 V 1 D 1 = ( D )( ) 2 V 2 V 1 L V 1 2 D 2 = 2(V 2 V 1 ) Model as conrolled curren source as a funcion of D. So DCM someimes occurs under ligh load, as dicaed by sizing of L. (5.57) Someimes we can no pracically make L big enough. Mus handle conrol (changes from CCM o DCM). Also, we ge parasiic ringing in boh swiches (see Figure 5.32). Vx Vx Ideal L Rings wih Parasiic C s D D2 Figure 5.32: Parasiic Ringing Someimes people design o always be in DCM. Inducor size becomes very small and we can ge fas di (see Figure 5.33). d
27 5.2. DISCONINUOUS CONDUCION MODE 59 CCM Desired i DCM di/d limied so canno respond fas. Figure 5.33: Design in DCM In his case we ge: 1. Very fas di capabiliy. d 2. Simple conrol model i ou = f(d). 3. Small inducor size (E L R L = 1) Bu we mus live wih: 1. Parasiic ringing 2. High peak and RMS currens 3. Need addiional filers DCM is someimes used when very fas response speed is needed (e.g. for volage regulaor modules in microprocessors), especially if means are available o cancel ripple (e.g. inerleaving of muliple converers). In many oher circumsances DCM is avoided, hough one may have o operae in DCM under lighload condiions o keep componen sizes accepable.
Chapter 2: Principles of steadystate converter analysis
Chaper 2 Principles of SeadySae Converer Analysis 2.1. Inroducion 2.2. Inducor volsecond balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer
More informationCircuit Types. () i( t) ( )
Circui Types DC Circuis Idenifying feaures: o Consan inpus: he volages of independen volage sources and currens of independen curren sources are all consan. o The circui does no conain any swiches. All
More informationCapacitors and inductors
Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationµ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ
Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high
More informationDCDC Boost Converter with Constant Output Voltage for Grid Connected Photovoltaic Application System
DCDC Boos Converer wih Consan Oupu Volage for Grid Conneced Phoovolaic Applicaion Sysem PuiWeng Chan, Syafrudin Masri Universii Sains Malaysia Email: edmond_chan85@homail.com, syaf@eng.usm.my Absrac
More informationA Mathematical Description of MOSFET Behavior
10/19/004 A Mahemaical Descripion of MOSFET Behavior.doc 1/8 A Mahemaical Descripion of MOSFET Behavior Q: We ve learned an awful lo abou enhancemen MOSFETs, bu we sill have ye o esablished a mahemaical
More informationLECTURE 9. C. Appendix
LECTURE 9 A. BuckBoos Converer Design 1. VolSec Balance: f(d), seadysae ransfer funcion 2. DC Operaing Poin via Charge Balance: I(D) in seadysae 3. Ripple Volage / C Spec 4. Ripple Curren / L Spec 5.
More informationPulseWidth Modulation Inverters
SECTION 3.6 INVERTERS 189 PulseWidh Modulaion Inverers Pulsewidh modulaion is he process of modifying he widh of he pulses in a pulse rain in direc proporion o a small conrol signal; he greaer he conrol
More informationI) EQUATION 1: SHUNTCONTROLLED
Swich Mode Power Supply (SMPS) Topologies (Par I) Auhor: Mohammad Kamil Microchip Technology Inc. EQUATION 1: SHUNTCONTROLLED REGULATOR POWER LOSS INTRODUCTION The indusry drive oward smaller, ligher
More informationSwitched Mode Converters (1 Quadrant)
(1 Quadran) Philippe Barrade Laboraoire d Elecronique Indusrielle, LEI STI ISE Ecole Polyechnique Fédérale de Lausanne, EPFL Ch1015 Lausanne Tél: +41 21 693 2651 Fax: +41 21 693 2600 Philippe.barrade@epfl.ch
More informationFullwave rectification, bulk capacitor calculations Chris Basso January 2009
ullwave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal
More informationModule 4. Singlephase AC circuits. Version 2 EE IIT, Kharagpur
Module 4 Singlephase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,
More informationPart II Converter Dynamics and Control
Par II onverer Dynamics and onrol 7. A equivalen circui modeling 8. onverer ransfer funcions 9. onroller design 1. Inpu filer design 11. A and D equivalen circui modeling of he disconinuous conducion mode
More informationSwitching Regulator IC series Capacitor Calculation for Buck converter IC
Swiching Regulaor IC series Capacior Calculaion for Buck converer IC No.14027ECY02 This applicaion noe explains he calculaion of exernal capacior value for buck converer IC circui. Buck converer IIN IDD
More informationRC (ResistorCapacitor) Circuits. AP Physics C
(ResisorCapacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED
More information9. Capacitor and Resistor Circuits
ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren
More informationVoltage level shifting
rek Applicaion Noe Number 1 r. Maciej A. Noras Absrac A brief descripion of volage shifing circuis. 1 Inroducion In applicaions requiring a unipolar A volage signal, he signal may be delivered from a bipolar
More informationSignal Rectification
9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, halfwae and fullwae. Le s firs consider he ideal
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College  Physics 2426  Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More informationPI4ULS5V202 2Bit Bidirectional Level Shifter with Automatic Sensing & Ultra Tiny Package
Feaures can be Less han, Greaer han or Equal o V CCB 1.2V o 5.5V on A Por and 1.2V o 5.5V on B Por High Speed wih 20 Mb/s Daa Rae for pushpull applicaion High Speed wih 2 Mb/s Daa Rae for opendrain applicaion
More informationMonotonic, Inrush Current Limited StartUp for Linear Regulators
Applicaion epor SLA156 March 2004 Monoonic, Inrush urren Limied SarUp for Linear egulaors Jeff Falin PMP Porable Producs ABSA he oupu volage of a linear regulaor ends o rise quickly afer i is enabled.
More informationRC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
More informationMaking Use of Gate Charge Information in MOSFET and IGBT Data Sheets
Making Use of ae Charge Informaion in MOSFET and IBT Daa Shees Ralph McArhur Senior Applicaions Engineer Advanced Power Technology 405 S.W. Columbia Sree Bend, Oregon 97702 Power MOSFETs and IBTs have
More informationLLC Resonant Converter Reference Design using the dspic DSC
LLC Resonan Converer Reference Design using he dspic DSC 2010 Microchip Technology Incorporaed. All Righs Reserved. LLC Resonan Converer Webinar Slide 1 Hello, and welcome o his web seminar on Microchip
More informationPHYS245 Lab: RC circuits
PHYS245 Lab: C circuis Purpose: Undersand he charging and discharging ransien processes of a capacior Display he charging and discharging process using an oscilloscope Undersand he physical meaning of
More informationUsing RCtime to Measure Resistance
Basic Express Applicaion Noe Using RCime o Measure Resisance Inroducion One common use for I/O pins is o measure he analog value of a variable resisance. Alhough a builin ADC (Analog o Digial Converer)
More informationChabot College Physics Lab RC Circuits Scott Hildreth
Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard
More informationNOTES ON OSCILLOSCOPES
NOTES ON OSCILLOSCOPES NOTES ON... OSCILLOSCOPES... Oscilloscope... Analog and Digial... Analog Oscilloscopes... Cahode Ray Oscilloscope Principles... 5 Elecron Gun... 5 The Deflecion Sysem... 6 Displaying
More informationCHARGE AND DISCHARGE OF A CAPACITOR
REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:
More informationAN1207. Switch Mode Power Supply (SMPS) Topologies (Part II) REQUIREMENTS AND RULES INTRODUCTION CONTENTS. Microchip Technology Inc.
Swich Mode Power Supply (SMPS) opologies (Par II) Auhor: INRODUCION his applicai noe is he secd of a wopar series Swich Mode Power Supply (SMPS) opologies. he firs applicai noe in his series AN1114 
More informationLecture10 BJT Switching Characteristics, Small Signal Model
1 Lecure1 BJT Swiching Characerisics, Small Signal Model BJT Swiching Characerisics: The circui in Fig.1(b) is a simple CE swich. The inpu volage waveform v s shown in he Fig.1(a) is used o conrol he
More informationAN Smart LED Lamp Driver IC with PFC Function. Introduction. SoftStart Function. Internal Digital Reference by ZCD.
www.fairchildsemi.com AN9744 Smar LED Lamp Driver IC wih PFC Funcion Inroducion The FL7701 is a PWM peak curren conroller for a buck converer opology operaing in Coninuous Conducion Mode (CCM) wih an
More informationAstable multivibrator using the 555 IC.(10)
Visi hp://elecronicsclub.cjb.ne for more resources THE 555 IC TIMER The 555 IC TIMER.(2) Monosable mulivibraor using he 555 IC imer...() Design Example 1 wih Mulisim 2001 ools and graphs..(8) Lile descripion
More informationSEMICONDUCTOR APPLICATION NOTE
SEMICONDUCTOR APPLICATION NOTE Order his documen by AN1542/D Prepared by: C. S. Mier Moorola Inc. Inpu filer design has been an inegral par of power supply designs. Wih he adven of inpu filers, he designer
More informationDesigning A HighVoltage NonIsolated BuckBoost Converter with the Si9121DY
Designing A HighVolage NonIsolaed BuckBoos Converer wih he Si9DY AN Niin Kalje The Si9DY is a nonisolaed buckboos converer IC, operaing from a wide inpu volage range of 0 o 0 V wih minimal exernal
More informationRC Circuit and Time Constant
ircui and Time onsan 8M Objec: Apparaus: To invesigae he volages across he resisor and capacior in a resisorcapacior circui ( circui) as he capacior charges and discharges. We also wish o deermine he
More informationDifferential Equations and Linear Superposition
Differenial Equaions and Linear Superposiion Basic Idea: Provide soluion in closed form Like Inegraion, no general soluions in closed form Order of equaion: highes derivaive in equaion e.g. dy d dy 2 y
More informationSINAMICS S120 drive system
SINAMICS S120 drive sysem Design PM340, frame sizes FSA o FSF The PM340 feaure he following connecions as sandard: DCP/R1 and DCN DC link Terminals DCP/R1 and R2 for connecion of an exernal braking PMIF
More information11/6/2013. Chapter 14: Dynamic ADAS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic DS dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuingedge
More informationCAPACITANCE AND INDUCTANCE
CHAPTER 6 CAPACITANCE AND INDUCTANCE THE LEARNING GOALS FOR THIS CHAPTER ARE: Know how o use circui models for inducors and capaciors o calculae volage, curren, and power Be able o calculae sored energy
More informationcooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)
Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More informationEntropy: From the Boltzmann equation to the Maxwell Boltzmann distribution
Enropy: From he Bolzmann equaion o he Maxwell Bolzmann disribuion A formula o relae enropy o probabiliy Ofen i is a lo more useful o hink abou enropy in erms of he probabiliy wih which differen saes are
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67  FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 2 TUTORIAL 1  TRANSIENTS
EDEXEL NAIONAL ERIFIAE/DIPLOMA UNI 67  FURHER ELERIAL PRINIPLE NQF LEEL 3 OUOME 2 UORIAL 1  RANIEN Uni conen 2 Undersand he ransien behaviour of resisorcapacior (R) and resisorinducor (RL) D circuis
More informationECEN4618: Experiment #1 Timing circuits with the 555 timer
ECEN4618: Experimen #1 Timing circuis wih he 555 imer cæ 1998 Dragan Maksimović Deparmen of Elecrical and Compuer Engineering Universiy of Colorado, Boulder The purpose of his lab assignmen is o examine
More informationModule 3. RL & RC Transients. Version 2 EE IIT, Kharagpur
Module 3  & C Transiens esson 0 Sudy of DC ransiens in  and C circuis Objecives Definiion of inducance and coninuiy condiion for inducors. To undersand he rise or fall of curren in a simple series
More informationHigh Efficiency DCDC Converter for EV Battery Charger Using Hybrid Resonant and PWM Technique
High Efficiency DCDC Converer for EV Baery Charger Using Hybrid Resonan and PWM Technique Hongmei Wan Thesis submied o he faculy of he Virginia Polyechnic Insiue and Sae Universiy in parial fulfillmen
More informationPhotovoltaic Power Control Using MPPT and Boost Converter
23 Phoovolaic Power Conrol Using MPP and Boos Converer A.Aou, A.Massoum and M.Saidi Absrac he sudies on he phoovolaic sysem are exensively increasing because of a large, secure, essenially exhausible and
More informationSignal Processing and Linear Systems I
Sanford Universiy Summer 214215 Signal Processing and Linear Sysems I Lecure 5: Time Domain Analysis of Coninuous Time Sysems June 3, 215 EE12A:Signal Processing and Linear Sysems I; Summer 1415, Gibbons
More informationProduct Operation and Setup Instructions
A9 Please read and save hese insrucions. Read carefully before aemping o assemble, insall, operae, or mainain he produc described. Proec yourself and ohers by observing all safey informaion. Failure o
More informationIR Receiver Modules for Mid Range Proximity Sensors
IR Receiver Modules for Mid Range TSOP4P.. Vishay Semiconducors 2 3 MECHANICAL DATA Pinning = OUT, 2 =, 3 = V S 6672 FEATURES Low supply curren Phoo deecor and preamplifier in one package Inernal filer
More informationPackage SJP. Parameter Symbol Conditions Rating Unit Remarks Transient Peak Reverse Voltage V RSM 30 V Repetitive Peak Reverse Voltage, V RM 30 V
V RM = 30 V, I F(AV) = A Schoky Diode Daa Shee Descripion is a Schoky diode ha is low forward volage drop, and achieves high efficiency recificaion circui. Package SJP (2) Feaures Low Sauraion Volage High
More informationNDP6020P / NDB6020P PChannel Logic Level Enhancement Mode Field Effect Transistor
Sepember 997 NP62P / NB62P PChannel Logic Level Enhancemen Mode Field Effec Transisor General escripion Feaures These logic level PChannel enhancemen mode power field effec ransisors are produced using
More informationGraduate Macro Theory II: Notes on Neoclassical Growth Model
Graduae Macro Theory II: Noes on Neoclassical Growh Model Eric Sims Universiy of Nore Dame Spring 2011 1 Basic Neoclassical Growh Model The economy is populaed by a large number of infiniely lived agens.
More informationLecture 2: Telegrapher Equations For Transmission Lines. Power Flow.
Whies, EE 481 Lecure 2 Page 1 of 13 Lecure 2: Telegraher Equaions For Transmission Lines. Power Flow. Microsri is one mehod for making elecrical connecions in a microwae circui. I is consruced wih a ground
More informationChapter 2 Problems. s = d t up. = 40km / hr d t down. 60km / hr. d t total. + t down. = t up. = 40km / hr + d. 60km / hr + 40km / hr
Chaper 2 Problems 2.2 A car ravels up a hill a a consan speed of 40km/h and reurns down he hill a a consan speed of 60 km/h. Calculae he average speed for he rip. This problem is a bi more suble han i
More informationAnalogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar
Analogue and Digial Signal Processing Firs Term Third Year CS Engineering By Dr Mukhiar Ali Unar Recommended Books Haykin S. and Van Veen B.; Signals and Sysems, John Wiley& Sons Inc. ISBN: 073807 Ifeachor
More informationChapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m
Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m
More information4 Convolution. Recommended Problems. x2[n] 1 2[n]
4 Convoluion Recommended Problems P4.1 This problem is a simple example of he use of superposiion. Suppose ha a discreeime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.11.
More information5.8 Resonance 231. The study of vibrating mechanical systems ends here with the theory of pure and practical resonance.
5.8 Resonance 231 5.8 Resonance The sudy of vibraing mechanical sysems ends here wih he heory of pure and pracical resonance. Pure Resonance The noion of pure resonance in he differenial equaion (1) ()
More informationThyristor Based Speed Control Techniques of DC Motor: A Comparative Analysis
Inernaional Journal of Scienific and Research Publicaions, Volume 2, Issue 6, June 2012 1 Thyrisor Based Speed Conrol Techniques of DC Moor: A Comparaive Analysis Rohi Gupa, Ruchika Lamba, Subhransu Padhee
More informationModule 3 Design for Strength. Version 2 ME, IIT Kharagpur
Module 3 Design for Srengh Lesson 2 Sress Concenraion Insrucional Objecives A he end of his lesson, he sudens should be able o undersand Sress concenraion and he facors responsible. Deerminaion of sress
More informationSteps for D.C Analysis of MOSFET Circuits
10/22/2004 Seps for DC Analysis of MOSFET Circuis.doc 1/7 Seps for D.C Analysis of MOSFET Circuis To analyze MOSFET circui wih D.C. sources, we mus follow hese five seps: 1. ASSUME an operaing mode 2.
More informationLecture 080 All Digital PPLs (5/15/03) Page 0801
Lecure 8 All Digial PPLs (5/15/3) Page 81 LECTURE 8 ALL DIGITAL PHASE LOCK LOOPS (ADPLL) (Reference [2]) Ouline Building Blocks of he ADPLL Examples of ADPLL Implemenaion ADPLL Design ADPLL Sysem Simulaion
More informationFrequency Modulation. Dr. HweePink Tan http://www.cs.tcd.ie/hweepink.tan
Frequency Modulaion Dr. HweePink Tan hp://www.cs.cd.ie/hweepink.tan Lecure maerial was absraced from "Communicaion Sysems" by Simon Haykin. Ouline Day 1 Day 2 Day 3 Angle Modulaion Frequency Modulaion
More informationIR Receiver Modules for Remote Control Systems
IR Receiver Modules for Remoe Conrol Sysems 1926 FEATURES Very low supply curren Phoo deecor and preamplifier in one package Inernal filer for PCM frequency Supply volage: 2.5 V o 5.5 V Improved immuniy
More informationOPERATION MANUAL. Indoor unit for air to water heat pump system and options EKHBRD011ABV1 EKHBRD014ABV1 EKHBRD016ABV1
OPERAION MANUAL Indoor uni for air o waer hea pump sysem and opions EKHBRD011ABV1 EKHBRD014ABV1 EKHBRD016ABV1 EKHBRD011ABY1 EKHBRD014ABY1 EKHBRD016ABY1 EKHBRD011ACV1 EKHBRD014ACV1 EKHBRD016ACV1 EKHBRD011ACY1
More informationsdomain Circuit Analysis
Domain ircui Analyi Operae direcly in he domain wih capacior, inducor and reior Key feaure lineariy i preered c decribed by ODE and heir Order equal number of plu number of Elemenbyelemen and ource ranformaion
More informationGate protection. Current limit. Overvoltage protection. Limit for unclamped ind. loads. Charge pump Level shifter. Rectifier. Open load detection
Smar ighside Power Swich for ndusrial Applicaions Feaures Overload proecion Curren limiaion Shor circui proecion Thermal shudown Overvolage proecion (including load dump) Fas demagneizaion of inducive
More informationTransient Analysis of First Order RC and RL circuits
Transien Analysis of Firs Order and iruis The irui shown on Figure 1 wih he swih open is haraerized by a pariular operaing ondiion. Sine he swih is open, no urren flows in he irui (i=0) and v=0. The volage
More informationPhoto Modules for PCM Remote Control Systems
Phoo Modules for PCM Remoe Conrol Sysems Available ypes for differen carrier frequencies Type fo Type fo TSOP173 3 khz TSOP1733 33 khz TSOP1736 36 khz TSOP1737 36.7 khz TSOP1738 38 khz TSOP174 4 khz TSOP1756
More informationChapter 2 Kinematics in One Dimension
Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how
More informationIR Receiver Module for Light Barrier Systems
IR Receiver Module for Ligh Barrier Sysems MECHANICAL DATA Pinning: 1 = OUT, 2 = GND, 3 = V S 19026 APPLICATIONS Reflecive sensors for hand dryers, owel or soap dispensers, waer fauces, oile flush Vending
More informationSection 7.1 Angles and Their Measure
Secion 7.1 Angles and Their Measure Greek Leers Commonly Used in Trigonomery Quadran II Quadran III Quadran I Quadran IV α = alpha β = bea θ = hea δ = dela ω = omega γ = gamma DEGREES The angle formed
More informationHigh Speed Optocoupler, 1 MBd, Photodiode with Transistor Output
High Speed Opocoupler, MBd, Phoodiode wih Transisor Oupu FEATURES Isolaion es volages: 53 V RMS TTL compaible NC A C NC 2 3 4 8 7 6 5 C (V CC ) B (V B ) C (V O ) E (GND) High bi raes: Mbi/s High commonmode
More informationVIPer12ADIP VIPer12AS
VIPer12ADIP VIPer12AS LOW POWER OFF LINE SMPS PRIMARY SWITCHER TYPICAL POWER CAPABILITY Mains ype SO8 DIP8 European (195265 Vac) 8 W 13 W US / Wide range (85265 Vac) 5 W 8 W n FIXED 60 KHZ SWITCHING
More information17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides
7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More informationI C... 1000 A V CES... 1700 V Flat base Type Copper (nonplating) base plate RoHS Directive compliant. UL Recognized under UL1557, File E323585
CMDUC34NF CMDUC34NF  MPD series using 5 h Generaion IGBT and FWDi  I C.... A CES....... 17 Fla base Type Copper (nonplaing) base plae RoHS Direcive complian Dual swich (HalfBridge) UL Recognized
More informationChapter Four: Methodology
Chaper Four: Mehodology 1 Assessmen of isk Managemen Sraegy Comparing Is Cos of isks 1.1 Inroducion If we wan o choose a appropriae risk managemen sraegy, no only we should idenify he influence ha risks
More informationMTH6121 Introduction to Mathematical Finance Lesson 5
26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random
More information< IGBT MODULES > CM400DY34A HIGH POWER SWITCHING USE INSULATED TYPE APPLICATION
Dual (HalfBridge) Collecor curren I C...... 4A Collecoremier volage CES... 7 Maximum juncion emperaure T jmax... 5 C Fla base Type Copper base plae (nonplaing) RoHS Direcive complian UL Recognized under
More informationMOSFET = Metal Oxide Semiconductor Field Effect Transistor 2) IGBT = Insulated Gate Bipolar Transistor
Fas Recovery Epiaxial Diodes (FRED) Characerisics  Applicaions  Examples Rüdiger Bürkel, Thomas Schneider During he las 10 years, power supply opology has undergone a basic change. Power supplies of
More informationSilicon Diffused Power Transistor
GENERAL DESCRIPTION High volage, highspeed swiching npn ransisors in a fully isolaed SOT99 envelope, primarily for use in horizonal deflecion circuis of colour elevision receivers. QUICK REFERENCE DATA
More information1. y 5y + 6y = 2e t Solution: Characteristic equation is r 2 5r +6 = 0, therefore r 1 = 2, r 2 = 3, and y 1 (t) = e 2t,
Homework6 Soluions.7 In Problem hrough 4 use he mehod of variaion of parameers o find a paricular soluion of he given differenial equaion. Then check your answer by using he mehod of undeermined coeffiens..
More informationRandom Walk in 1D. 3 possible paths x vs n. 5 For our random walk, we assume the probabilities p,q do not depend on time (n)  stationary
Random Walk in D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes
More informationAP Calculus AB 2013 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a missiondriven noforprofi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was
More informationWATER MIST FIRE PROTECTION RELIABILITY ANALYSIS
WATER MIST FIRE PROTECTION RELIABILITY ANALYSIS Shuzhen Xu Research Risk and Reliabiliy Area FM Global Norwood, Massachuses 262, USA David Fuller Engineering Sandards FM Global Norwood, Massachuses 262,
More informationCoolMOS 1) Power MOSFET ISOPLUS  electrically isolated surface to heatsink Surface Mount Power Device
MKE 38RK6DFELB CoolMOS 1) Power MOSFET ISOPLUS  elecrically isolaed surface o heasink Surface Moun Power Device S = 6 V 25 = 5 R DS(on) max = 45 mw Preliminary daa G KS D T D K Isolaed surface o heasink
More informationTwo Compartment Body Model and V d Terms by Jeff Stark
Two Comparmen Body Model and V d Terms by Jeff Sark In a onecomparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics  By his, we mean ha eliminaion is firs order and ha pharmacokineic
More informationDifferential Equations. Solving for Impulse Response. Linear systems are often described using differential equations.
Differenial Equaions Linear sysems are ofen described using differenial equaions. For example: d 2 y d 2 + 5dy + 6y f() d where f() is he inpu o he sysem and y() is he oupu. We know how o solve for y given
More informationIR Receiver Modules for Remote Control Systems
TSOP382.., TSOP384.. IR Receiver Modules for MECHANICAL DATA Pinning: = OUT, 2 =, 3 = V S 926 FEATURES Very low supply curren Phoo deecor and preamplifier in one package Inernal filer for PCM frequency
More informationAppendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.
Appendi A: Area workedou s o OddNumbered Eercises Do no read hese workedou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa
More informationCointegration: The Engle and Granger approach
Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be nonsaionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require
More informationStrategic Optimization of a Transportation Distribution Network
Sraegic Opimizaion of a Transporaion Disribuion Nework K. John Sophabmixay, Sco J. Mason, Manuel D. Rossei Deparmen of Indusrial Engineering Universiy of Arkansas 4207 Bell Engineering Cener Fayeeville,
More informationRA 30 095/06.98 1/8. Replaces: 11.97 29 949, 29 951. Table of contents RA 30 095/06.98
RA 30 095/06.98 Elecronic amplifier for he conrol of proporional direcional valves ih elecrical posiion feedback Models T 5005 o T 5008, Series X RA 30 095/06.98 Replaces:.97 9 949, 9 95 The amplifiers
More informationDuration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.
Graduae School of Business Adminisraion Universiy of Virginia UVAF38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised
More informationJournal Of Business & Economics Research September 2005 Volume 3, Number 9
Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy YiKang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo
More informationA Family of Zero Current Switching Switched Capacitor DCDC Converters
A Family of Zero Curren Swiching Swiched Capacior DCDC Converers Dong Cao Deparmen of Elecrical & Compuer Engineering Michigan Sae Universiy Eas Lansing, MI 48824, USA caodong@msu.edu Fang Zheng Peng
More information