6.334 Power Electronics Spring 2007

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "6.334 Power Electronics Spring 2007"

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>=(1-D) 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 ligh-load condiions o keep componen sizes accepable.

Chapter 2: Principles of steady-state converter analysis

Chapter 2: Principles of steady-state converter analysis Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer

More information

Circuit Types. () i( t) ( )

Circuit 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 information

Capacitors and inductors

Capacitors 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 information

Chapter 7. Response of First-Order RL and RC Circuits

Chapter 7. Response of First-Order RL and RC Circuits Chaper 7. esponse of Firs-Order 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 information

µ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ

µ 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 information

DC-DC Boost Converter with Constant Output Voltage for Grid Connected Photovoltaic Application System

DC-DC Boost Converter with Constant Output Voltage for Grid Connected Photovoltaic Application System DC-DC Boos Converer wih Consan Oupu Volage for Grid Conneced Phoovolaic Applicaion Sysem Pui-Weng Chan, Syafrudin Masri Universii Sains Malaysia E-mail: edmond_chan85@homail.com, syaf@eng.usm.my Absrac

More information

A Mathematical Description of MOSFET Behavior

A 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 information

LECTURE 9. C. Appendix

LECTURE 9. C. Appendix LECTURE 9 A. Buck-Boos Converer Design 1. Vol-Sec Balance: f(d), seadysae ransfer funcion 2. DC Operaing Poin via Charge Balance: I(D) in seady-sae 3. Ripple Volage / C Spec 4. Ripple Curren / L Spec 5.

More information

Pulse-Width Modulation Inverters

Pulse-Width Modulation Inverters SECTION 3.6 INVERTERS 189 Pulse-Widh Modulaion Inverers Pulse-widh 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 information

I) EQUATION 1: SHUNT-CONTROLLED

I) EQUATION 1: SHUNT-CONTROLLED Swich Mode Power Supply (SMPS) Topologies (Par I) Auhor: Mohammad Kamil Microchip Technology Inc. EQUATION 1: SHUNT-CONTROLLED REGULATOR POWER LOSS INTRODUCTION The indusry drive oward smaller, ligher

More information

Switched Mode Converters (1 Quadrant)

Switched Mode Converters (1 Quadrant) (1 Quadran) Philippe Barrade Laboraoire d Elecronique Indusrielle, LEI STI ISE Ecole Polyechnique Fédérale de Lausanne, EPFL Ch-1015 Lausanne Tél: +41 21 693 2651 Fax: +41 21 693 2600 Philippe.barrade@epfl.ch

More information

Full-wave rectification, bulk capacitor calculations Chris Basso January 2009

Full-wave rectification, bulk capacitor calculations Chris Basso January 2009 ull-wave 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 information

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur Module 4 Single-phase 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 information

Part II Converter Dynamics and Control

Part 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 information

Switching Regulator IC series Capacitor Calculation for Buck converter IC

Switching 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 information

RC (Resistor-Capacitor) Circuits. AP Physics C

RC (Resistor-Capacitor) Circuits. AP Physics C (Resisor-Capacior 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 information

9. Capacitor and Resistor Circuits

9. 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 information

Voltage level shifting

Voltage 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 bi-polar

More information

Signal Rectification

Signal 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, half-wae and fullwae. Le s firs consider he ideal

More information

Inductance and Transient Circuits

Inductance 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 information

PI4ULS5V202 2-Bit Bi-directional Level Shifter with Automatic Sensing & Ultra Tiny Package

PI4ULS5V202 2-Bit Bi-directional 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 push-pull applicaion High Speed wih 2 Mb/s Daa Rae for open-drain applicaion

More information

Monotonic, Inrush Current Limited Start-Up for Linear Regulators

Monotonic, Inrush Current Limited Start-Up for Linear Regulators Applicaion epor SLA156 March 2004 Monoonic, Inrush urren Limied Sar-Up 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 information

RC, RL and RLC circuits

RC, 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 information

Making Use of Gate Charge Information in MOSFET and IGBT Data Sheets

Making 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 information

LLC Resonant Converter Reference Design using the dspic DSC

LLC 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 information

PHYS245 Lab: RC circuits

PHYS245 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 information

Using RCtime to Measure Resistance

Using 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 buil-in ADC (Analog o Digial Converer)

More information

Chabot College Physics Lab RC Circuits Scott Hildreth

Chabot 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 information

NOTES ON OSCILLOSCOPES

NOTES 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 information

CHARGE AND DISCHARGE OF A CAPACITOR

CHARGE 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 information

AN1207. Switch Mode Power Supply (SMPS) Topologies (Part II) REQUIREMENTS AND RULES INTRODUCTION CONTENTS. Microchip Technology Inc.

AN1207. 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 wo-par series Swich Mode Power Supply (SMPS) opologies. he firs applicai noe in his series AN1114 -

More information

Lecture-10 BJT Switching Characteristics, Small Signal Model

Lecture-10 BJT Switching Characteristics, Small Signal Model 1 Lecure-1 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 information

AN Smart LED Lamp Driver IC with PFC Function. Introduction. Soft-Start Function. Internal Digital Reference by ZCD.

AN Smart LED Lamp Driver IC with PFC Function. Introduction. Soft-Start Function. Internal Digital Reference by ZCD. www.fairchildsemi.com AN-9744 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 information

Astable multivibrator using the 555 IC.(10)

Astable 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 information

SEMICONDUCTOR APPLICATION NOTE

SEMICONDUCTOR 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 information

Designing A High-Voltage Non-Isolated Buck-Boost Converter with the Si9121DY

Designing A High-Voltage Non-Isolated Buck-Boost Converter with the Si9121DY Designing A High-Volage Non-Isolaed Buck-Boos Converer wih he Si9DY AN Niin Kalje The Si9DY is a non-isolaed buck-boos converer IC, operaing from a wide inpu volage range of 0 o 0 V wih minimal exernal

More information

RC Circuit and Time Constant

RC Circuit and Time Constant ircui and Time onsan 8M Objec: Apparaus: To invesigae he volages across he resisor and capacior in a resisor-capacior circui ( circui) as he capacior charges and discharges. We also wish o deermine he

More information

Differential Equations and Linear Superposition

Differential 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 information

SINAMICS S120 drive system

SINAMICS 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 PM-IF

More information

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements Inroducion Chaper 14: Dynamic D-S 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 cuing-edge

More information

CAPACITANCE AND INDUCTANCE

CAPACITANCE 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 information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

cooking 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 information

The Transport Equation

The 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 information

Entropy: From the Boltzmann equation to the Maxwell Boltzmann distribution

Entropy: 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 information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67 - FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 2 TUTORIAL 1 - TRANSIENTS

EDEXCEL 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 resisor-capacior (R) and resisor-inducor (RL) D circuis

More information

ECEN4618: Experiment #1 Timing circuits with the 555 timer

ECEN4618: 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 information

Module 3. R-L & R-C Transients. Version 2 EE IIT, Kharagpur

Module 3. R-L & R-C 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 information

High Efficiency DC-DC Converter for EV Battery Charger Using Hybrid Resonant and PWM Technique

High Efficiency DC-DC Converter for EV Battery Charger Using Hybrid Resonant and PWM Technique High Efficiency DC-DC 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 information

Photovoltaic Power Control Using MPPT and Boost Converter

Photovoltaic 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 information

Signal Processing and Linear Systems I

Signal Processing and Linear Systems I Sanford Universiy Summer 214-215 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 14-15, Gibbons

More information

Product Operation and Setup Instructions

Product 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 information

IR Receiver Modules for Mid Range Proximity Sensors

IR 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 information

Package SJP. Parameter Symbol Conditions Rating Unit Remarks Transient Peak Reverse Voltage V RSM 30 V Repetitive Peak Reverse Voltage, V RM 30 V

Package 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 information

NDP6020P / NDB6020P P-Channel Logic Level Enhancement Mode Field Effect Transistor

NDP6020P / NDB6020P P-Channel Logic Level Enhancement Mode Field Effect Transistor Sepember 997 NP62P / NB62P P-Channel Logic Level Enhancemen Mode Field Effec Transisor General escripion Feaures These logic level P-Channel enhancemen mode power field effec ransisors are produced using

More information

Graduate Macro Theory II: Notes on Neoclassical Growth Model

Graduate 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 information

Lecture 2: Telegrapher Equations For Transmission Lines. Power Flow.

Lecture 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 information

Chapter 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

Chapter 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 information

Analogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar

Analogue 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: 0-7-380-7 Ifeachor

More information

Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m

Chapter 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 information

4 Convolution. Recommended Problems. x2[n] 1 2[n]

4 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 discree-ime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.1-1.

More information

5.8 Resonance 231. The study of vibrating mechanical systems ends here with the theory of pure and practical resonance.

5.8 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 information

Thyristor Based Speed Control Techniques of DC Motor: A Comparative Analysis

Thyristor 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 information

Module 3 Design for Strength. Version 2 ME, IIT Kharagpur

Module 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 information

Steps for D.C Analysis of MOSFET Circuits

Steps 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 information

Lecture 080 All Digital PPLs (5/15/03) Page 080-1

Lecture 080 All Digital PPLs (5/15/03) Page 080-1 Lecure 8 All Digial PPLs (5/15/3) Page 8-1 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 information

Frequency Modulation. Dr. Hwee-Pink Tan http://www.cs.tcd.ie/hweepink.tan

Frequency Modulation. Dr. Hwee-Pink Tan http://www.cs.tcd.ie/hweepink.tan Frequency Modulaion Dr. Hwee-Pink 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 information

IR Receiver Modules for Remote Control Systems

IR 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 information

OPERATION MANUAL. Indoor unit for air to water heat pump system and options EKHBRD011ABV1 EKHBRD014ABV1 EKHBRD016ABV1

OPERATION 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 information

s-domain Circuit Analysis

s-domain 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 information

Gate protection. Current limit. Overvoltage protection. Limit for unclamped ind. loads. Charge pump Level shifter. Rectifier. Open load detection

Gate 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 information

Transient Analysis of First Order RC and RL circuits

Transient 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 information

Photo Modules for PCM Remote Control Systems

Photo 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 information

Chapter 2 Kinematics in One Dimension

Chapter 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 information

IR Receiver Module for Light Barrier Systems

IR 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 information

Section 7.1 Angles and Their Measure

Section 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 information

High Speed Optocoupler, 1 MBd, Photodiode with Transistor Output

High 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 common-mode

More information

VIPer12ADIP VIPer12AS

VIPer12ADIP VIPer12AS VIPer12ADIP VIPer12AS LOW POWER OFF LINE SMPS PRIMARY SWITCHER TYPICAL POWER CAPABILITY Mains ype SO-8 DIP8 European (195-265 Vac) 8 W 13 W US / Wide range (85-265 Vac) 5 W 8 W n FIXED 60 KHZ SWITCHING

More information

17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides

17 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 information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

PROFIT 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 information

I C... 1000 A V CES... 1700 V Flat base Type Copper (non-plating) base plate RoHS Directive compliant. UL Recognized under UL1557, File E323585

I C... 1000 A V CES... 1700 V Flat base Type Copper (non-plating) base plate RoHS Directive compliant. UL Recognized under UL1557, File E323585 CMDUC-34NF CMDUC-34NF - MPD series using 5 h Generaion IGBT and FWDi - I C.... A CES....... 17 Fla base Type Copper (non-plaing) base plae RoHS Direcive complian Dual swich (Half-Bridge) UL Recognized

More information

Chapter Four: Methodology

Chapter 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 information

MTH6121 Introduction to Mathematical Finance Lesson 5

MTH6121 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 > CM400DY-34A HIGH POWER SWITCHING USE INSULATED TYPE APPLICATION

< IGBT MODULES > CM400DY-34A HIGH POWER SWITCHING USE INSULATED TYPE APPLICATION Dual (Half-Bridge) Collecor curren I C...... 4A Collecor-emier volage CES... 7 Maximum juncion emperaure T jmax... 5 C Fla base Type Copper base plae (non-plaing) RoHS Direcive complian UL Recognized under

More information

MOSFET = Metal Oxide Semiconductor Field Effect Transistor 2) IGBT = Insulated Gate Bipolar Transistor

MOSFET = 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 information

Silicon Diffused Power Transistor

Silicon Diffused Power Transistor GENERAL DESCRIPTION High volage, high-speed swiching npn ransisors in a fully isolaed SOT99 envelope, primarily for use in horizonal deflecion circuis of colour elevision receivers. QUICK REFERENCE DATA

More information

1. 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,

1. 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 information

Random Walk in 1-D. 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 1-D. 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 information

AP Calculus AB 2013 Scoring Guidelines

AP Calculus AB 2013 Scoring Guidelines AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a mission-driven no-for-profi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was

More information

WATER MIST FIRE PROTECTION RELIABILITY ANALYSIS

WATER 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 information

CoolMOS 1) Power MOSFET ISOPLUS - electrically isolated surface to heatsink Surface Mount Power Device

CoolMOS 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 information

Two Compartment Body Model and V d Terms by Jeff Stark

Two Compartment Body Model and V d Terms by Jeff Stark Two Comparmen Body Model and V d Terms by Jeff Sark In a one-comparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics - By his, we mean ha eliminaion is firs order and ha pharmacokineic

More information

Differential Equations. Solving for Impulse Response. Linear systems are often described using differential equations.

Differential 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 information

IR Receiver Modules for Remote Control Systems

IR 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 information

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches. Appendi A: Area worked-ou s o Odd-Numbered Eercises Do no read hese worked-ou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa

More information

Cointegration: The Engle and Granger approach

Cointegration: The Engle and Granger approach Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be non-saionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require

More information

Strategic Optimization of a Transportation Distribution Network

Strategic 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 information

RA 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 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 information

Duration 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.

Duration 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 UVA-F-38 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 information

Journal Of Business & Economics Research September 2005 Volume 3, Number 9

Journal 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 Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo

More information

A Family of Zero Current Switching Switched- Capacitor DC-DC Converters

A Family of Zero Current Switching Switched- Capacitor DC-DC Converters A Family of Zero Curren Swiching Swiched- Capacior DC-DC Converers Dong Cao Deparmen of Elecrical & Compuer Engineering Michigan Sae Universiy Eas Lansing, MI 48824, USA caodong@msu.edu Fang Zheng Peng

More information