Design Considerations for VRM Transient Response Based on the Output Impedance *
|
|
- Marjory Ramsey
- 6 years ago
- Views:
Transcription
1 Design nsideratins fr VRM Transient Respnse Based n the Output Impedane * Kaiwei Ya, Yu Meng, Peng Xu and Fred. ee enter fr Pwer Eletrnis Systems The Bradley Department f Eletrial and mputer Engineering Virginia Plytehni Institute and State University Blaksburg, VA 246 USA Abstrat This paper disusses the transient respnse f vltage regulatr mdules (VRMs) based n the small-signal mdels. The nept f nstant resistive utput impedane design fr the VRM is prpsed, and its limitatin in appliatin is analyzed. The impat f the utput filter and the feedbak ntrl bandwidth shws that there is an ptimum design fr the VRM t ahieve fast transient respnse, small size and gd effiieny. Simulatins and experimental results prve the theretial analysis. I. INTRODUTION As the lk speed f mirpressrs is develped t be faster than GHz, a lwer peratin vltage is better fr data pressing effiieny. urrently, the supply vltage level is abut.5v, and it will derease further in the future. Fr suh a lw value, the allwable differene between the maximum and minimum vltage is very small. Fr example, a Pentium IV nly allws a tlerane f abut 3mV[]. nversely, the mirpressr is mre pwer-hungry beause f the high-density semindutr integratin. The supply urrent is already mre than 5A fr a Pentium IV, and it will be even larger fr the next generatin f mirpressrs. The large supply urrent nt nly pses a stringent hallenge n effiieny, but als adds a heavy burden n the transient respnse. One reasn is the large urrent step; anther ne is the very fast urrent slew rate (5A/us nw, and muh higher in the future). Simply put, as a speial pwer supply fr the mirpressr, the vltage regulatr mdule (VRM) must maintain a lw utput vltage within a tight tlerane range during the large urrent step transient with high slew rate. T meet suh transient requirements, many apaitrs are used in the VRM utput, whih inreases the size and st. Originally, the feedbak ntrl keeps the VRM utput vltage at the same level fr the entire lad range. As a result, the utput vltage spike during the transient must be smaller than half f the vltage tlerane windw. If the utput vltage level is a little higher than the minimum value at full lad and a little lwer than the maximum value at light lad, the whle vltage tlerane range an be used fr the vltage jump r drp during the transient. This is the nept f adaptive vltage psitin (AVP) design [2~3]. Fig. shws * This wrk was supprted by Intel, Texas Instruments, Natinal Semindutrs, Intersil, TDK, Hitahi, Hipr, Pwer-One and Delta Eletrnis. Als, this wrk made use f ER shared failities supprted by the Natinal Siene Fundatin under Award Number EE the transient mparisn between nn-avp and AVP designs. It is very lear that the AVP design allws the use f fewer utput apaitrs, and hene redues the VRM st. Anther benefit f the AVP design is that the VRM utput pwer at full lad is redued, whih greatly failitates the thermal design. V min V min W/O AVP W/ AVP i O.5*( -V min ) -V min Fig.. Transient withut and with AVP designs. The AVP is related t the steady-state peratin f the VRM. If the transients between the tw steady-state stages have n spikes and n sillatins, whih situatin is shwn in Fig. 2, the AVP design is ptimal. The transient an take advantage f the whle vltage tlerane windw. The mparisn between the urrent and the related utput vltage wavefrms (Fig. 2) reveals that the VRM equals an ideal vltage sure in series with a resistr R O.Fig.3shws the equivalent iruit fr the VRM. V min i O V O Fig. 2. The ideal AVP design fr the transient. I O V O Nw it is very lear that the nstant resistive utput impedane design fr the VRM is an ptimum design fr the transient. Atually, imprving the dynami regulatin f a nverter based n the utput impedane nsideratin is an ld nept [4~7]. Hwever, nt every nverter an ahieve nstant resistive utput impedane. Additinally, it is nt lear hw t design the feedbak ntrl lp. This paper /2/$7. () 2 IEEE
2 larifies these issues. Setin II prpses a simple methd t realize the nstant utput impedane. Bth the vltage and urrent mde ntrls are disussed. Setin III investigates the limitatin f the nstant utput impedane design based n the small-signal analysis methd. Finally, Setin IV shws an example f ptimal design. R O = V O / I O VRM i O + V O - PU the parasiti resistane f the traes. The is the equivalent series resistane (ESR) f the utput apaitr. The is the pwer stage duble ple and the T(s) is the lsed-lp gain. Fig. 5 shws the pen-lp utput impedane. At high frequenies, determines the utput impedane. N matter hw the lsed-lp gain T(s) is designed, has the same value as beynd the bandwidth. Feedbak ntrl an nly attenuate the utput impedane in the lw-frequeny range. As a result, the is the nly value that is able t ahieve the nstant utput impedane. 4 R Fig. 3. The equivalent iruit f the VRM fr the ideal AVP design. II. ONSTANT OUTPUT IMPEDANE DESIGN urrently, the multi-phase synhrnus buk nverter is widely used fr VRMs. The small-signal mdel an be simplified as a single-phase buk nverter in ntinuusurrent mde [8]. As a result, a simple buk nverter, shwn in Fig. 4, is used t analyze the utput impedane with pen lp and with lsed lp. The equivalent series indutr (ES) f the utput apaitr is ignred here sine the highfrequeny erami apaitrs in parallel greatly redue its effet. V in Q T Gate Driver d F m Q B - G n + V V ref R Fig. 4. Output impedane analysis using a buk nverter. Based n the small-signal analysis methd [9~], it is easy t derive the pen-lp utput impedane and the lsed-lp utput impedane : ( + s / ) ( + s / ) = R () 2 2 s /( Q ) + s / =, (2) T =, =, ESR R, / Q. (3) R + Here, R inludes the D resistane f the indutr, the ndutin resistane R ds-n f the MOSFETs Q T and Q B,and Fig. 5. The utput impedane with pen and lsed lps.. The design methd is simple. First, the lsed-lp utput impedane is derived: it is a funtin f the mpensatr transfer funtin G n (s). Then, G n (s) an be derived by slving the equatin =. Finally, the mpensatr an be designed t be as lse as pssible t the ideal transfer funtin G n (s). Thus, sme simple mpensatr designs an ahieve apprximately nstant resistive utput impedane. Bth the vltage mde and peak urrent mde ntrls are disussed in the fllwing setin. A. Vltage Mde ntrl Fr vltage mde ntrl, the lsed-lp utput impedane is: = =, (4) T Fm Gvd Gn where F m is the mparatr gain and G vd (s) is the transfer funtin f the utput vltage V t the duty yle d. Fig. 6 shws the ideal mpensatr transfer funtin t ahieve =. Sine the small-signal mdel is n lnger effetive beynd the half swithing frequeny, the real mpensatr design nly needs t be aurate fr the lwfrequeny range. A single ple and zer mpensatr an satisfy this requirement. s / zv Gn = K (5) V s / pv Further mathemati analysis shws the detailed values f the D gain, ple and zer. R ESR K v = (6) ESR Vin Fm = (7) pv /2/$7. () 2 IEEE
3 2 b b 4 a zv = (8) 2 a R ESR a = 2 b = R ( ESR + ) Q = R (9) f (Hz) mpensatr Gain zv pv mpensatr Phase Fig. 7 shws the lsed-lp utput impedane using this mpensatr design. It is almst nstant. Simulatin results in Fig. 8 shw the nearly perfet transient respnse with AVP ntrl. B. urrent Mde ntrl Fr urrent mde ntrl, the analysis is slightly mre mpliated. Fig. 9 shws the dual-lp feedbak ntrl system. The peak urrent mde ntrl is used as an example fr this analysis. Sine the urrent lp design is nrmally fixed arding t the applied ntrl hip, the majr issue is hw t design the vltage lp mpensatr. V in Q T Gate Driver d F m T i R S Q B R i i T v - G n + V R K V ref f (Hz) Fig. 6. mpensatr design fr vltage mde ntrl. 3 db Fig. 7. The utput impedane with vltage mde ntrl. 25A di/dt=5a/us Fig. 8. Simulatin results with vltage mde ntrl. Fig. 9. A buk nverter using urrent mde ntrl. With the urrent lp lsed, the utput impedane with the pen vltage lp is: Ti Gvd Gii i = +, () Ti Gid where T i (s) is the urrent lp gain, G ii (s) is the indutr urrent t the lad urrent transfer funtin, and G id (s) is the indutr urrent t the duty yle transfer funtin. The utput impedane with the bth lps lsed is: i ( + Ti ) i = =, () T2 Ti + Fm Gvd Gn where T 2 (s) is the uter lp gain, whih determines the system bandwidth and phase margin. Fig. shws the ideal mpensatr transfer funtin t ahieve =. As is the ase fr vltage mde ntrl, a real mpensatr with ne ple and ne zer is gd enugh t me lse t the ideal design. s / zi Gn( s) = K (2) i + s / pi Further mathemati analysis shws the detailed values f the D gain, ple and zer as fllws: Ri K i, (3) ESR =, and (4) pi zi =, (5) π f s /2/$7. () 2 IEEE
4 where R i is the urrent sensing gain and f s is the swithing frequeny. There is mre physial meaning fr the mpensatr design than was the ase fr vltage mde ntrl. A ple mpensates the utput apaitr ESR zer, and a zer mpensates the duble right half plane zer intrdued by the urrent sample and hld effet. Fig. shws the lsed-lp utput impedane with this mpensatr design. It is almst nstant. Simulatin results in Fig. 2 shw the nearlyt perfet transient respnse with AVP ntrl mpensatr Gain mpensatr Phase pi zi Fig.. mpensatr design fr urrent mde ntrl i Fig.. The utput impedane with urrent mde ntrl. I V I V III. IMITATION OF THEONSTANTOUTPUT IMPEDANE DESIGN Based n the previus analysis, it seems that a VRM with any r values an ahieve nstant utput impedane, but this is nt true. Fr vltage mde ntrl, if R <,whih is pssible fr VRM design, the D gain will be negative, arding t Equatin. 6. This is impssible fr a real design. Even with R >, the D gain is t lw t attenuate the swithing nise. Als, it is nt easy t ahieve urrent sharing between multi-hannels with vltage mde ntrl. The urrent mde ntrl is different. The lsed urrent lp makes the nverter perate like a urrent sure, whih has very high utput impedane at lw frequeny. The i in Fig. shws this learly. As a result, the uter lp T 2 needs a high D gain t attenuate the utput impedane at lw frequeny. Hwever, there is a speial requirement fr the bandwidth in rder t ahieve the nstant utput impedane. Mathematial analysis shws that the bandwidth is just n the ESR zer f the utput apaitr, as fllws: f =. (6) 2 π ESR This is easy t understand, sine the pen-lp utput impedane i (vltage lp pen, but urrent lp lsed) has a zer just n that pint. Fig. 3 shws the relatinship learly. The ESR zers f different kinds f utput apaitrs are als different. Fig. 3 shws that if the bandwidth is t near t half f the swithing frequeny, the system will nt have suffiient phase margins and will beme unstable. As a result, if the ESR zer is t high, it is impssible t realize nstant utput impedane Gain Phase i T 2 T 2 f 2 π.5 f s Fig. 2. Simulatin results with urrent mde ntrl. Fig. 3. The required uter lp gain /2/$7. () 2 IEEE
5 Table I lists the ESR zers f three majr kinds f utput apaitrs fr the VRM appliatin. Fr the Osn apaitr, there is n diffiulty in ahieving 6KHz rssver frequeny with ~3KHz swithing frequeny. The ESRE is a speial kind f eletrial film apaitr prdued by rnell Dubilier; its size is muh smaller than that f the Osn. Hwever, a higher swithing frequeny is required t ahieve the 4KHz bandwidth. Fr the erami apaitr, it is impssible t ahieve nstant utput impedane with the state-f-the-art tehnlgy. TABE I. ESR ERO FOR DIFFERENT KINDS OF APAITORS. ap Type apaitane ESR ESR er Osn (SanY) 8µF 2mΩ 6KHz ESRE (DE) 27µF 5mΩ 4KHz erami (TDK) µf.4mω.mhz The preeding analysis is based n the small-signal mdel. If the duty yle is saturated, the lsed-lp utput impedane an n lnger be used fr transient analysis. Instead, the pen-lp utput impedane is effetive in the transient. Sine the pen-lp utput impedane is muh larger than that f the lsed-lp, the transient respnse f the frmer will be wrse. T guarantee a gd transient vltage wavefrm, the duty yle shuld nt beme saturated. The ritial indutane nept [8,2] reveals the pint at whih the duty yle will g t saturatin in a vltage mde ntrlled VRM. The rssver frequeny determines the ritial indutane value, abve whih the duty yle will g t saturatin. V = in v min( D, D) (7) 4 I f In the same way, a ritial indutane value an be als derived fr the urrent mde ntrl. Fig. 4 shws the urrent transfer funtin G ii (s), and Fig. 5 shws the step respnse indutr urrent with peak urrent mde ntrl. The indutr urrent with lsed lp respnds t the step lad urrent hange as a first-rder system, in whih the time nstant is simply the bandwidth. The average indutr urrent during transient is Apprximately: t 2 π f i ( t) = I ( e ), (8) where f is the rssver frequeny. The indutr urrent slew rate with average small-signal mdel is: t 2 π f Si ( t) = I 2 π f e. (9) Hwever, the maximum indutr urrent slew rate annt exeed the Faraday aw limitatin, in whih di/dt=v / fr step dwn and di/dt=(v in -V )/ fr step up. arger value frm Equatin (9) means the duty yle is saturated and the small-signal mdel is n lnger effetive. The equivalent pints give the ritial indutane value: Vin i = min( D, D). () 2 π I f 4 4 Outer-p Gain f = 2 π f Open-p = 2 π lsed-p Fig. 4. The indutr urrent transfer-funtin f urrent mde ntrl S max / = ts ( ) i Fig. 5. The step-respnse f the indutr urrent. As a result, in rder t avid duty yle saturatin, the utput filter indutr shuld nt be designed with a higher value than the ritial indutane. Sine a larger indutane value an imprve effiieny by reduing the urrent ripple, the ritial indutane value is a gd design pint fr bth transient and effiieny nsideratins. IV. A DESIGN EXAMPE Based n the understanding f the nstant utput impedane design and its related limitatins, an ptimum design fr ertain utput apaitrs an be ahieved, whih simultaneusly nsiders VRM size, transient and effiieny. A design press is shwn here fr a 2V t.6v/25a VRM using the Osn apaitr shwn in Table I. The required vltage tlerane is mv. With the nstant utput impedane design, the ESR f the utput apaitr limits the transient vltage spike. In rder t meet the mv vltage transient vltage spike requirement with 25A lad urrent transient, the ESR f the utput apaitrs shuld be less than 4mΩ. As a result, fur apaitrs shuld be used in parallel. A mmerial peak urrent ntrller (SI65) fr twphase interleaving is seleted fr the VRM design. It an ahieve urrent-sharing autmatially, and the mpensatr an be designed arding t the disussin in Setin II t ahieve nstant utput impedane. The uter-lp bandwidth is at exatly 6KHz, whih is the ESR zer f the Osn apaitr /2/$7. () 2 IEEE
6 Then, the utput filter indutane an be determined based n the ritial indutane value. 5nH is seleted arding t Equatin s that eah hannel indutane is µh. This indutane value an guarantee that the duty yle will nt beme saturated during the transient. Finally, the swithing frequeny is seleted arding the bandwidth and the indutr urrent ripple. Here, a 25KHz swithing frequeny is seleted, whih easily ahieves 6KHz rssver frequeny with a stable system and is gd enugh t limit the indutr urrent ripple t 2% f the indutr D urrent. Als, the swithing frequeny is nt s high that the swithing lss is relatively small. Tw MOSFETs with SO-8 pakages are used in eah hannel, ne fr the tp swith Q T and anther fr the bttm swith Q B. Si4842 is seleted fr Q T beause f its lw gate harge, and Si4442 is seleted fr Q B beause f its lw R ds_n. The gate driver M2726 is seleted fr its fast driving apability and very small dead time. Vishay s surfaemunted indutr IHP-55E is used fr its small size and lw prfile. Fig. 6 shws the tested transient respnse wavefrm with the nstant utput impedane design. Perfet AVP is ahieved. Fig. 7 shws the extended transient wavefrms during the step-up and step-dwn perids. The duty yle is nt saturated during the transient with the ritial indutane design. The tested uter-lp bandwidth in Fig. 8 shws that the rssver frequeny is just n the ESR zer f the utput apaitr. Fig. 9 shws the high effiieny ahieved by using nly fur SO-8 MOSFETs based n the ptimum design press. VI. ONUSION This paper disusses the nstant utput impedane design methd utilized t ahieve perfet AVP fr the VRM transient respnse. Bth the vltage mde and urrent mde ntrls an ahieve the nstant utput impedane. The limitatin f vltage mde ntrl is disussed. Fr urrent mde ntrl, the bandwidth is just n the ESR zer f the utput apaitr, suh that the utput apaitr determines the feasibility f the nstant utput impedane design methd. Als, the limitatin f the small-signal mdel shws the design guideline fr the utput filter indutane. Finally, an ptimum design press is prpsed, and a design example is given that ahieves small size, high effiieny and gd transient respnse. Simulatin and experimental results prve that the nstant utput impedane design is a gd design methd. AKNOWEDGMENTS The authrs wuld like t thank Silinix and Vishay fr supplying free devie samples. A I V Fig. 6. Experimental results fr the transient. I V (a) (b) D I V D Fig. 7. Extended transient wavefrms: (a) step-dwn and (b) step-dwn /2/$7. () 2 IEEE
7 Effiieny Outer-p Gain f=6.6khz Phase Fig. 8. The tested uter-lp gain and phase. 85% ad urrent (A) Fig. 9. The tested effiieny. REFERENES [] Intel dument, VRM 9. D-D nverter design guidelines, Order number: , April. [2] M. hang, Pwering Intel Pentium 4 pressrs, Intel Tehnlgy Sympsium,. [3] A.Waizman and.y. hung, "Resnant free pwer netwrk design using extended adaptive vltage psitining (EAVP) methdlgy," IEEE Trans. Advaned Pakaging,vl.24,pp , Aug.. [4] R. Redl and N. O. Skal, Near-ptimum dynami regulatin f D-D nverters using feed-frward f utput urrent and input vltage with urrent-mde ntrl, IEEE Trans. Pwer Eletrn., vl., pp. 8 92, July 986. [5] G. K. Shneman and D. M. Mithell, Output impedane nsideratins fr swithing regulatrs with urrent-injeted ntrl, in Pr. IEEE PES, 987, pp [6].D. Varga and N.A. si, Synthesis f zer-impedane nverter, IEEE Trans. Pwer Eletrn.,vl.7,pp.52 7, Jan [7] R. Redl, B.P. Erisman and. ansky, Optimizing the lad transient respnse f the buk nverter, in Pr. IEEE APE, 998, pp [8] P.. Wng, Perfrmane imprvements f multi-hannel interleaving vltage regulatr mdules with integrated upling indutrs, Dissertatin f Virginia Plytehni Institute and State University, Marh. [9] R. Tymerski, V. Vrperian, F.. ee and W.T. Baumann, Nnlinear mdeling f the PWM swith, IEEE Trans. Pwer Eletrn., vl. 4, pp , April 989. [] R.B. Ridley, B.H. h and F.. ee, Analysis and interpretatin f lp gains f multilp-ntrlled swithing regulatrs, IEEE Trans. Pwer Eletrn., vl. 3, pp , Ot [] R.B. Ridley, A new ntinuus-time mdel fr urrent-mde ntrl, IEEE Trans. Pwer Eletrn.,vl.6,pp.27 28, April 99. [2] P.. Wng, F.. ee, P. Xu and K. Ya, ritial indutane in vltage regulatr mdules, in Pr. IEEE APE, /2/$7. () 2 IEEE
Cross Regulation in Flyback Converters: ANALYTIC MODEL
Crss Regulatin in Flybak Cnverters: ANALYTC MODEL Chuanwen Ji and eyue. M. Smedley Det. f Eletrial & Cmuter Engineering University f Califrnia, rvine, CA 9697, USA Abstrat An analytial mdel fr studying
Content 1. Introduction 2. The Field s Configuration 3. The Lorentz Force 4. The Ampere Force 5. Discussion References
Khmelnik. I. Lrentz Fre, Ampere Fre and Mmentum Cnservatin Law Quantitative. Analysis and Crllaries. Abstrat It is knwn that Lrentz Fre and Ampere fre ntradits the Third Newtn Law, but it des nt ntradit
1. Transformer A transformer is used to obtain the approximate output voltage of the power supply. The output of the transformer is still AC.
PHYSIS 536 Experiment 4: D Pwer Supply I. Intrductin The prcess f changing A t D is investigated in this experiment. An integrated circuit regulatr makes it easy t cnstruct a high-perfrmance vltage surce
Content 1. Introduction 2. The Field s Configuration 3. The Lorentz Force 4. The Ampere Force 5. Discussion References
Khmelnik S. I. Lrentz Fre, Ampere Fre and Mmentum Cnservatin Law Quantitative. Analysis and Crllaries. Abstrat It is knwn that Lrentz Fre and Ampere fre ntradits the Third Newtn Law, but it des nt ntradit
Heat Transfer and Friction Characteristics of Heat Exchanger Under Lignite Fly-Ash
The 20th Cnferene f Mehanial Engineering Netwrk f Thailand 18-20 Otber 2006, Nakhn Rathasima, Thailand Heat Transfer and Fritin Charateristis f Heat Exhanger Under ignite Fly-Ash Pipat Juangjandee 1*,
Comparison of Thermoelectric and Stirling Type Cryocoolers Using Control Thermodynamic Model
Cmparisn f Thermeletri and Stirling Type Crylers Using Cntrl Thermdynami Mdel A Razani 1,, C Ddsn 3, and T Rberts 3 1 The University f New Mexi Albuquerque, NM 87131 Applied Tehnlgy Assiates Albuquerque,
Optimal Design of the Active Droop Control Method for the Transient Response
Optimal Design f the Actie Drp ntrl Meth fr the Transient espnse Kaiwei Ya, Kisun ee, Ming Xu an Fre. ee enter fr Pwer Electrnics Systems The Braley Department f Electrical an mputer Engineering Virginia
ZVS Boost Converter. (a) (b) Fig 6.29 (a) Quasi-resonant boost converter with M-type switch. (b) Equivalent circuit.
EEL6246 Pwer Electrnics II Chapter 6 Lecture 6 Dr. Sam Abdel-Rahman ZVS Bst Cnverter The quasi-resnant bst cnverter by using the M-type switch as shwn in Fig. 6.29(a) with its simplified circuit shwn in
Lecture 20a. Circuit Topologies and Techniques: Opamps
Lecture a Circuit Tplgies and Techniques: Opamps In this lecture yu will learn: Sme circuit tplgies and techniques Intrductin t peratinal amplifiers Differential mplifier IBIS1 I BIS M VI1 vi1 Vi vi I
Uncertainty Reduction Through Active Disturbance Rejection
8 Amerian Cntrl Cnferene Westin Seattle Htel, Seattle, Washingtn, USA June -3, 8 FrAI. Unertainty Redutin Thrugh Ative Disturbane Rejetin Jeffrey Csank and Zhiqiang Ga Department f Eletrial and Cmputer
OP AMP CHARACTERISTICS
O AM CHAACTESTCS Static p amp limitatins EFEENCE: Chapter 5 textbk (ESS) EOS CAUSED BY THE NUT BAS CUENT AND THE NUT OFFSET CUENT Op Amp t functin shuld have fr the input terminals a DC path thrugh which
Lab 11 LRC Circuits, Damped Forced Harmonic Motion
Physics 6 ab ab 11 ircuits, Damped Frced Harmnic Mtin What Yu Need T Knw: The Physics OK this is basically a recap f what yu ve dne s far with circuits and circuits. Nw we get t put everything tgether
(2) Even if such a value of k was possible, the neutrons multiply
CHANGE OF REACTOR Nuclear Thery - Curse 227 POWER WTH REACTVTY CHANGE n this lessn, we will cnsider hw neutrn density, neutrn flux and reactr pwer change when the multiplicatin factr, k, r the reactivity,
Gains in Activation Energy from Quasi Fermi Splitting, In Selectively Doped MQW Solar Cells
Gains in Ativatin Energy frm Quasi ermi Splitting, In Seletively Dped MQW Slar Cells ARGYRIOS C. VARONIDES, ROBERT A. SPALLETTA ANDREW W. BERGER Department f Physis and Eletrial Engineering, University
Relationships Between Frequency, Capacitance, Inductance and Reactance.
P Physics Relatinships between f,, and. Relatinships Between Frequency, apacitance, nductance and Reactance. Purpse: T experimentally verify the relatinships between f, and. The data cllected will lead
Dead-beat controller design
J. Hetthéssy, A. Barta, R. Bars: Dead beat cntrller design Nvember, 4 Dead-beat cntrller design In sampled data cntrl systems the cntrller is realised by an intelligent device, typically by a PLC (Prgrammable
Series and Parallel Resonances
Series and Parallel esnances Series esnance Cnsider the series circuit shwn in the frequency dmain. The input impedance is Z Vs jl jl I jc C H s esnance ccurs when the imaginary part f the transfer functin
Supporting information for: Large Protonation-Gated Photochromism of an OPE-Embedded Difurylperfluorocyclopentene
Eletrni Supplementary Material (ESI) fr Physial Chemistry Chemial Physis. This jurnal is the Owner Sieties 015 1/9 Supprting infrmatin fr: Large Prtnatin-Gated Phthrmism f an OPE-Embedded Difurylperflurylpentene
Chemistry 20 Lesson 11 Electronegativity, Polarity and Shapes
Chemistry 20 Lessn 11 Electrnegativity, Plarity and Shapes In ur previus wrk we learned why atms frm cvalent bnds and hw t draw the resulting rganizatin f atms. In this lessn we will learn (a) hw the cmbinatin
SCHMIDT THEORY FOR STIRLING ENGINES
SHMIDT THOY FO STILING NGINS KOIHI HIATA Musashin-jjutaku 6-10, Gakuen -6-1, Musashimurayama, Tky 08, Japan Phne & Fax: +81-45-67-0086 e-mail: khirata@gem.bekkame.ne.jp url: http://www.bekkame.ne.jp/~khirata
ECEN 4872/5827 Lecture Notes
ECEN 4872/5827 Lecture Ntes Lecture #5 Objectives fr lecture #5: 1. Analysis f precisin current reference 2. Appraches fr evaluating tlerances 3. Temperature Cefficients evaluatin technique 4. Fundamentals
READING STATECHART DIAGRAMS
READING STATECHART DIAGRAMS Figure 4.48 A Statechart diagram with events The diagram in Figure 4.48 shws all states that the bject plane can be in during the curse f its life. Furthermre, it shws the pssible
High-Efficiency Voltage Regulator and Stabilizer for Outdoor Lighting Installations
High-Effiieny Vltage Regulatr and Stabilizer fr utdr Lighting Installatins F. R. Blánquez, E. Rebll, F. Blázquez and C. A. Plater P. Frías Abstrat This paper presents a high perfrmane system f regulatin
Design and Simulation of Dc-Dc Voltage Converters Using Matlab/Simulink
American Jurnal f Engineering Research (AJER) 016 American Jurnal f Engineering Research (AJER) e-issn: 30-0847 p-issn : 30-0936 Vlume-5, Issue-, pp-9-36 www.ajer.rg Research Paper Open Access Design and
Greedy Algorithms. Kye Halsted. Edited by Chuck Cusack. These notes are based on chapter 17 of [1] and lectures from CSCE423/823, Spring 2001.
#! Greedy Algrithms Kye Halsted Edited by Chuk Cusak These ntes are based n hapter 17 f [1] and letures frm CCE423/823, pring 2001. Greedy algrithms slve prblems by making the hie that seems best at the
T(s) 1+ T(s) 2. Phase Margin Test for T(s) a. Unconditionally Stable φ m = 90 o for 1 pole T(s) b. Conditionally Stable Case 1.
Lecture 49 Danger f Instability/Oscillatin When Emplying Feedback In PWM Cnverters A. Guessing Clsed Lp Stability Frm Open Lp Frequency Respnse Data. T(s) versus T(s) + T(s) 2. Phase Margin Test fr T(s)
ECE-320: Linear Control Systems Homework 1. 1) For the following transfer functions, determine both the impulse response and the unit step response.
Due: Mnday Marh 4, 6 at the beginning f la ECE-: Linear Cntrl Sytem Hmewrk ) Fr the fllwing tranfer funtin, determine bth the imule rene and the unit te rene. Srambled Anwer: H ( ) H ( ) ( )( ) ( )( )
GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS. J.e. Sprott. Plasma Studies. University of Wisconsin
GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS J.e. Sprtt PLP 924 September 1984 Plasma Studies University f Wiscnsin These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated.
The Mathematical Model of a Three-Phase Diode Rectifier with Multi-Converter Power Electronic Loads
Recent Researches in Pwer Systems and Systems Science The Mathematical Mdel f a Three-Phase Dide Rectifier with Multi-nverter Pwer Electrnic ads T. Spapirm, -N. Areerak, -. Areerak Pwer electrnics, Machines
ON-LINE PHYSICS 122 EXAM #2 (all online sections)
ON-LINE PHYSIS EXAM # (all nline setins) ) Bubble in the ID number setin f the santrn. ) This Exam is hurs lng - 34 multiple-hie questins. hse the ne BEST answer fr eah questin. Yu are nt penalized fr
Department of Electrical Engineering, University of Waterloo. Introduction
Sectin 4: Sequential Circuits Majr Tpics Types f sequential circuits Flip-flps Analysis f clcked sequential circuits Mre and Mealy machines Design f clcked sequential circuits State transitin design methd
Supplementary Course Notes Adding and Subtracting AC Voltages and Currents
Supplementary Curse Ntes Adding and Subtracting AC Vltages and Currents As mentined previusly, when cmbining DC vltages r currents, we nly need t knw the plarity (vltage) and directin (current). In the
Response of a biologically inspired MEMS differential microphone diaphragm
Su, Q., R. N. Miles, M. G. Weinstein, R. A. Miller, L. Tan, W. Cui, Respnse f a bilgially inspired MEMS differential mirphne diaphragm, Preedings f the SPIE AerSense 00, Orland Fl. Paper number [4743-15].
Determining the Accuracy of Modal Parameter Estimation Methods
Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system
Chemical Engineering 160/260 Polymer Science and Engineering. Lecture 15: Molecular Aspects of Polymer Rheology February 21, 2001
Chemial Engineering 160/260 Plymer Siene and Engineering Leture 15: Mleular Aspets f Plymer Rhelgy February 21, 2001 Objetives! T intrdue the nept f saling analysis t aunt fr the nentratin and mleular
Current/voltage-mode third order quadrature oscillator employing two multiple outputs CCIIs and grounded capacitors
Indian Jurnal f Pure & Applied Physics Vl. 49 July 20 pp. 494-498 Current/vltage-mde third rder quadrature scillatr emplying tw multiple utputs CCIIs and grunded capacitrs Jiun-Wei Hrng Department f Electrnic
A small simulation study of moisture content variations in furniture in different tropical climates
A small simulatin study f misture ntent variatins in furniture in different trpial limates Wadsö, Lars 1994 Link t publiatin Citatin fr published versin (APA): Wadsö, L. (1994). A small simulatin study
Chem 116 POGIL Worksheet - Week 8 Equilibrium Continued - Solutions
Chem 116 POGIL Wrksheet - Week 8 Equilibrium Cntinued - Slutins Key Questins 1. Cnsider the fllwing reatin At 425 C, an equilibrium mixture has the fllwing nentratins What is the value f K? -2 [HI] = 1.01
Electromagnetic (EM) waves also can exhibit a Doppler effect:
4.5 The Dppler ffet and letrmagneti Waves letrmagneti (M) waves als an exhibit a Dppler effet:. Inrease in bserved frequeny fr sure and bserver apprahing ne anther. Derease in bserved frequeny fr sure
A Novel Isolated Buck-Boost Converter
vel slated uck-st Cnverter S-Sek Kim *,WOO-J JG,JOOG-HO SOG, Ok-K Kang, and Hee-Jn Kim ept. f Electrical Eng., Seul atinal University f Technlgy, Krea Schl f Electrical and Cmputer Eng., Hanyang University,
Lecture 02 CSE 40547/60547 Computing at the Nanoscale
PN Junctin Ntes: Lecture 02 CSE 40547/60547 Cmputing at the Nanscale Letʼs start with a (very) shrt review f semi-cnducting materials: - N-type material: Obtained by adding impurity with 5 valence elements
Bicycle Generator Dump Load Control Circuit: An Op Amp Comparator with Hysteresis
Bicycle Generatr Dump Lad Cntrl Circuit: An Op Amp Cmparatr with Hysteresis Sustainable Technlgy Educatin Prject University f Waterl http://www.step.uwaterl.ca December 1, 2009 1 Summary This dcument describes
A Novel Electro-thermal Simulation Approach to Power IGBT Modules for Automotive Traction Applications
Special Issue Recent R&D Activities f Pwer Devices fr Hybrid Electric Vehicles 27 Research Reprt A Nvel Electr-thermal Simulatin Apprach t Pwer IGBT Mdules fr Autmtive Tractin Applicatins Takashi Kjima,
On the Origin of the Special Relativity Anomalies
On the Origin f the Speial Relatiity Anmalies Radwan M. Kassir February 2015 radwan.elkassir@dargrup.m ABSTRACT In this paper, the nlusie rigin f the Speial Relatiity (SR) mathematial nflits identified
Copyright Paul Tobin 63
DT, Kevin t. lectric Circuit Thery DT87/ Tw-Prt netwrk parameters ummary We have seen previusly that a tw-prt netwrk has a pair f input terminals and a pair f utput terminals figure. These circuits were
Diodes Waveform shaping Circuits. Sedra & Smith (6 th Ed): Sec. 4.5 & 4.6 Sedra & Smith (5 th Ed): Sec. 3.5 & 3.6
des Waefrm shapng Cruts Sedra & Smth (6 th Ed): Se. 4.5 & 4.6 Sedra & Smth (5 th Ed): Se. 3.5 & 3.6 Tw-prt netwrks as buldng blks Reall: Transfer funtn f a tw-prt netwrk an be fund by slng ths rut ne.
SPH3U1 Lesson 06 Kinematics
PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.
Three charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter).
Three charges, all with a charge f 0 are situated as shwn (each grid line is separated by meter). ) What is the net wrk needed t assemble this charge distributin? a) +0.5 J b) +0.8 J c) 0 J d) -0.8 J e)
Keysight Technologies Understanding the Kramers-Kronig Relation Using A Pictorial Proof
Keysight Technlgies Understanding the Kramers-Krnig Relatin Using A Pictrial Prf By Clin Warwick, Signal Integrity Prduct Manager, Keysight EEsf EDA White Paper Intrductin In principle, applicatin f the
1) What is the reflected angle 3 measured WITH RESPECT TO THE BOUNDRY as shown? a) 0 b) 11 c) 16 d) 50 e) 42
Light in ne medium (n =.) enunters a bundary t a send medium (with n =. 8) where part f the light is transmitted int the send media and part is refleted bak int the first media. The inident angle is =
Diodes Waveform shaping Circuits
des Waefrm shapng Cruts Leture ntes: page 2-2 t 2-31 Sedra & Smth (6 th Ed): Se. 4.5 & 4.6 Sedra & Smth (5 th Ed): Se. 3.5 & 3.6 F. Najmabad, ECE65, Wnter 212 Tw-prt netwrks as buldng blks Reall: Transfer
This document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore.
Thi dument i dwnladed frm DR-NTU Nanyang Tehnlgial Univerity Library Singapre. Title An advaned-time-haring withing trategy fr multipleinput buk nverter Authr() Xian Liang; Wang Yuyi Citatin Xian L. &
AP Physics Kinematic Wrap Up
AP Physics Kinematic Wrap Up S what d yu need t knw abut this mtin in tw-dimensin stuff t get a gd scre n the ld AP Physics Test? First ff, here are the equatins that yu ll have t wrk with: v v at x x
T T A BA T B 1 5 7
Hmewrk 5. Write the fllwing equatins in matrix frm: (a) 3x5z7 4z5 3xz 3 5 4 3 x z 7 5 (b) x3z 4x56z 7x89z3 3 4 5 6 7 8 9 x z 3. The transpse peratin hanges a lumn vetr t a rw vetr and visa-vera. (a) Find
Verification of Quality Parameters of a Solar Panel and Modification in Formulae of its Series Resistance
Verificatin f Quality Parameters f a Slar Panel and Mdificatin in Frmulae f its Series Resistance Sanika Gawhane Pune-411037-India Onkar Hule Pune-411037- India Chinmy Kulkarni Pune-411037-India Ojas Pandav
Keywords: Auger recombination, leakage current, lead salts, quantum efficiency INTRODUCTION
Researh Jurnal f Applied Sienes, Engineering and Tehnlgy (5: 67-6, 6 DOI:.96/rjaset..689 ISSN: 4-7459; e-issn: 4-7467 6 axwell Sientifi Publiatin Crp. Submitted: Otber 9, 5 Aepted: Otber 3, 5 Published:
1.1 The main transmission network of Eskom The classical two generator model 11
LIST OF FIGURS Figure Page 1.1 The main transmissin netwrk f skm 4 2.1 The classical tw generatr mdel 11 2.2 Obtaining the lcatin f the electrical centre. The line cnnecting A with B represents the netwrk
HCB-3 Edition. Solutions Chapter 12 Problems. SOLUTION: Refer to saturated steam table (Table A3-SI) and superheated steam table (Table A4-SI)
HCB- Editin 12.1 Slutins Chapter 12 Prbles GIVEN: Fllwing table fr water: T (C p (kpa v ( /kg Phase 60 (1.25 (2 ( 175 (4 Saturated vapr 00 00 (5 (6 100 10 (7 (8 (9 (10 0.001097 Saturated vapr 1000 10 (11
, which yields. where z1. and z2
The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin
Instituto de Sistemas e Robótica
Institut de Sistemas e Rbótia Pól de Lisba Attitude Cntrl Strategies fr Small Satellites Paul Tabuada, Pedr Alves, Pedr Tavares, Pedr Lima Setembr 1998 RT-44-98 ISR-Trre Nrte Av. Rvis Pais 196 Lisba CODEX
Analysis on the Stability of Reservoir Soil Slope Based on Fuzzy Artificial Neural Network
Research Jurnal f Applied Sciences, Engineering and Technlgy 5(2): 465-469, 2013 ISSN: 2040-7459; E-ISSN: 2040-7467 Maxwell Scientific Organizatin, 2013 Submitted: May 08, 2012 Accepted: May 29, 2012 Published:
the results to larger systems due to prop'erties of the projection algorithm. First, the number of hidden nodes must
M.E. Aggune, M.J. Dambrg, M.A. El-Sharkawi, R.J. Marks II and L.E. Atlas, "Dynamic and static security assessment f pwer systems using artificial neural netwrks", Prceedings f the NSF Wrkshp n Applicatins
A Comparison of AC/DC Piezoelectric Transformer Converters with Current Doubler and Voltage Doubler Rectifiers
A Cmparisn f AC/DC Piezelectric Transfrmer Cnverters with Current Dubler and ltage Dubler Rectifiers Gregry vensky, Svetlana Brnstein and Sam Ben-Yaakv* Pwer Electrnics abratry Department f Electrical
THE BOY WHO CRIED WOLF REVISITED: THE IMPACT OF FALSE ALARM INTOLERANCE ON COST-LOSS SCENARIOS
THE BOY WHO CRIED WOLF REVISITED: THE IMPACT OF FALSE ALARM INTOLERANCE ON COST-LOSS SCENARIOS M.S. Rulstn+? and L.A. Smith+? 1 Pembrke Cllege, Oxfrd University, U.K. 2 Centre fr the Analysis f Time Series,
ChE 471: LECTURE 4 Fall 2003
ChE 47: LECTURE 4 Fall 003 IDEL RECTORS One f the key gals f chemical reactin engineering is t quantify the relatinship between prductin rate, reactr size, reactin kinetics and selected perating cnditins.
Tutorial 3: Building a spectral library in Skyline
SRM Curse 2013 Tutrial 3 Spectral Library Tutrial 3: Building a spectral library in Skyline Spectral libraries fr SRM methd design and fr data analysis can be either directly added t a Skyline dcument
THERMAL-VACUUM VERSUS THERMAL- ATMOSPHERIC TESTS OF ELECTRONIC ASSEMBLIES
PREFERRED RELIABILITY PAGE 1 OF 5 PRACTICES PRACTICE NO. PT-TE-1409 THERMAL-VACUUM VERSUS THERMAL- ATMOSPHERIC Practice: Perfrm all thermal envirnmental tests n electrnic spaceflight hardware in a flight-like
Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.
Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage
Section I5: Feedback in Operational Amplifiers
Sectin I5: eedback in Operatinal mplifiers s discussed earlier, practical p-amps hae a high gain under dc (zer frequency) cnditins and the gain decreases as frequency increases. This frequency dependence
Computational modeling techniques
Cmputatinal mdeling techniques Lecture 2: Mdeling change. In Petre Department f IT, Åb Akademi http://users.ab.fi/ipetre/cmpmd/ Cntent f the lecture Basic paradigm f mdeling change Examples Linear dynamical
Simulation of Push-pull Multi-output Quasi-resonant Converter
IOSR Jurnal f Electrical and Electrnics Engineering (IOSR-JEEE) e-issn: 78-1676,p-ISSN: 3-3331, Vlue 9, Issue 1 Ver. V (Feb. 14), PP 19-4 Siulatin f Push-pull Multi-utput Quasi-resnant Cnverter T.Anitha
2.161 Signal Processing: Continuous and Discrete Fall 2008
MIT OpenCurseWare http://cw.mit.edu 2.161 Signal Prcessing: Cntinuus and Discrete Fall 2008 Fr infrmatin abut citing these materials r ur Terms f Use, visit: http://cw.mit.edu/terms. Massachusetts Institute
Math Foundations 20 Work Plan
Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant
Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax
.7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical
Kinetic Model Completeness
5.68J/10.652J Spring 2003 Lecture Ntes Tuesday April 15, 2003 Kinetic Mdel Cmpleteness We say a chemical kinetic mdel is cmplete fr a particular reactin cnditin when it cntains all the species and reactins
ALUMINIUM ELECTROLYTIC CAPACITORS PG - LL9 Long Life Grade
Useful Life : Useful life is the perid f time which the capacitr takes t reach end-f-life Fr PG-LL9 capacitrs the useful life is estimated as 100 hurs at maximum rated temperature, ripple current and vltage
Bootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) >
Btstrap Methd > # Purpse: understand hw btstrap methd wrks > bs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(bs) > mean(bs) [1] 21.64625 > # estimate f lambda > lambda = 1/mean(bs);
ECE 2100 Circuit Analysis
ECE 00 Circuit Analysis Lessn 6 Chapter 4 Sec 4., 4.5, 4.7 Series LC Circuit C Lw Pass Filter Daniel M. Litynski, Ph.D. http://hmepages.wmich.edu/~dlitynsk/ ECE 00 Circuit Analysis Lessn 5 Chapter 9 &
Concurrent Error Detection for Reliable SHA-3 Design
5/18/2016 1 Cncurrent Errr Detectin fr Reliable SHA-3 Design Pei LUO 1 Cheng LI 2 Yunsi FEI 1 1. Nrtheastern Universit Energ-Efficient and Secure Sstems Lab http://nueess.ce.neu.edu Electrical & Cmputer
PHYSICS NOTES. SUBJECT: Physics LEVEL: Higher TEACHER: Pat Doyle. The Institute of Education Topics Covered: Sound & Waves
PHYSICS NOTES The Institute Eduatin 208 SUBJECT: Physis LEVEL: Higher TEACHER: Pat Dyle Tpis Cvered: Sund & Waves Abut Pat: Pat graduated with a Masters Degree in Physis in 986 and has taught Physis in
NUROP CONGRESS PAPER CHINESE PINYIN TO CHINESE CHARACTER CONVERSION
NUROP Chinese Pinyin T Chinese Character Cnversin NUROP CONGRESS PAPER CHINESE PINYIN TO CHINESE CHARACTER CONVERSION CHIA LI SHI 1 AND LUA KIM TENG 2 Schl f Cmputing, Natinal University f Singapre 3 Science
NUMBERS, MATHEMATICS AND EQUATIONS
AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t
Multiple Source Multiple. using Network Coding
Multiple Surce Multiple Destinatin Tplgy Inference using Netwrk Cding Pegah Sattari EECS, UC Irvine Jint wrk with Athina Markpulu, at UCI, Christina Fraguli, at EPFL, Lausanne Outline Netwrk Tmgraphy Gal,
CHAPTER 2 Algebraic Expressions and Fundamental Operations
CHAPTER Algebraic Expressins and Fundamental Operatins OBJECTIVES: 1. Algebraic Expressins. Terms. Degree. Gruping 5. Additin 6. Subtractin 7. Multiplicatin 8. Divisin Algebraic Expressin An algebraic
Fabrication Thermal Test. Methodology for a Safe Cask Thermal Performance
ENSA (Grup SEPI) Fabricatin Thermal Test. Methdlgy fr a Safe Cask Thermal Perfrmance IAEA Internatinal Cnference n the Management f Spent Fuel frm Nuclear Pwer Reactrs An Integrated Apprach t the Back-End
CAUSAL INFERENCE. Technical Track Session I. Phillippe Leite. The World Bank
CAUSAL INFERENCE Technical Track Sessin I Phillippe Leite The Wrld Bank These slides were develped by Christel Vermeersch and mdified by Phillippe Leite fr the purpse f this wrkshp Plicy questins are causal
NATIONAL COMMUNICATIONS SYSTEM
NCS TIB 80- NATINAL CMMUNICATINS SYSTEM li LIBRARY RESEARCH REPRTS DIVISIN NAVAL PSTGRADUATE SCHL MNTEREY, CALIFRNIA 994 TECHNICAL INFRMATIN BULLETIN 80- EMP VULNERABILITIES F TELECMMUNICATINS FACILITIES
IXD4902. Three-Terminal Negative Voltage Regulator FEATURES DESCRIPTION APPLICATIONS
Three-Terminal Negative Vltage Regulatr FEATURES Output Current up t 200 ma (350 ma max) Input Vltage Range -2.4 V - -16 V Output Vltage Range frm -2.5 V t -12 V (fixed values) Drput Vltage 400 mv @ 100
The ZCS Boost Converter
EEL646 Pwer Elernis II Chaper 6 Leure Dr. Sam Abdel-Rahman The ZCS Bs Cnverer The bs-quasi-resnan nverer wih an M-ype swih as shwn Fig. 6.(a, wih is equivalen irui shwn Fig. 6.(b. (a (b Fig 6. (a ZCS bs
HFA-PFC Systems for Tactical Mobile Electric Power Systems
ATIZFR-95/0010 HFA-PFC Systems fr Tatial Mbile Eletri Pwer Systems Mark BQadky Axim Tehnlgy Internatinal Crpratin 1995 CEM Belvir RD&E Center DISTRIBUTIN STATEMENT A Apprved fr Publi Release Distributin
Review Problems 3. Four FIR Filter Types
Review Prblems 3 Fur FIR Filter Types Fur types f FIR linear phase digital filters have cefficients h(n fr 0 n M. They are defined as fllws: Type I: h(n = h(m-n and M even. Type II: h(n = h(m-n and M dd.
Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India
CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce
ENSC Discrete Time Systems. Project Outline. Semester
ENSC 49 - iscrete Time Systems Prject Outline Semester 006-1. Objectives The gal f the prject is t design a channel fading simulatr. Upn successful cmpletin f the prject, yu will reinfrce yur understanding
Limiting False Data Attacks on Power System State Estimation
Limiting False Data Attaks n Pwer System State Estimatin Oliver Ksut, Liyan Jia, Rbert J. Thmas, and Lang Tng Shl f Eletrial and Cmputer Engineering Crnell University, Ithaa, NY 14853 Email: {ek2.lj92.rjtl.lt35}@rnell.edu
OTHER USES OF THE ICRH COUPL ING CO IL. November 1975
OTHER USES OF THE ICRH COUPL ING CO IL J. C. Sprtt Nvember 1975 -I,," PLP 663 Plasma Studies University f Wiscnsin These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated.
Floating Point Method for Solving Transportation. Problems with Additional Constraints
Internatinal Mathematical Frum, Vl. 6, 20, n. 40, 983-992 Flating Pint Methd fr Slving Transprtatin Prblems with Additinal Cnstraints P. Pandian and D. Anuradha Department f Mathematics, Schl f Advanced
You need to be able to define the following terms and answer basic questions about them:
CS440/ECE448 Sectin Q Fall 2017 Midterm Review Yu need t be able t define the fllwing terms and answer basic questins abut them: Intr t AI, agents and envirnments Pssible definitins f AI, prs and cns f
Optimization of frequency quantization. VN Tibabishev. Keywords: optimization, sampling frequency, the substitution frequencies.
UDC 519.21 Otimizatin f frequency quantizatin VN Tibabishev Asvt51@nard.ru We btain the functinal defining the rice and quality f samle readings f the generalized velcities. It is shwn that the timal samling
Modelling of NOLM Demultiplexers Employing Optical Soliton Control Pulse
Micwave and Optical Technlgy Letters, Vl. 1, N. 3, 1999. pp. 05-08 Mdelling f NOLM Demultiplexers Emplying Optical Slitn Cntrl Pulse Z. Ghassemly, C. Y. Cheung & A. K. Ray Electrnics Research Grup, Schl