a spice compatible model of magamp post regulators_图文_百

IEEE Applied Power Electronics Conference (APEC 92), Boston, February 23-27, pp. 793-800, 1992.A SPICE Compatible Model of Magamp Post RegulatorsDaniel Edry and Sam Ben- Yaakov*Deparunent of Electrical and Computer EngineeringBen-Gurion University of the NegevP. 0. Box 653, Beer-ShevaISRAELA bstract -An equivalent circuit that emulates theaverage functional behavior of a saturable reactor(SR) Is developed and applled to simulate MagneticAmpllrler (Magamp) post regulators. The equivalentcircuit produces a voltage coded signal which Isproportional to the effective duty cycle (DO N ) ofthe regulator. The proposed approach converts theswitching circuitry or the Magamp post regulator toa SPICE compatible equivalent circuit by replacingthe SR and the switched Inductor with theirrespective equlvalent-clrcult models. Th~ resultingequivalent circuit of the system can then be used tosimulate the large and small signal behavior of theregulator under static and dynamic conditions. Theproposed approach was verified by comparingsimulation results to previously reported analyticaland experimental data. The two sets or Independentresults were found to be In excellent agreement. Thepaper demonstrates how the proposed model can beused to simplify the analysis and design orpractical Magamp post regulators.I. INTRODUCTIONRecent advances in magnetic materials and fabricationmethods have revived the interest in Magnetic Amplifiers(Magamp) based regulators as a viable design alternative. Ofparticular interest is the application of the Magamp as a postregulator in PWM converters. Notwithstanding the simplicityof the Saturable Reactor (SR) which is used as a switch inMagamps, analysis and design of the complete regulator is farfrom being simple or easy [1-3]. This is particularly truewhen one wishes to examine possible interactions betweenthe pre and post regulators. This could be accomplisheffectively, if computer aided methods are developed toalleviate. the burden of complex derivations and objectives of this study were to develop SPICEcompatible models of Magamps. The basic premise behindthis approach is that SPICE based simulators are powerfuland readily available tools for electronic circuit , once a SPICE compatible model of Magamps isdeveloped, their analysis and design can be carried out onreadily available, and in most cases already existing, puter . THE SWITCHED INDUCTOR MODEL (SIM)The proposed Magamp model is based on the SwitchedInductor Model {SIM) that has been previously described [4]and extended to many topologies and modes of operations[5,6]. For the sake of brevity, only the SIM aspects essentialto the present discussion will be presented examination of all PWM topologies reveal thatthey share three basic blocks (Fig. I): the Power Stage, DutyCycle {ID') Generator and Feedback Network. Among these,the latter is a relatively simple linear network that can beeasily studied, designed and simulated by a variety ofcomputer aided tools such as electronic circuit simulators. Asalready shown [6], the switched inductor (Fig. 2) which isfundamental to all PWM topologies, can be emulated by theequivalent circuit of Fig. al representation

converter .of a switch mode DC-DC* To whom correspondence should be SPICE compatible SIM model of Fig. 3 is an average(low frequency) equivalent circuit presentation of dIe switchedinductor assembly. That is, dIe average voltages and currentsof a PWM converter can be simulated by SPICE (or anyodIer electronic circuit simulator) by replacing dIe switchedinductor widI the SIM. The SIM equivalent circuit is non-linear since it includes dependent sources which are a functionof two variables. For example, the current source ILDON(Fig. 3) is function of the average inductor current and the

cycle, both of which could be time dependent. In thesimple PWM converter, the control variable DON isgener? i by a PWM modulator. In other cases, such as incurrel11 1Iiode control or in the Magamp post regulator, thefuncllonal dependance between the duty cycle and otherparameters of the circuit is more complex. This functionalrelationship is by definition the 'D' Generator of Fig. I. Itspurpose is to produce a duty cycle according to a prescribedprocess. The process can be analyzed by simulating the actualelectronic circuits and waveforms of the convener or, asproposed here, by emulating the mathematical relationshipsthat describe it. The latter approach will be described inconnection with a Magamp regulator system.A0---IA=ILL

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V X(2) switched inductor . nIB SR MODELConsider the Magamp post regulator presented in Fig. functional relationship of the signals that determine itsbehavior can be represented by the block diagram of Fig. this presentation it becomes clear that the saturablereactor circuitry controls the action of the switched predominant duty cycle (DON), is a function of theparameters of the SR as well as the magnitude of varioussignals according to (see the Appendix I for detailedderivation):I ~

~

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-'0000'

where V X is dIe amplitude of dIe master PWM wave, KS isdIe SR constant which in turn is a function of its averagepermeability (JlM), dimensional constants (Ae,le), thenumber of turns (N) and dIe switching frequency (fS>:Ks =

JlMN2Aefsle {3)The basic Magamp relationship of equation (I) can beemulated by an electronic circuit in which dIe variousparameters are coded into voltages (Fig. 6). The SPICEcompatible Saturable Reactor Model (SRM) of Fig. 6 carriesYoLc--v xRlIRt2RLR2=-R3 :.ICEI'I

:

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3out the calculation and produces a (voltage coded) duty cycle(DOf'l'-> VD) as a function of dIe controlling variables: dIe(volt' e coded) master duty cycle (DQ->VDQ), the PWMpul~( "mplitude (VX) and the reset current (IR->HIR). Thedefinitions for the dependent sources of the model, given inFig. 6, are as follows:ED = VDQ -VHIR VFM (4)HIR = IR (5)EFM = VFM + VFMVX -KS (6)where VFM is the voltage coded FM (equation 2).Note that equation (6) is a simulation based solution ofequation (2). The dependent voltage source EFM is made afunction of the voltage VFM which is the voltage acrossEFM itself (eq. 6). This could be true only if the term(VFMVX -KS) is zero. Hence the continuous numericalsolution of the circuit, during simulation, automaticallyadjusts the dIe voltage VFM to be equal to ~ ' as compatible equivalent circuit for dte SaturableReactor Model (SRM).A SPICE compatible equivalent circuit of the complete SRregulator circuit (Fig. 4) is obtained by replacing dIe relevantsections with the SIM (Fig. 3) and SRM (Fig. 6). Theresulting equivalent circuit (Fig. 7) can now be an~lyzedsymbolically or numerically. The latter can be convenientlycarried out on electronic circuit simulators such as SPICE [7]which have a built in capability to perform DC, large andsmall signal analyses on circuits which include non lineardependent sources as in Fig. 7. The non linearity stems fromthe fact that some of the sources are defined as a non linearfunction of one or more variable of dIe system. For example,dIe source EFM (Fig. 6, equation 6) which generates thecontrol voltage VFM is defined as a non linear function ofV X (equation 2).Consequently, the 'D. generator (Fig. 5) is anon linear system and can not be handled by linear algebramanipulations. Fortunately, all SPICE derived electroniccircuit simulators have a built in capability to deal with thesetypes of non linearities. The benefit of this is that once aSPICE compatible equivalent circuit is developed, the systemcan be analyzed for its DC, AC (small signal) and largesignal behavior without further mathematical derivations ormanipulations. The definitions of the dependent sourcesassuming the averaged model described in Fig. 7 are asfollowed:IDl = IL(l -VD)(7)ID2 = IL VD(8)EL = VBVD+ VC(l- VD)(9)ED=VDQ-VHIRVFMHIR = I(VJR)EFM = VFM + VFMVx -KsEEA = {VREF -VRVlO5(10)(11)(12)(13)SIMv x 0 .cRLRCR3.~~Ir"' -E~v0---~RErr I=

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Fig.5Functional block diagram of the post regulator shown in Fig. 4.~SECfION--0Vref

HSPICE (are, Inc., Campt ' .CA, USA)compatible input file for the complete equiv..Jelll circuit ofFig. 7 is given in Appendix . SIMULA TION RESUL .1 ~The proposed model was verified by comparing the SPf'...Fsimulation results of the small signal transfer funl.;tions ofthe regulator under study (Fig. 4) to the experimental andanalytical results reported in [3]. The two sets of results werefound to be practically identical. Fig. 8 is an example of acomparison between the open loop transfer function obtainedby simulation runs of this model and the experimental datagiven in [3]. It should be noted that the slight discrepancyfound at the high frequency region are similar to thediscrepancy between the analytical and experimental resultsreported in [3].Application of the simulation model presented heresimplifies the analysis and design of Magamp regulators bycircumventing the need to do any calculation and/orprograming. Since the model is compatible with SPICE andsimilar electronic circuit simulation packages, one gets at hisdisposal the full power of modern circuit cally all circuit simulators include the capability ofrunning DC, small signal and transient analysis and includepost processors for graphic display of the results. Since noextra derivation or computation is required, one can easily testthe behavior of the converter under various operatingconditions. Basic analysis features of pmctically all modemcircuit simulators include:I. DC Analysis which simulates the steady state conditionsin open or closed loop situations for any given set of inputs(which can be swept over a desired mnge) .This analysis isuseful to examine transfer functions and steady state values ofvoltages and currents in the gain (IG'Fcompl: magnitude;

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~. ~... ...:.0 ....0 4 8 12(b) Control Voltage (Ve) [Volt]the inner loop closed). (b) The power dissipation of thetransisitor. For various V x the simulator calculates the values of all relevantvariables at the operating point and linearizes the networkaround the operating point. All is done automatically by builtin subroutines of the circuit simulator. Once the linearizationis performed, the simulator can be applies to examine thesmall signal transfer function between various points of thesystem and to calculate impedances both under open andclosed loop conditions. As an example to this feature wepresent in Fig. 10 the open loop transfer function of theregulator given in Fig. 4 for different ESR values of theoutput capacitor. Fig. 11 is another example of the power ofthis analysis mode. It depicts the closed loop outputimpedance of the post r(',gulator of Fig. 4 for various valuesof the inductoi.S parh-;ltic resistance. As will be discussedbelow, AC analysis is an invaluable tool for the design andev(1iuation of the control loops in switch mode system suchas Magamp post [db] Phase [deg]20 ~ ~ ~ : ~ ;400i.-...: ~ 0.-~ ~.-20; ;. -40-: : : .:..., ,

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vof theregulator of Fig. 3 for various ESR values.(a) Rc = 100mll (b) Rc = 10mQ. (c) Rc = 1m.Q. .3. Transient analysis which simulate the time domainresponse of the system. This analysis enables one to examinethe large signal response of the system under a givenexcitation. For example, this analysis mode can be used tosimulate the transient recovery of the output following a stepchange in the load. The simulation results of Fig. 12 showsthe output transient of the post regulator under studyresulting from a step change of the load.v. ST ABILITY AND DYNAMIC RESPONSEThe proposed modeling and simulation methodology canbe used to ease the design chores of Magamp ically, the proposed approach can help to design thephase compensation networks in a single or multiplefeedback loop configurations to meet specified an example, consider the specific regulator under study(Fig. 4). From a system point of view this is a two feedbackloop system. The path of one loop, the 'inner loop', isthrough the transistor whereas the outer, or main, loop isthrough the error amplifier. Since no theoretical tools areavailable for the concurrent design of the two loops, areasonable approach would 00 to fIrst close one loop and thenthe second one.

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Time [m-sec]3 4Fig. 12. Transient recovery of output voltage (Vo) and inductorcurrent (IV following a load open loop gain of the inner loop is composed of twotransfer functions in cascade (Fig. 5) from Vo to DO N(H2(jro)) and from DON to Vo (H1(jro)). These two transferfunctions can be easily simulated by the model presentedhere. Fig. 13 depicts the two responses for the originaltransistor circuit (without the compensation componentsCE.R3). Also shown is the reciprocal of the transfer functionmagnitude of the second block (1/H2(jro)). This presentationis very useful since the intersection of this curve with that of

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where :le is the mean length ofmagnetic path of the S.R [ill].N is the number of turns oftt1e SR .By substituting (17) into (15) :J.1MAeNAcI>off= ~IRBy applying Faraday's law to the 'on'stage, we get :V -NAcI>onx- AT(18)11.6

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~6(19)(20)where :Fig. 14. Transient response of the inner loop following aload . CONCLUSIONSBy applying the SIM and the SRM, the switching networkof a PWM-Magamp system is converted into a continuous,SPICE compatible, network. The topology independent SIMand SRM can considerably simplify the analysis of rathercomplicated regulators with multiple feedback loops and helpoptimize the overall performance of the converter-regulatorsystem. The methodology presented here can also be used todevelop an SRM for a voltage reset SR post regulator. Oncedeveloped, the SRM and the SIM modules can be defined asSPICE (or other electronic circuit simulator) subcircuits andthen applied in the simulation of different circuitimplementations. As will be presented in a forthcomingreport. the models can also be extended to the analysis anddesign of post regulators which include current modeling and simulation approaches presented here donot replace (as yet ?) the human designer. They do help,however, to reduce the burden of circuit analysis which isinherent to the design cycle of switch mode IX IDerivation of Equation( 1 )The SR flux swing at the 'off stage is :~off = ~Rwhere :LR is the flux swing due to is the S.R Reset the B-H characteristics :LR = AeLBR = Ae~MLHRwhere :~BR~HR~M.1T = .1DT s.1D is the change in the dutycycle due to the S.R action.T s is the switching period.V x is the input pulse tuting (19) into (18) andreauanging :.1c1>on = Vx.1DTs= ~N NFsEquating the flux swing of thetwo stages:.1c1>off = .1c1>onSubstituting (18) and (21) into (22)and rearranging, we obtain :LlD = ~IR~fining:Kg = ~MN2AeFgle&PM = v x(21)(22)leVx(23)(24)(25)we get :ilD = IRFMThe equation of DON is :where :DoN is the effective duty is the input pulse duty tuting (26) into (27) :DON = DQ -IRFMDON=DQ-ilD(26)(27)(15)(28)(16)is the flux density swing due to IR [Tesla].is the magnetic intensity swing due to IR [A- Tim].is the average permeability of the SR[Tesla/(A- Tim)].APPENDIX IIHSPICE (Meta-Software Inc. Campbell, CA, USA) InputFile for the Equivalent Circuit of Fig. 7MAGAMP -A VERAGE-MODEL* Closed loop POST $ Enables HSPLOT postprocessor file

8* Path for library file (for the T2N2907A

]'model))-, ~cr)l:r 0?+ SEARCH='A$DIAO:[MET

* Circuit + C=1200U L=190U RB=lK+ RS=IK RE=47 R3=15.8+ CE=7.6U RF=64K CF=7.5N+ CHF=5.37P R1=9.5K R2=2.5K+ RC=0.1 PI=3.14 UM=29393U+ N=38 AE=0.076E-4 LE=6.18E-2+ FS=50E3 RLF=IE-3+ KS='0.4*PI*UM*N*N* AE*FS/LE'+ RD1=O RD2=O VD1=O VD2=0* Input sectionVX VX 0 DC 72VVD2 VX VD2 VD2RD2 VD2 VB RD2* Averaged current source for ID2GID2 VB 0 POL Y(2) VHIL 0 VD 0+ 00001* GID2=VHIL*VD* Freewheeling diode sectionVD1 0 VD1 VD1RD1 VD1 VC RD1* A veraged current source for ID 1GID1 VC 0 POL Y(2) VHIL 0 VD 0+ 0 lOO -1* GID1=VHIL -VHIL*VD* Switched inductor model* A veraged voltage sourceEL VEL 0 POLY(3) VB 0 VC 0 VD 0+ 00I000I0-I* EL=VC + VB*VD -VC*VDLF VEL VIL LVIL VIL VRLF 0HlLVHILOVIL1RLF VRLF VO RLF* Output sectionC VO VRC CRC VRC 0 RCRLVO03* 'D' generator for current reset magampED VD 0 POLY(3) VDQ 0 VHIR 0 VFM 0+MIN=OMAX=1 0I000000-I* ED=VDQ-VHIR*VFMVDQ VDQ 0 0.25HIR VHIR 0 VIR 1EFM VFM 0 POLY(2) VFM 0 VX 0+ '-KS' lOO 1* EFM=VFM + VFM*VX -KS* Inner loopXQ1 TC TB 1E T2N"907AVIRTC00RS VE TB RSRB TB VO RBRE 1E VO RE* Inner loop compensationR3 VO VCE R3CE VCE 1E CE* Outer loopR1 VO VR2 R1R2VR20R2VREF VREF 0 DC 2.5 AC 1EEA VE 0 VREF VR2 MIN=O 1E5* Outer loop compensationRF VR2 VCF RFCF VCF VE CFCHF VR2 VE CHF* AC DEC 10 10 NOWLEDGEMENTThe study was partially supported by the Luck-HilleChair for Instrumentation Design awarded to the NCES[I] D. Y. Chen, I. Lee, and C. Iamerson, "A Simple ModelPredicts of Magamp Post-Regulator", IEEE Transactions onPower Electronics, Vol. 4, 402-408, October, 1989.I. I. Lee, D. Chen, Y. P. Wu and C. Iamerson, "ModelingofControl Loop Behavior of Magamp Post Regulators",IEEE Transactions on Power Electronics, Vol. 5, 476-483,October, 1990.C. H. Yang, D. Y. Chen, C. Iamerson and Y. P. Wu,"Stabilizing Magamp Control Loop by Using an Inner-Loop Compensation",IEEE PESC, 365-372 1991S. Ben- Yaakov," SPICE simulation of PWM DC-DCconvertor systems: voltage feedback, continuous inductorconduction mode," IEE Electronics Letters, Vol. 25, No. 16,pp 1061-1063, August 1989.D. Kimhi and S. Ben-Yaakov. A SPICE model for currentmode PWM converters operating under continuous inductorcurrent conditions, IEEE Transactions on Power Electronics,6, pp. 281-286, 1991Y. Amran F. Huliehel and S. Ben- Yaakov, " A unified SPICE[2]

[3]

[4]

[5]

[6]

compatible average model of PWM converters," IEEE Electronics (in press)[7] , "SPICE.2: A computer program to simulatesemiconductor circuits", Memorandum No. ERL-M520,University of California, Berkeley, 1975.