JUN 895 SANDIA NATIONAL LABORATORIES NEW MEXICO

TRANSFORMER DESIGN CONSIDERATIONSFOR NON-CONTINUOUS MODE, BOOST, FLYBACK CONVERTERSRECE1v F QROBERT NAGELJUN 1 9 895SANDIA NATIONAL LABORATORIESALBUQUERQUE, NEW MEXICOThis paper presents some design considerations forsmall, flyback transformers used to charge energystorage capacitors to 0.1 to 5 KV f r m a low voltageDC source.The flyback circuit got it's name from use in earlycathode ray tubes. A cathode ray tube uses avoltage ramp to sweep the trace a m the screen.The flyback circuit was used to qui*return thevoltage to zero and start another sweep. Thus thespot appeared to "flyback" between sweeps and thecircuit is still referred to by this name. Flybackvoltage converter circuits are excellent for lowpower, high voltage applications.Figure 1In a flyback converter, capacitor charging circuit(figure l),low voltage energy is placed in an inductorL, then transferred to capacitor C. tf a diode is usedto prevent capacitor C from dischargkng back into theinductor &, a series of energy packets from theinductor can be accumulated in the capacitor. Sincethe volume of the inductor is related b the amount ofenergy (1Q LIZ)stored in it, reducing h e size of theconverter package begins with reducing the size ofthe inductor. This procedure is analogous to filling abucket (charge the capacitor to energy level 1/2CV,)' using many cups of water (energy 1/2 L,I' percup). The smaller the cup, the more cups it takes tofill the bucketPhis work was supoorted by the UnitedStates Department of Energy underContract DE-AC84-94AF85000.vLpOSTIC I IU. rI - -- tuntorrtimeFigure 2Figure 2 gives the time sequence of events for thecircuit (figure 1). The switch is closed for time k,applying the source voltage V to resistor R and L.,Current ,I increases to some peak value 1 andenergy 112 L,I2 is stored in the inductor. When theswitch is opened, the voltage reverses polarity,forward biasing the diode in the secondary circuitand energy flows to capacitor C. Note capacitor C,is also charged at this time. C, representstransformer secondary winding capacitance, circuitstray capacitance and some diode capacitance.This capacitance is directly across the secondarywinding, is charged / discharged every cycle andputs a lower limit on 112 L,I' (112 L,? 1/2 c,v:).For operation in the noncontinuousmode, foffshould be sufficient to let the all of the inductiveenergy from L, move to C which is approximately1/4 cycle of the natural frequency given by L, and C.This approximation neglects circuit stray inductanceand C, which are usually small compared to L, andC. After several cycles, V, is at some higher valueand, following the end of ton , VL, rises at a ratedetermined by L, and C, until the diode is forwardbiased. The remaining energy is transferred to C.The transformer in figure 1 has two functions. First itis an energy storage device and second, it serves toratio the primary and secondary voltages. Considerthe first function, energy storage in the primary loop.For a series R, L and V circuit, most of the energygoes to the inductor immediately following switch

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closure and later, most of the energy is dissipated inthe resistor. In figure 1, R represents the circuitresistance, source resistance, switch resistance andprimary winding resistance. Figure 3 gives therelative energy stored in the inductor divided by thetotal energy taken from source V as a function oftime measured in Lm time constants. This indicatest,equal to 0.1 time constant gives an energystorage efficiency of 0.83. For efficient converteroperation it is desirable to keep t, less than 0.1LJR.iTime Constant, UR10Figure 3Figure 3 was developed using an ideal inductor. Aphysically realizable inductor using a magnetic corehas additional constraints. Figure 4 shows the firstquadrant of a hysteresis loop. When driven with acurrent (I kH), the cure starts at B,, moves to theright and buiMs to a higher flux density B as thecurrent increases. The two shaded areas to the leftof the right side of the loop represents the energy putinto the inductor. When the current drops back tozero and B retums to B,, 6 follows the left side of theloop and the energy released is that shaded area onthe left side of the loop. The shaded area within theloop represents energy loss in the core.core rdth n o a i r g s pcore w i t h a r g a pFigure 4HA dotted line is used to indicate the left side of theloop for a core without an air gap. The shaded areato left of this line represents energy stored in thecore. This area is a small part of the shaded area tothe left of the loop for a gapped core. The differenceis due to the energy stored in the gap. Flybackconverters usually use gapped cores to improveenergy storage capacity of the inductor.The second transformer function is to ratio primaryand secondary voltages. This ratio is determined byinput voltage, maximum output voltage and reversevoltage rating of the switch. When the switch (figure1) is opened, the voltage across it is the secondaryvoltage divided by n (1:n turns ratio) plus the sourcevoltage V. The energy storage inductor L, is capableof delivering a high voltage without a secondarywinding so the main reason for a secondary windingis to reduce the primary voltage for the switch.Some safety margin should be included in the switchreverse voltage rating.A word of caution here. If there is no load on thesecondary winding, the voltage can go to a high leveland cause breakdown in the circuit, transformer orswitch.Following circuit analysis, transformer design thenproceeds with selection of a “suitable core”.Experience is a big help and reference 1 hasconsiderable information on core selection. Ferritepot cores or modified versions such as the RM coreare good because they are commercially availablewith air gaps ground in the center leg to give aspecified inductance per 1000 turns. Powdered,ferrous metal, toroidal cores also work well for low tomoderate voltages. For high voltages, toroidsgenerally use insulation less efficiently and have agreater production variation in winding capacitancethan solenoidal wound coils. Ferrous metal coreshave more stable magnetic characteristics as afunctions of temperature and higher saturation fluxdensity than ferrite cores. Ferrite cores have lowerlosses at high frequency, are less expensive and areavailable in a wider variety of shapes.Transformer design can be an iterative procedureand computer programs are very useful inperforming the repetitive calculations. At least onesoftware program is available for designing flybackconverter transformers. Following is an example ofsteps used in flyback transformer design. Circuitanalysis gave a desired L,, n, lmax (primary), LdR

c-.and C, max. With this information and the initial coreselected, calculate the following:1. Primary turns n, (LJL,)" lOOOwhere ,L, isthe core inductance per thousand turns.2. Check the core AB for saturation and core losscharacteristics, if necessary, select a different coreand repeat steps 1 132 to keep the core fromsaturating or overheating.3. Calculate the number of secondary turns ns npxnwhere n2 max(vJ/(V,- V) .V, is the allowableswitch reverse voltage.4. Select a primary wire size for given lmax andRrnin (ton 0.lLJR). Include wire eddy currenteffects in the winding resistance. Check heatingeffects in primary and secondary windings.Change wire size and repeat if until a satisfactorycopper loss is achieved.5. Consider the vottage gradients and temperaturesto select magnet wire insulation. Add layerinsulation where needed.6. Will the wire and insulationfit on selected core? ifnot select a different core and repeat steps 1through 5.7.Calculate secondary winding capacitance (Ref. 2)and venfy 1/2 CsVSz 1/2Lf, if not, increase layerinsulation in secondary winding, repeat step 6.8. Use care in lead placement and insulationparticularly for the high voltage winding. Packagingis very important for high reliability.Minor adjustments in L, , Imax, switch reversevoltage and wire size may allow use of the next sizesmaller core.Optimizingthe design requires cooperation of thecircuit engineer, component engineer andtransformer engineer. Switch ratings have a largeimpact on the transformer design. Flyback convertercircuits are generally used in applications belowIOOwatts. The basic circuit is simple but regulationcircuitry can add several components.REFERENCES1) Colonel Wm. T. McLyman, Magnetic CoreSelection for Transformers and Inductors, MarcellDekker Inc./New York and Basel 1982. ISBN: 08247-1873-92) Colonel Wm. T. McLyman, Transformer andInductor Design Handbook, Marcell Dekker lncJNew York and Basel 1978. ISBN 0-8247-6801-9

Transformer design can be an iterative procedure and computer programs are very useful in performing the repetitive calculations. At least one software program is available for designing flyback converter transformers. Following is an example of steps used in flyback transformer design. Circuit analysis gave a desired L,, n, lmax (primary), LdR .