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june 1996 flyback transformer design for topswitch ? power supplies application note AN-17 total flyback component cost is lower when compared to other techniques. between 75 and 100 watts, increasing voltage and current stresses cause flyback component cost to increase significantly. at higher power levels, topologies with lower voltage and current stress levels (such as the forward converter) may be more cost effective even with higher component counts. flyback transformer design, which requires iteration through a set of design equations, is not difficult. simple spreadsheet iteration reduces design time to under 10 minutes for a transformer when developing topswitch flyback power supplies, transformer design is usually the biggest stumbling block. flyback transformers are not designed or used like normal transformers. energy is stored in the core. the core must be gapped. current effectively flows in either the primary or secondary winding but never in both windings at the same time. why use the flyback topology? flyback power supplies use the least number of components. at power levels below 75 watts, ? figure 1. st202a power supply operates from universal input voltage and delivers 15 watts. pi-1787-021296 7.5 v rtn c5 47 m f d2 ug8bt d3 1n4148 r2 68 w vr2 1n5995b 6.2 v c3 120 m f 25 v d1 uf4005 c2 680 m f 25 v vr1 p6ke200 circuit performance: line regulation - ?.5% (85-265 vac) load regulation - ?% (10-100%) ripple voltage ?50 mv meets vde class b br1 c1 33 m f (c in ) r1 39 w u2 nec2501-h u1 top202yai drain source control c4 0.1 m f c7 1000 nf y1 l1 3.3 m h j1 c6 0.1 m f l2 22 mh l n i pri i sec v diode v drain
AN-17 c 6/96 2 that usually works the first time. this method, used for continuous mode as well as discontinuous mode designs, has three distinct steps: 1) identify and estimate a set of independent variables (input) depending on application details, transformer core, and selected topswitch . 2) identify and calculate a set of dependent parameters (output). 3) iterate specified independent variables until selected dependent parameters fall within defined limits for a practical flyback transformer. a simple pc spreadsheet (available from power integrations for excel or compatible spreadsheet programs) automates the transformer design method presented in this application note. (note: this improved version has been completely revised and may give slightly different answers compared to earlier versions. refer to the last page of this application note for a complete description of the changes.) a new parameter, the ratio of primary ripple current to peak current (k rp ), is introduced to describe the topswitch drain current waveform shape and simplify subsequent calculations such as rms current and ac flux density. application specific independent variables include minimum and maximum ac input voltage, line frequency, topswitch switching frequency, output and bias voltages, output power, bridge rectifier conduction time, size of input energy storage capacitor, power supply efficiency and power loss allocation between primary and secondary circuitry. variables depending on the transformer core and construction include effective core cross sectional area and magnetic path length, ungapped effective inductance, bobbin physical winding width, margin width (for creepage distance and safety isolation), number of primary layers, and number of secondary turns. variables depending on topswitch include switching frequency, reflected output voltage, ripple to peak current ratio, and topswitch voltage drop. for a given application and transformer core, 20 of these 23 independent variables will be calculated or estimated once and then remain fixed during iteration. only three variables, number of secondary turns n s , ripple to peak current ratio k rp , and number of primary winding layers l will be changed during the iteration process. dependent parameters are divided into four groups: dc input voltage, primary current waveform shape, transformer design, and voltage stress. dc input voltage parameters are simply the minimum and maximum dc input voltage after the ac mains have been rectified and filtered. primary current waveform shape parameters include maximum duty cycle, average current, peak current, ripple current, and rms current to completely define transformer primary current and determine operation in either continuous or discontinuous mode. transformer design parameters include primary inductance, number of primary turns, number of bias winding turns, gapped effective inductance, maximum flux density, ac flux density, ungapped core relative permeability, estimated gap length, effective bobbin width, insulated primary wire diameter, insulation thickness, bare conductor cross section, primary current capacity, and secondary design parameters. voltage stress parameters determine the maximum topswitch off-state drain voltage and output rectifier peak inverse voltage. of all these dependent parameters, only three require examination and comparison within limits during iteration. maximum flux density b m , gap length l g , and primary current capacity cma are checked with each iteration until all three parameters are within specified limits. the remaining dependent parameters are either intermediate calculations or parameters used by the manufacturer for construction or the designer for specifying components. understanding primary and secondary current waveform shape in both continuous and discontinuous mode operation is necessary before beginning transformer design. figure 1 shows a typical flyback power supply using the top202 topswitch from power integrations, inc. topswitch combines an integrated high voltage mosfet switch with a complete switching power supply controller and protection circuitry in a single 3 pin to220 package. the topswitch power supply operates from 85 to 265 vac and delivers 15 watts at 7.5 volt output. ac power is rectified and filtered by br1 and c1 (c in ) to create the high voltage dc bus applied to the primary winding of t1. the other side of the transformer primary is driven by topswitch . d1 and vr1 clamp voltage spikes caused by transformer leakage inductance. d2, c2, l1, and c3 rectify and filter the power secondary. topswitch bias voltage is provided by d3 and c4 which rectify and filter the bias winding. emi filter components l2, c6, and c7 reduce conducted emission currents. bypass capacitor c5 filters internal topswitch gate charge current spikes and also compensates the control loop. regulation is achieved when the output voltage rises sufficiently above zener diode voltage (vr2) to cause optocoupler photodiode current to flow. optocoupler phototransistor current flows into the topswitch control pin to directly control the duty cycle and output voltage. r1 together with series impedances of vr2 and topswitch determine the control loop dc gain. r2 and vr2 provide a slight preload to improve regulation at light loads. figures 2 and 3 show typical voltage and current waveforms taken from the same power supply delivering 15 watts from 110 vac input voltage but with different flyback transformer
c 6/96 AN-17 3 pi-1526-091395 0 10 20 -20 v -10 v 10 v 0 v 200 v 0 v v drain 0 ma 500 ma i pri 0 a 5 a i sec v diode time ( m s) i r i p pi-1527-051695 0 10 20 time ( m s) -20 v -10 v 10 v 0 v 200 v 0 v v drain 0 ma 500 ma i pri 0 a 5 a i r i p i sec v diode 5 a 500 ma 0 ma figure 3. voltage and current waveforms for transformer primary and secondary in continuous mode. figure 2. voltage and current waveforms for transformer primary and secondary in discontinuous mode. primary inductance. topswitch turns on to effectively apply the dc input voltage across the transformer winding with the dot side at lower potential than the no-dot side. primary current i pri increases linearly with a rate of change (di/dt) that varies directly with dc input voltage and inversely with primary inductance. ripple current i r is defined as the incremental linear current rise (di) over the entire topswitch on time (t on ). peak primary current i p is the final value occurring as topswitch turns off. energy, proportional to the square of peak current i p , is stored by magnetic field in the transformer core as if the primary winding were a simple inductor. the secondary winding carries a reflected voltage proportional to primary voltage by turns ratio with the same dot polarity. while topswitch is on, output diode d2 and bias diode d3 are reverse biased which prevents secondary current flow. when topswitch turns off, the decreasing magnetic field induces an abrupt voltage reversal on all transformer windings such that the dot side is now higher potential than the no-dot side. diode d2 and d3 become forward biased and secondary current rises quickly to a peak value (proportional by the inverse turns ratio to primary peak current i p ). primary current immediately drops to zero. topswitch drain voltage quickly rises to a voltage equal to the sum of the dc input voltage and reflected output voltage. secondary winding current now linearly decreases at a rate that varies directly with output voltage and inversely with secondary inductance. duty cycle is defined as the ratio of topswitch on time t on to switching period t. d can also be calculated from t on and switching frequency f s as shown. d t t tf on on s == figure 2 shows topswitch and output diode triangular current waveforms which define discontinuous mode of operation resulting from low primary inductance. the secondary current linearly decreases to zero before topswitch turns on again. the stored energy is completely delivered to the load. topswitch drain voltage v drain relaxes and rings back towards the dc bus voltage when no current is flowing in either primary or secondary. figure 3 shows trapezoidal current waveforms which define continuous mode of operation resulting from high primary inductance. secondary current is still flowing when topswitch turns on at the beginning of the next cycle. the stored energy is not completely delivered to the load. energy (due to non-zero magnetic field) remains in the core when topswitch turns on again which causes the initial step in topswitch current. note that topswitch drain voltage v drain stays at a high value equal to the sum of the dc input voltage and reflected output voltage until topswitch turns on again. current never flows in the primary and secondary winding at the same time. neither primary or secondary current is actually continuous. in flyback power supplies, continuous/ discontinuous mode refers to magnetic field continuity in the transformer core over one complete switching cycle. (the flyback power supply is an isolated version of the simple buck- boost converter where continuous and discontinuous modes are easily defined by inductor current continuity.) each primary current waveform has a peak value (i p ), a ripple current value (i r ), an average or dc value (i avg ), and an rms value (i rms ). i p determines the number of primary turns and the core size necessary to limit peak flux density and must also be below topswitch peak current limit. i avg is the average or dc primary current (as well as the power stage dc input current) which is proportional to output power. i rms causes power losses due to winding resistance and topswitch r dson . the ratio (k rp ) of ripple current i r to peak current i p defines the continuous or discontinuous waveform. k rp also simplifies subsequent calculations. transformers designed for discontinuous operation have a higher peak current and a ripple current to peak current ratio k rp of one. practical continuous designs have lower peak
AN-17 c 6/96 4 currents and a ripple to peak current ratio k rp of less than one but typically greater than 0.4. k rp is inversely proportional to primary inductance so a continuous design with lower k rp will have a higher inductance. continuous transformer designs have a practical primary inductance upper limit approximately four times that of a discontinuous design at the same input voltage and output power due to the difference in peak currents and value of k rp . the primary current waveforms shown in figures 2 and 3 deliver the same output power and therefore (assuming equal efficiency) must have equal i avg . the discontinuous current waveform has a higher peak value and therefore must have a higher rms current value. discontinuous mode requires less inductance and reduces transformer size but operates with higher losses and lower efficiency due to higher rms currents. continuous mode requires higher inductance and larger transformer size but offers improved efficiency and lower power losses. the trade-off between transformer size and power supply efficiency depends on the packaging and thermal environment in each application. some control loop comments regarding continuous mode are in order here. most designers tend to avoid the continuous mode whenever possible because the feedback control loop is more difficult to analyze. discontinuous mode power supplies are modeled with a single pole response and are simple to stabilize. continuous mode offers improved efficiency, reduced losses, lower component temperatures, or higher output power but analysis is more difficult because a right half plane zero and complex pole pair all shift with duty cycle. however, stabilizing a continuous mode topswitch power supply is quite straightforward. adequate phase margins are achievable over all line and load combinations because the 70% maximum topswitch duty cycle dc max (from the data sheet) limits right half plane zero and complex pole pair migration. phase margin is generally higher than expected once the damping effect of effective series power path resistance and output capacitor esr is taken into account. crossover bandwidths of 1 khz (or wider) are easily achievable with phase margins of at least 45 degrees. refer to an-14 for circuit techniques to use in continuous mode designs. transformer core, winding, and safety issues must also be discussed before beginning design. transformer core and construction parameters depend on the selected core and winding techniques used in assembly. physical height and cost are usually most important when selecting cores. this is especially true in ac mains adapter power supplies normally packaged in sealed plastic boxes. applications allowing at least 0.75 inches of component height can use low cost ee or ei cores from magnetics, inc., japanese vendors tdk and tokin, or european vendors philips, siemens, and thomson. applications requiring lower profile can benefit from efd cores available from the european vendors. eer cores offer a large window area, require few turns, and have bobbins available with high pin counts for those applications requiring multiple outputs. etd cores are useful in the higher power designs when space is not a problem. pq cores are more expensive but take up slightly less pc board space and require less turns than e cores. safety isolation requirements make pot cores, rm cores, and toroids generally not suitable for flyback power supplies operating from the ac mains. flyback transformers must provide isolation between primary and secondary in accordance with the regulatory agencies of the intended market. for example, information technology equipment must meet the requirements of iec950 in europe and ul1950 in the u.s. these documents specify creepage and clearance distances as well as insulation systems used in transformer construction. 5 to 6 mm creepage distance is usually sufficient between primary and secondary (check with the appropriate agency and specification). isolation is usually specified by electric strength and is tested with a voltage of typically 3000 vac applied for 60 seconds. two layers of insulation (basic and supplementary) can be used between primary and secondary if each layer exceeds the electric strength requirement. three layers of insulation (reinforced) can also be used if all combinations of two layers (out of total three layers) meets the electric strength requirement. figure 4a shows the margin winding technique used in most flyback transformers. the margin is usually constructed with layers of tape slit to the width of the desired margin and wrapped in sufficient layers to match the winding height. the margin is generally half the required primary to secondary creepage distance (2.5 mm in this example). cores and bobbins should be selected large enough that the actual winding width is at least twice the total creepage distance to maintain transformer coupling and reduce leakage inductance. the primary is wound between the margins. to reduce the risk of interlayer voltage breakdown due to insulation abrasion, improve layer to layer insulation, and decrease capacitance, the primary layers should be separated by at least one layer of ul listed polyester film tape (3m 1298) cut to fit between the margins. impregnation with varnish or epoxy can also improve the layer to layer insulation and electric strength but does not reduce capacitance. the bias winding may then be wound over the primary. supplementary or reinforced insulation consisting of two or three layers of ul listed polyester film tape cut to the full width of the bobbin may then be wrapped over the primary and bias windings. margins are again wound. the secondary winding is wound between the margins. another two or three layers of tape is added to secure the windings. insulation sleeving may be needed over the leads of one or all windings to meet creepage distance requirements at lead exits. nylon or
c 6/96 AN-17 5 bias bias (alternate location) primary pi-1678-091395 secondary (insulated) bias m m primary (z wound) alternate primary winding secondary safety insulation tape (a) margin winding (b) c winding pi-1521-091395 figure 5. triple insulated wire wound transformer. figure 4. margin wound transformer. teflon sleeving with a minimum wall thickness of 0.41 mm should be used to meet the safety agency requirements. consider the core as isolated dead metal (which means the core is conductive but not part of any circuit and safely insulated from the consumer). the sum of distance from primary winding (or lead exits) to the core added to the distance from the core to the secondary (or lead exits) must be equal to or greater than the required creepage distance. both z winding (figure 4a) and c winding (figure 4b) techniques for multiple primary layers are shown. note that the dot side which connects to topswitch is buried under the second layer for self shielding to reduce emi (common mode conducted emission currents). z winding decreases transformer capacitance, decreases ac topswitch losses, and improves efficiency but is more difficult and costly to wind. the c winding is easier and lower cost to wind but at the expense of higher loss and lower efficiency. figure 5 shows a new technique using double or triple insulated wire on the secondary to eliminate the need for margins (insulated wire sources can be found at the end of this application note). in double insulated wire, each layer is usually capable of meeting the electric strength requirement of the safety agency. in triple insulated wire, all three combinations of two layers taken together must usually meet the electric strength requirement. special care is necessary to prevent insulation damage during winding and soldering. this technique reduces transformer size and eliminates the labor cost of adding margins but has higher material cost and may increase winding costs. the primary winding is wound over the full width of the bobbin flange. the bias winding can be wound if desired over the primary. one layer of tape is usually necessary between primary or bias and secondary to prevent abrasion of the insulated wire. the double or triple insulated wire is then wound. another layer of tape is added to secure insulated winding. figure 5 also shows an alternate position for the bias winding wound directly over the secondary to improve coupling to the secondary winding and reduce leakage inductance (to improve load regulation in bias winding feedback circuits). note that because the bias winding is a primary circuit, margin wound transformers must have another layer of supplementary or reinforced insulation between the secondary and alternate bias winding. refer to an-18 for more information regarding transformer construction guidelines. flyback transformer design now begins by specifying the three groups of independent variables shown in the spreadsheet (figure 6). application variables: output power p o , output voltage v o , ac mains frequency f l , topswitch switching frequency f s (100khz), minimum (v acmin ), and maximum (v acmax ) ac mains voltage come directly from the application. for efficiency ( h ), start with an estimate based on measurements in similar power supplies (or use a value of 0.8 if data is unavailable). efficiency can be used to calculate total power loss p l in the power supply as shown below. some power losses occurring in series primary components such as the bridge rectifier, common
AN-17 c 6/96 6 figure 6. spreadsheet for st202a flyback transformer design . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 abcde f input output enter application variables vacmin 8 5 volts minimum ac input voltage vacmax 2 6 5 volts maximum ac input voltage fl 6 0 hertz ac mains frequency fs 100000 hertz topswitch switching frequency vo 7.5 volts output vo ltage po 15 watts output power n 0.8 efficiency estimate z 0.5 loss allocation factor vb 10.4 volts bias voltage tc 3.2 mseconds bridge rectifier conduction time estimate cin 3 3 ufarads input filter capacitor enter topswitch variables vor 85 volts reflected output voltage vds 10 volts topswitch on-state drain to source voltage vd 0.4 volts output winding diode forward voltage drop vdb 0.7 volts bias winding diode forward voltage drop krp 0.92 ripple to peak current ratio (0.4 < krp < 1.0) enter transformer core/construction variables ee22-z core type ae 0.41 cm^2 core effective cross sectional area le 3.96 cm core effective path length al 2400 nh/t^2 ungapped core effective inductance bw 8.43 mm bobbin physical winding width m 0 mm safety margin width (half the primary to secondary creepage distance) l2 number of primary layers ns 5 number of secondary turns dc input voltage parameters vmin 9 3 volts minimum dc input voltage vmax 3 7 5 volts maximum dc input voltage current waveform shape parameters dmax 0.51 duty cycle at minimum dc input voltage (vmin) iavg 0.20 amps average primary current i p 0.74 amps peak primary current i r 0.68 amps primary ripple current irms 0.32 amps primary rms current transformer primary design parameters lp 623 uhenries primary inductance np 5 4 primary winding number of turns nb 7 bias winding number of turns alg 215 nh/t^2 gapped core effective inductance bm 2085 gauss maximum flux density (2000 < bm < 3000) bac 9 5 9 gauss ac flux density for core loss curves (0.5 x peak to peak) ur 1845 relative permeability of ungapped core lg 0.22 mm gap length (lg >> 0.051 mm) bwe 16.86 mm effective bobbin width od 0.31 mm maximum primary wire diameter including insulation ins 0.05 mm estimated total insulation thickness (= 2 * film thickness) dia 0.26 mm bare conductor diameter awg 3 0 awg primary wire gauge (rounded to next smaller standard awg value) cm 1 0 2 cmils bare conductor effective area in circular mils cma 3 2 1 cmils/amp primary winding current capacity (200 < cma < 500) transformer secondary design parameters isp 7.95 amps peak secondary current isrms 3.36 amps secondary rms current io 2.00 amps power supply output current iripple 2.70 amps output capacitor rms ripple current cms 1079 cmils secondary bare conductor minimum circular mils awgs 1 9 awg secondary wire gauge (rounded up to next larger standard awg value) dias 0.91 mm secondary minimum bare conductor diameter ods 1.69 mm secondary maximum insulated wire outside diameter inss 0.39 mm maximum secondary insulation wall thickness voltage stress parameters vdrain 5 7 3 volts maximum drain voltage estimate (includes effect of leakage inductance) pivs 4 2 volts output rectifier maximum peak inverse voltage pivb 5 9 volts bias rectifier maximum peak inverse voltage additional outputs vx 12 volts auxiliary output voltage vdx 0.7 volts auxiliary diode forward voltage drop nx 8.04 auxiliary number of turns pivx 6 8 volts auxiliary rectifier maximum peak inverse voltage
c 6/96 AN-17 7 mode choke, and topswitch are not associated directly with energy stored in the flyback transformer core. the remaining power losses, occurring in the output rectifier and clamp zener diode when energy is released from the flyback transformer, are now defined as secondary loss p ls . loss allocation factor z, defined below as the ratio of secondary loss p ls to total loss p l , is a scaling factor which distributes the losses between primary and secondary. loss allocation factor z is typically between 0.4 and 0.6 which means that secondary loss p ls is usually 40% to 60% of total power supply loss p l . pp lo = - () 1 h h z p p ls l = bias voltage v b is determined by the feedback control circuit and is usually between 10 volts and 30 volts (see an-16). for bridge rectifier conduction time t c , 3 milliseconds is typical (measure on a similar power supply or set equal to zero for a conservative first design). for input filter capacitor c in , start with a standard value in microfarads between two and three times the output power in watts (appropriate for universal or 115 vac input). for example: 30 m f to 45 m f is a suitable capacitance range for a 15 watt supply. 33 m f is the lowest standard value within the range. topswitch variables: reflected output voltage v or appears across the transformer primary when topswitch is off and current is flowing through the secondary and output rectifier diode. transformers optimized for topswitch applications should be designed with a maximum reflected voltage v or of 60v or less for the top1xx series and 135v or less for the top2xx series. for more information, refer to an-16. v ds is the on-state topswitch voltage from the data sheet (typically 10 volts) at the specified value for peak topswitch drain current i p . output rectifier forward voltage drop v d depends on output voltage. for lower output voltages (typically 8 volts and below) a schottky diode is commonly used and v d is typically 0.4 volts. in some cases, a schottky diode can be used for output voltages as high as 12v depending on input voltage range and transformer turns ratio. for higher output voltage, an ultrafast recovery pn junction diode is figure 7. bridge ac current, ac voltage, and dc voltage waveforms. normally used and v d is typically 0.7 volts. bias winding diode forward voltage drop (v db ) is also typically 0.7 volts ripple current to peak current ratio k rp determines how far into the continuous mode a flyback transformer will operate. continuous mode transformers optimized for topswitch applications operating from 100/115 vac or universal input voltage should have a minimum k rp of 0.4. applications operating from 230 vac input voltage should have a minimum k rp of 0.6. discontinuous mode transformers optimized for topswitch applications always have a k rp equal to 1.0. k i i rp r p = transformer core/construction variables: the following effective parameters are specified by the core and bobbin manufacturer in data sheets: cross sectional area a e (cm 2 ), path length l e (cm), ungapped inductance a l (specified in either mh/(1000 turns) 2 or nh/t 2 ), and physical bobbin winding width b w (mm). margin width m, determined by insulation methods and regulatory requirements discussed above, is usually between 2.5 to 3.0 mm for margin wound or set to zero for insulated wire wound transformers. for number of layers l, one or two layers of primary winding are normally used. higher number of layers increase cost, increase capacitance, reduce coupling, and increase leakage inductance.
AN-17 c 6/96 8 number of secondary turns n s is a key iteration variable. one turn per volt of output voltage is a good value to begin with for n s (for example: start with 5 turns for a +5v output). the four groups of dependent parameters can now be calculated. dc input voltage parameters: minimum dc input voltage v min depends on the ac input voltage, bridge rectifier, and energy storage capacitor. figure 7 shows how c in charges to the peak of the ac input voltage during a short conduction time t c . because of full wave rectification, c in has a ripple voltage at twice line frequency. c in must supply the entire average primary current during the discharge time between the peaks of the ac input voltage. minimum dc voltage v min can be found from the following equation where p o is the power supply output power, h is an estimate of efficiency, f l is line voltage frequency, v acmin is the minimum ac mains voltage, c in is the value of the filter capacitor, and t c is an estimate for conduction time. as an example, for 60 hz, 85 vac input voltage, efficiency of 0.8, 15 watt output power, 33 uf input filter capacitance, and estimated conduction time of 3.2 ms, v min is 93 volts dc. vv p f t c min acmin o l c in = - - ()( () ) 2 2 1 2 2 h = - - = ()( (.) . ) 285 215 1 260 32 08 33 93 2 ms f v m maximum dc input voltagev max is simply the peak value of the highest ac input voltage (v acmax ) expected in the application. operation from 265 vac input results in a maximum dc bus voltage v max of 375 volts dc. vv v max acmax === 2 265 2 375 current waveform shape parameters: d max is the actual duty cycle occurring when the topswitch power supply delivers maximum output power from minimum input voltage. d max has an upper limit equal to the minimum value of the topswitch data sheet parameter dc max (64%). d max is calculated from reflected voltage v or , minimum dc input voltage v min , and topswitch on-state drain to source voltage v ds : d v vvv max or or min ds = +- () average current i avg is calculated from minimum dc input voltage v min , output power p o , and efficiency h : i p v avg o min = h peak primary current ip is calculated from average current i avg , ripple to peak current ratio k rp , and maximum duty cycle d max : ii kd p avg rp max = - 2 2 () ripple current i r is calculated from average current i avg , peak primary current i p , and maximum duty cycle d max : ii i d rp avg max = - 2( ) rms current i rms is calculated from maximum duty cycle d max , peak primary current i p , and ripple to peak ratio k rp . i rms can also be calculated directly from d max , i p , and ripple current i r . iid k k rms p max rp rp = - + () 2 3 1 =-+ diii i max p p r r (( ) ) 2 2 3 transformer design parameters: primary inductance l p (in m h) is determined by the flyback transformer energy equation defined below. the flyback transformer stores energy proportional to the square of primary current. when topswitch is on, primary current linearly ramps up over a current range, defined earlier as ripple current i r , and increases the energy stored in the flyback transformer core. when topswitch turns off, the stored energy increment associated with ripple current i r is delivered to the load and secondary losses (rectifier and clamp). inductance l p can now by calculated from output power p o , efficiency h , loss allocation factor z, peak current i p , switching frequency f s , and ripple current to peak current ratio k rp (which determines i r ).
c 6/96 AN-17 9 l p z fik k p o sp rp rp = - + - 10 1 1 2 6 2 ( (( )) ) () hh h primary inductance l p (in m h) can also be determined from a simple function of ripple current i r , effective primary voltage (v min -v ds ), maximum duty cycle d max , and switching frequency f s as shown below but the resulting value for primary inductance may be slightly different due to the selected value for loss allocation factor z and topswitch on-state drain to source voltage v ds . the energy equation given above is preferred for selecting the value of inductance l p while the ripple current equation given below is best for verifying the l p value using in-circuit measurements. l vvd if p measured min ds max rs () () = - 10 6 number of primary turns n p depends on number of secondary turns n s , output voltage v o , diode forward voltage drop v d , effective primary voltage (v min -v ds ), and maximum duty cycle d max : nn vv vv d d ps min ds od max max = - + - 1 the number of bias winding turns n b is calculated from the output voltage v o , output diode voltage v d , secondary number of turns n s , target bias voltage v b , and bias diode voltage v bd : n vv vv n b bbd od s = + + a lg is the effective inductance for the gapped core in nh/t 2 . some core vendors offer standard gapped core sets with specified a lg . the transformer manufacturer either procures the gapped core for the given a lg value or grinds the gap to meet the inductance specification in the finished transformer. a lg is also used to simplify subsequent calculations. a lg is calculated from primary inductance l p (in m h) and number of primary turns n p . note that a lg is specified in nh/(turn) 2 . a l n lg p p = 1000 2 maximum flux density b m is a dependent iteration variable to be manipulated between the limits of 2000 and 3000 gauss by varying number of secondary turns n s which directly varies number of primary turns n p as previously shown. b m is calculated from peak current i p , number of primary turns n p , effective gapped inductance a lg , and effective core cross sectional area a e . b m can also be calculated from effective primary voltage (v min -v ds ), output voltage v o , output diode voltage v d , and maximum duty cycle d max : b nia a m pp lg e = 10 = - + - n ia a vv vv d d s plg e min ds od max max 10 1 b ac is the ac flux density component. the equation gives peak ac flux density (rather than peak to peak) to use with core loss curves provided by the core vendor. b ac can be calculated from maximum flux density b m and ripple to peak current ratio k rp . b ac can also be calculated from effective primary voltage (v min -v ds ), duty cycle, frequency, effective core cross sectional area, and number of primary turns n p : b bk v v d fan ac m rp min ds max se p = = - 2 10 2 8 () relative permeability m r of the ungapped core must be calculated to estimate the gap length l g . m r is found from core parameters a e (cm 2 ), l e (cm), and ungapped effective inductance a l : m p r le e al a = 04 10 . gap length l g is the air gap ground into the center leg of the transformer core. grinding tolerances and a lg accuracy place a minimum limit of 0.051 mm on l g . l g (in mm) is calculated from number of primary turns n p , core effective cross sectional area a e , primary inductance l p (in m h), core effective path length l e , and relative permeability m r : l na l l g pe p e r = - ? ? ? ? 04 100 10 2 . p m effective bobbin width bw e takes into account physical bobbin width bw, margins m, and number of layers l: bw l bw m e = - (()) 2
AN-17 c 6/96 10 cma cm i rms = this completes all calculations necessary for the primary winding. secondary peak current, rms current, average output current, output capacitor ripple current, and secondary minimum and maximum conductor diameter must also be calculated. peak secondary current i sp is a simple function of peak primary current i p , primary turns n p , and secondary turns n s . ii n n sp p p s = secondary rms current i srms is found from maximum duty cycle d max , secondary peak current i sp , and ripple to peak current ratio k rp (k rp is identical for primary and secondary). ii d k k srms sp max rp rp = - - + ()( ) 1 3 1 2 output current i o is simply the ratio of output power p o to output voltage v o : i p v o o o = output capacitor ripple current i ripple is not a true transformer parameter but is needed for capacitor selection and easy to calculate from other transformer parameters. i ripple is found from secondary rms current i srms and output current i o . iii ripple srms o =- 22 minimum secondary bare conductor diameter dia s (in mm) based on previously calculated current capacity cma and secondary rms current must be determined. from the primary cma and secondary rms current i srms , the minimum secondary bare conductor cm s is calculated. cm cma i s srms = minimum secondary awg s is then calculated from another empirical equation. secondary calculated wire gauge awg s is always rounded down to the next integer value which selects the next larger standard wire size. primary insulated wire diameter od in mm is found from effective bobbin width bw e and number of primary turns n p : od bw n e p = the bias winding is usually wound with the same wire diameter as the primary to reduce the number of different wire gauges necessary for production. actual magnet wire outside diameter od is slightly larger than the diameter dia of the bare copper conductor. insulation thickness varies inversely with bare copper conductor american wire gauge (awg) size which means that smaller diameter conductors have thinner insulation thickness. data from several different manufacturers were tabulated to generate an empirical expression for total insulation thickness ins (in mm) as a function of heavy insulated magnet wire outside diameter (in mm). ins log od = + (. ( )) . 0 0594 0 0834 dia od ins =- another empirical equation determines the awg for magnet wire with a given bare conductor diameter dia. integer awg values are the standard sizes of available wire so the calculated awg value should always be rounded up to the next integer or standard value (the next smaller standard conductor diameter) before proceeding with the current capacity or cma calculation. awg log dia = - 9 97 1 8277 2 . ( . ( ( ))) magnet wire for transformer winding usually has the cross sectional area specified in circular mils. a circular mil is the cross sectional area of a wire with a diameter of 1 mil (or 0.0254 mm). the effective cross sectional area in circular mils (cm) of a standard awg size bare conductor wire is found from the following simple expression. cm awg = - ? ? ? ? 2 50 3 circular mils per amp or cma is a convenient way to specify winding current capacity. cma, which is the inverse of current density, is simply the ratio of cross sectional area in circular mils to the rms value of primary current. cma should be between 200 and 500 and is calculated from cross sectional wire area in cm and rms primary current i rms .
c 6/96 AN-17 11 awg log cm ss = - 9 97 5 017 .(. ()) (secondary conductors larger than 26 awg should not be used due to skin effects. refer to an-18 for suggestions on parallel conductor techniques.) bare conductor diameter (in mm) is now determined. dia s awg s = - ? ? ? ? 42 127 25 4 1000 50 3 . . p the maximum wire outside diameter od s (in mm) for a single layer based on number of secondary turns and bobbin width must also be calculated: od bw m n s s = - () 2 secondary wire insulation thickness can now be calculated from the bare conductor outside diameter (determined by cma) and the insulated wire outside diameter (determined by number of turns and effective bobbin width). note that secondary insulation thickness ins s (in mm) is the insulation wall thickness rather than the total insulation thickness used in the primary winding calculation. ins od dia s ss = - 2 obviously, if insulation thickness ins s is not a positive number, another transformer design iteration is necessary with either more secondary layers, a smaller number of secondary turns, or a transformer core with a wider bobbin. for insulated wire secondaries, ins s must be equal to or greater than insulation thickness of the selected wire. parallel combinations of wire with half the diameter may be easier to wind and terminate but the effective secondary cma will be half the value of the single winding. voltage stress parameters: maximum drain voltage is the sum of maximum dc input voltage v max , an estimated drain clamp voltage term based on v or , and an estimated voltage term related to typical blocking diode forward recovery. refer to an-16 for more detail. vv v v drain max or =++ (. . ) 14 15 20 maximum peak inverse voltage piv s for the output rectifier is determined by transformer primary and secondary number of turns n p and n s , maximum dc input voltage v max , and output voltage v o . piv v v n n s o max s p =+ () maximum peak inverse voltage piv b for the bias rectifier is determined from a similar equation using number of bias turns n b . piv v v n n b b max b p =+ () additional or auxiliary output winding number of turns n x and rectifier diode peak inverse voltage piv x can be determined from the desired value for auxiliary output voltage v x , auxiliary rectifier diode forward voltage drop v dx , output voltage v o , output rectifier diode forward voltage drop v d , and number of secondary turns n s . n vv vv n x xdx od s = + + piv v v n n x x max x p =+ () iteration can now be used to reach a final and acceptable solution for the flyback transformer design. iterate number of secondary turns n s or primary ripple to peak current ratio k rp until maximum flux density b m is between indicated limits and check that gap length l g is higher than indicated minimum value. b m will decrease and l g will increase as n s or k rp is increased. examine primary current capacity in circular mils per amp (cma). if cma is below the specified lower limit of 200, consider increasing number of primary layers from one to two or use the next larger core size and perform new iteration. if cma is greater than 500, consider using the next smaller core size. (cma greater than 500 simply means that the wire diameter is oversized for the expected rms current). the transformer design is now complete. the transformer
AN-17 c 6/96 12 manufacturer needs the following information: core part number and gapped effective inductance a lg bobbin part number wire gauge and insulation style on all windings safety or electric strength and creepage distance specifications primary inductance l p number of turns (n p , n s , n b , etc.) for each winding bobbin pin connections winding layer placement and winding instructions temperature class of operation (class a is 105 c, class b is 130 c, etc.) spreadsheet improvements the order of the spreadsheet has been changed to simplify the iteration process. reflected voltage v or and ripple to peak current ratio k rp are now independent variables which make peak current ip and duty cycle d max dependent variables. loss allocation factor z is introduced to distinguish between power losses occurring before energy is stored in the transformer (primary losses) and power losses occurring after energy is released from the transformer (secondary losses). primary inductance l p is now calculated from output power p o , k rp , efficiency h , and loss allocation factor z. the spreadsheet now takes into account primary magnet wire insulation thickness as well as the discrete steps of standard awg wire sizes. metric dimensions are used throughout (with the exception of circular mils for wire cross sectional area). drain voltage v drain now includes an estimate for the effect of leakage inductance induced voltage spikes on typical primary clamp circuits. references bisci, j., part iv: magnet wire: selection determines performance, pcim, october 1994, pp. 37. leman, b., finding the keys to flyback power supplies produces efficient design, edn, april 13, 1995, pp. 101-113. mclyman, c., transformer and inductor design handbook, marcel dekker, inc. 1978 insulated wire sources rubudue wire company 5150 e. lapalma ave, suite 108 anaheim hills, ca 92807 usa (714) 693-5512 (714) 693-5515 fax furukawa electric america, inc. 200 westpark dr., suite 190 peachtree city, ga 30269 usa (770) 487-1234 (770) 487-9910 fax the furukawa electric co., ltd. 6-1, marunouchi 2-chome, chiyoda-ku, tokyo 100, japan 81-3-3286-3226 81-3-3286-3747 fax power integrations reserves the right to make changes to its products at any time to improve reliability or manufacturability. power integrations does not assume any liability arising from the use of any device or circuit described herein, nor does it convey any license under its patent rights or the rights of others. pi logo and topswitch are registered trademarks of power integrations, inc. ?copyright 1994, power integrations, inc. 477 n. mathilda avenue, sunnyvale, ca 94086 japan power integrations, inc. keihin-tatemono 1st bldg. 12-20 shin-yokohama 2-chome.kohoku-ku yokohama-shi, kanagawa 222 japan phone: 81?(0)?45?471?1021 fax: 81?(0)?45?471?3717 asia & oceania for your nearest sales/rep office please contact customer service phone: 408?523?9265 fax: 408?523?9365 world headquarters power integrations, inc. 477 n. mathilda avenue sunnyvale, ca 94086 usa main: 408?523?9200 customer service: phone: 408?523?9265 fax: 408?523?9365 americas for your nearest sales/rep office please contact customer service phone: 408?523?9265 fax: 408?523?9365 applications hotline world wide 408?523?9260 applications fax americas 408?523?9361 europe/africa 44?(0)?1753?622?209 japan 81?(0)?45?471?3717 asia/oceania 408?523?9364 europe & africa power integrations (europe) ltd. mountbatten house fairacres windsor sl4 4le united kingdom phone: 44?(0)?1753?622?208 fax: 44?(0)?1753?622?209

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