® Flyback Transformer Design For TOPSwitch® Power Supplies Application Note AN-17 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, 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 VDIODE D2 UG8BT L1 3.3 µH 7.5 V ISEC VR1 P6KE200 C1 33 µF (CIN) L2 22 mH IPRI VDRAIN C6 0.1 µF R2 68 Ω C3 120 µF 25 V C2 680 µF 25 V U2 NEC2501-H D1 UF4005 BR1 R1 39 Ω VR2 1N5995B 6.2 V RTN D3 1N4148 C5 47µF DRAIN SOURCE CONTROL L U1 TOP202YAI C7 1000 nF C4 Y1 0.1 µF CIRCUIT PERFORMANCE: Line Regulation - ±0.5% (85-265 VAC) Load Regulation - ±1% (10-100%) Ripple Voltage ± 50 mV Meets VDE Class B N J1 PI-1787-021296 Figure 1. ST202A Power Supply Operates from Universal Input Voltage and Delivers 15 Watts. June 1996 AN-17 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 (KRP), 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 NS, ripple to peak current ratio KRP, 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 2 C 6/96 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 BM, gap length LG , 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 (CIN) 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 0V IP 0A 20 IR 500 mA IP 0 mA 0 mA 10 V 0V -10 V -20 V 5A 5A 0 10 Time (µs) ISEC 10 Time (µs) 0 ISEC 5A 0V 500 mA VDIODE VDIODE 0 mA 10 V 0V -10 V -20 V 200 V IPRI 500 mA IPRI IR PI-1527-051695 200 V VDRAIN PI-1526-091395 VDRAIN AN-17 0A 20 Figure 2. Voltage and Current Waveforms for Transformer Primary and Secondary in Discontinuous Mode. Figure 3. Voltage and Current Waveforms for Transformer Primary and Secondary in Continuous 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 IPRI increases linearly with a rate of change (di/dt) that varies directly with DC input voltage and inversely with primary inductance. Ripple current IR is defined as the incremental linear current rise (di) over the entire TOPSwitch on time (tON). Peak primary current IP is the final value occurring as TOPSwitch turns off. Energy, proportional to the square of peak current IP, 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 IP). 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 tON to switching period T. D can also be calculated from tON and switching frequency f S as shown. The stored energy is completely delivered to the load. TOPSwitch drain voltage VDRAIN relaxes and rings back towards the DC bus voltage when no current is flowing in either primary or secondary. D= t ON = t ON × f S T 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. 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 VDRAIN 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 buckboost converter where continuous and discontinuous modes are easily defined by inductor current continuity.) Each primary current waveform has a peak value (IP), a ripple current value (IR), an average or DC value (I AVG), and an RMS value (IRMS). IP 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. IAVG is the average or DC primary current (as well as the power stage DC input current) which is proportional to output power. IRMS causes power losses due to winding resistance and TOPSwitch RDSON. The ratio (KRP) of ripple current IR to peak current IP defines the continuous or discontinuous waveform. KRP also simplifies subsequent calculations. Transformers designed for discontinuous operation have a higher peak current and a ripple current to peak current ratio KRP of one. Practical continuous designs have lower peak C 6/96 3 AN-17 currents and a ripple to peak current ratio KRP of less than one but typically greater than 0.4. KRP is inversely proportional to primary inductance so a continuous design with lower KRP 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 KRP. The primary current waveforms shown in Figures 2 and 3 deliver the same output power and therefore (assuming equal efficiency) must have equal IAVG. 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 DCMAX (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 4 C 6/96 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 AN-17 SECONDARY SAFETY INSULATION TAPE BIAS PRIMARY (Z WOUND) SECONDARY (INSULATED) BIAS (ALTERNATE LOCATION) BIAS M M PRIMARY (a) MARGIN WINDING ALTERNATE PRIMARY WINDING (b) C WINDING PI-1521-091395 PI-1678-091395 Figure 4. Margin Wound Transformer. Figure 5. Triple Insulated Wire 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. insulated wire. The double or triple insulated wire is then wound. Another layer of tape is added to secure insulated winding. 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 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 PO, output voltage VO , AC mains frequency fL, TOPSwitch switching frequency f S (100KHz), minimum (VACMIN), and maximum (VACMAX) AC mains voltage come directly from the application. For efficiency (η), 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 PL in the power supply as shown below. Some power losses occurring in series primary components such as the bridge rectifier, common C 6/96 5 AN-17 A 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 B C INPUT ENTER APPLICATION VARIABLES VACMIN 85 VACMAX 265 fL 60 fS 100000 VO 7.5 PO 15 n 0.8 Z 0.5 VB 10.4 tC 3.2 CIN 33 D OUTPUT E Volts Volts Hertz Hertz Volts Watts Volts mSeconds uFarads ENTER TOPSWITCH VARIABLES VOR 85 VDS 10 VD 0.4 VDB 0.7 KRP 0.92 Volts Volts Volts Volts F Minimum AC Input Voltage Maximum AC Input Voltage AC Mains Frequency TOPSwitch Switching Frequency Output Voltage Output Power Efficiency Estimate Loss Allocation Factor Bias Voltage Bridge Rectifier Conduction Time Estimate Input Filter Capacitor Reflected Output Voltage TOPSwitch on-state Drain to Source Voltage Output Winding Diode Forward Voltage Drop Bias Winding Diode Forward Voltage Drop Ripple to Peak Current Ratio (0.4 < KRP < 1.0) ENTER TRANSFORMER CORE/CONSTRUCTION VARIABLES EE22-Z AE 0.41 cm^2 LE 3.96 cm AL 2400 nH/T^2 BW 8.43 mm M 0 mm L 2 NS 5 Core Type Core Effective Cross Sectional Area Core Effective Path Length Ungapped Core Effective Inductance Bobbin Physical Winding Width Safety Margin Width (Half the Primary to Secondary Creepage Distance) Number of Primary Layers Number of Secondary Turns DC INPUT VOLTAGE PARAMETERS VMIN VMAX 9 3 Volts 3 7 5 Volts Minimum DC Input Voltage Maximum DC Input Voltage CURRENT WAVEFORM SHAPE PARAMETERS DMAX IAVG IP IR IRMS 0.51 0.20 0.74 0.68 0.32 Duty Cycle at Minimum DC Input Voltage (VMIN) Average Primary Current Peak Primary Current Primary Ripple Current Primary RMS Current TRANSFORMER PRIMARY DESIGN PARAMETERS LP NP NB ALG 215 BM BAC 959 ur 1845 LG BWE 16.86 OD INS 0.05 DIA AWG CM 102 CMA 6 2 3 uHenries 54 7 nH/T^2 2 0 8 5 Gauss Gauss 0 . 2 2 mm mm 0.31 mm mm 0.26 mm 3 0 AWG Cmils 3 2 1 Cmils/Amp TRANSFORMER SECONDARY DESIGN PARAMETERS ISP 7.95 ISRMS 3.36 IO 2.00 IRIPPLE 2.70 CMS AWGS DIAS ODS INSS VOLTAGE STRESS PARAMETERS VDRAIN PIVS PIVB ADDITIONAL OUTPUTS VX 12 VDX 0.7 NX PIVX 1079 0.39 Amps Amps Amps Amps Amps Amps Amps Amps Primary Inductance Primary Winding Number of Turns Bias Winding Number of Turns Gapped Core Effective Inductance Maximum Flux Density (2000 < BM < 3000) AC Flux Density for Core Loss Curves (0.5 X Peak to Peak) Relative Permeability of Ungapped Core Gap Length (Lg >> 0.051 mm) Effective Bobbin Width Maximum Primary Wire Diameter including insulation Estimated Total Insulation Thickness (= 2 * film thickness) Bare conductor diameter Primary Wire Gauge (Rounded to next smaller standard AWG value) Bare conductor effective area in circular mils Primary Winding Current Capacity (200 < CMA < 500) Peak Secondary Current Secondary RMS Current Power Supply Output Current Output Capacitor RMS Ripple Current Cmils 1 9 AWG 0.91 mm 1.69 mm mm Secondary Bare Conductor minimum circular mils Secondary Wire Gauge (Rounded up to next larger standard AWG value) Secondary Minimum Bare Conductor Diameter Secondary Maximum Insulated Wire Outside Diameter Maximum Secondary Insulation Wall Thickness 5 7 3 Volts 4 2 Volts 5 9 Volts Maximum Drain Voltage Estimate (Includes Effect of Leakage Inductance) Output Rectifier Maximum Peak Inverse Voltage Bias Rectifier Maximum Peak Inverse Voltage Volts Volts 8.04 6 8 Volts Auxiliary Output Voltage Auxiliary Diode Forward Voltage Drop Auxiliary Number of Turns Auxiliary Rectifier Maximum Peak Inverse Voltage Figure 6. Spreadsheet for ST202A Flyback Transformer Design. 6 C 6/96 AN-17 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 PLS. Loss Allocation Factor Z, defined below as the ratio of secondary loss PLS to total loss PL, 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 PLS is usually 40% to 60% of total power supply loss PL . PL = PO × ( 1−η ) η P Z = LS PL Figure 7. Bridge AC Current, AC Voltage, and DC Voltage Waveforms. normally used and VD is typically 0.7 Volts. Bias voltage VB is determined by the feedback control circuit and is usually between 10 volts and 30 volts (see AN-16). For bridge rectifier conduction time tC, 3 milliSeconds is typical (measure on a similar power supply or set equal to zero for a conservative first design). For input filter capacitor CIN , 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: 30µF to 45µF is a suitable capacitance range for a 15 Watt supply. 33µF is the lowest standard value within the range. TOPSwitch Variables: Reflected output voltage VOR 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 VOR of 60V or less for the TOP1XX series and 135V or less for the TOP2XX series. For more information, refer to AN-16. VDS is the on-state TOPSwitch voltage from the data sheet (typically 10 volts) at the specified value for peak TOPSwitch drain current IP. Output rectifier forward voltage drop VD depends on output voltage. For lower output voltages (typically 8 Volts and below) a Schottky diode is commonly used and VD 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 Bias winding diode forward voltage drop (VDB) is also typically 0.7 Volts Ripple current to peak current ratio KRP 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 KRP of 0.4. Applications operating from 230 VAC input voltage should have a minimum KRP of 0.6. Discontinuous mode transformers optimized for TOPSwitch applications always have a KRP equal to 1.0. K RP = IR IP Transformer Core/Construction Variables: The following effective parameters are specified by the core and bobbin manufacturer in data sheets: cross sectional area Ae (cm2), path length Le (cm), ungapped inductance AL (specified in either mH/(1000 turns)2 or nH/T2), and physical bobbin winding width BW (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. C 6/96 7 AN-17 Number of secondary turns NS is a key iteration variable. One turn per Volt of output voltage is a good value to begin with for NS (for example: start with 5 turns for a +5V output). voltage VDS: DMAX = The four groups of dependent parameters can now be calculated. Average current IAVG is calculated from minimum DC input voltage VMIN, output power PO, and efficiency η: DC Input Voltage Parameters: Minimum DC input voltage VMIN depends on the AC input voltage, bridge rectifier, and energy storage capacitor. Figure 7 shows how CIN charges to the peak of the AC input voltage during a short conduction time tC. Because of full wave rectification, CIN has a ripple voltage at twice line frequency. CIN must supply the entire average primary current during the discharge time between the peaks of the AC input voltage. Minimum DC voltage VMIN can be found from the following equation where PO is the power supply output power, η is an estimate of efficiency, fL is line voltage frequency, VACMIN is the minimum AC mains voltage, CIN is the value of the filter capacitor, and tC 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, VMIN is 93 Volts DC. VMIN = (2 × V 2 ACMIN )−( 1 − tC ) 2 × fL ) η × CIN 2 × PO × ( 1 2 × 15 × ( − 3.2 mS ) 2 2 × 60 = (2 × 85 ) − ( ) = 93V 0.8 × 33µF Maximum DC input voltageVMAX is simply the peak value of the highest AC input voltage (VACMAX ) expected in the application. Operation from 265 VAC input results in a maximum DC bus voltage VMAX of 375 Volts DC. VMAX = VACMAX × 2 = 265 × 2 = 375V Current Waveform Shape Parameters: DMAX is the actual duty cycle occurring when the TOPSwitch power supply delivers maximum output power from minimum input voltage. DMAX has an upper limit equal to the minimum value of the TOPSwitch Data Sheet parameter DCMAX (64%). DMAX is calculated from reflected voltage VOR, minimum DC input voltage VMIN, and TOPSwitch on-state Drain to Source 8 C 6/96 VOR VOR + (VMIN − VDS ) I AVG = PO η × VMIN Peak primary current Ip is calculated from average current IAVG, ripple to peak current ratio KRP, and maximum duty cycle DMAX: IP = I AVG × 2 (2 − K RP ) × DMAX Ripple current IR is calculated from average current IAVG, peak primary current IP, and maximum duty cycle DMAX: I R = 2 × ( IP − I AVG ) DMAX RMS current IRMS is calculated from maximum duty cycle DMAX, peak primary current IP, and ripple to peak ratio KRP. I RMS can also be calculated directly from DMAX, IP, and ripple current IR. I RMS = IP × DMAX × ( 2 K RP − K RP + 1) 3 = DMAX × ( IP2 − ( IP × I R ) + I R2 ) 3 Transformer Design Parameters: Primary inductance LP (in µH) 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 IR, and increases the energy stored in the flyback transformer core. When TOPSwitch turns off, the stored energy increment associated with ripple current IR is delivered to the load and secondary losses (rectifier and clamp). Inductance LP can now by calculated from output power PO, efficiency η, loss allocation factor Z, peak current IP, switching frequency fS, and ripple current to peak current ratio KRP (which determines IR). AN-17 ( Z × (1 − η)) + η PO × ( ) η 6 LP = 10 × K fS × IP2 × K RP × (1 − RP ) 2 Primary inductance LP (in µH) can also be determined from a simple function of ripple current IR, effective primary voltage (VMIN-VDS), maximum duty cycle DMAX, and switching frequency fS 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 VDS. The energy equation given above is preferred for selecting the value of inductance LP while the ripple current equation given below is best for verifying the LP value using in-circuit measurements. LP ( MEASURED) = 10 6 × (VMIN − VDS ) × DMAX I R × fS Number of primary turns NP depends on number of secondary turns NS, output voltage VO, diode forward voltage drop VD, effective primary voltage (VMIN-VDS), and maximum duty cycle DMAX: V − VDS DMAX N P = NS × MIN × VO + VD 1 − DMAX The number of bias winding turns NB is calculated from the output voltage VO, output diode voltage V D, secondary number of turns NS, target bias voltage VB, and bias diode voltage VBD: NB = VB + VBD × NS VO + VD ALG is the effective inductance for the gapped core in nH/T2. Some core vendors offer standard gapped core sets with specified ALG. The transformer manufacturer either procures the gapped core for the given ALG value or grinds the gap to meet the inductance specification in the finished transformer. ALG is also used to simplify subsequent calculations. ALG is calculated from primary inductance LP (in µH) and number of primary turns NP. Note that ALG is specified in nH/(turn)2. ALG L = 1000 × P2 NP Maximum flux density BM is a dependent iteration variable to be manipulated between the limits of 2000 and 3000 Gauss by varying number of secondary turns NS which directly varies number of primary turns NP as previously shown. BM is calculated from peak current IP, number of primary turns NP, effective gapped inductance ALG, and effective core cross sectional area Ae. BM can also be calculated from effective primary voltage (VMIN-VDS), output voltage VO , output diode voltage VD , and maximum duty cycle DMAX: BM = N P × IP × ALG 10 × Ae = NS × IP × ALG VMIN − VDS DMAX × × VO + VD 10 × Ae 1 − DMAX BAC 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. BAC can be calculated from maximum flux density BM and ripple to peak current ratio KRP. BAC can also be calculated from effective primary voltage (VMIN-VDS), duty cycle, frequency, effective core cross sectional area, and number of primary turns NP: BAC = BM × K RP (VMIN − VDS ) × DMAX × 108 = 2 2 × fS × Ae × N P Relative permeability µr of the ungapped core must be calculated to estimate the gap length Lg. µr is found from core parameters Ae (cm2), Le (cm), and ungapped effective inductance AL: µr = AL × LE 0.4 × π × Ae × 10 Gap length Lg is the air gap ground into the center leg of the transformer core. Grinding tolerances and ALG accuracy place a minimum limit of 0.051 mm on Lg. L g (in mm) is calculated from number of primary turns NP, core effective cross sectional area Ae, primary inductance LP (in µH), core effective path length Le, and relative permeability µr: 0.4 × π × N P2 × Ae Le Lg = − × 10 LP × 100 µr Effective bobbin width BWE takes into account physical bobbin width BW, margins M, and number of layers L: BWE = L × ( BW − (2 × M )) C 6/96 9 AN-17 Primary insulated wire diameter OD in mm is found from effective bobbin width BWE and number of primary turns NP: OD = BWE NP 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 = (0.0594 × LOG(OD)) + 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 = 9.97 × (1.8277 − (2 × LOG( DIA))) 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. 50 − AWG 3 CM = 2 “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 IRMS. 10 C 6/96 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 ISP is a simple function of peak primary current IP, primary turns NP, and secondary turns NS. ISP = IP × NP NS Secondary RMS current ISRMS is found from maximum duty cycle DMAX, secondary peak current ISP, and ripple to peak current ratio KRP (KRP is identical for primary and secondary). ISRMS 2 K RP = ISP × (1 − DMAX ) × ( − K RP + 1) 3 Output current IO is simply the ratio of output power PO to output Voltage VO: IO = PO VO Output capacitor ripple current IRIPPLE is not a true transformer parameter but is needed for capacitor selection and easy to calculate from other transformer parameters. IRIPPLE is found from secondary RMS current ISRMS and output current I O. 2 I RIPPLE = ISRMS − IO2 Minimum secondary bare conductor diameter DIAS (in mm) based on previously calculated current capacity CMA and secondary RMS current must be determined. From the primary CMA and secondary RMS current ISRMS, the minimum secondary bare conductor CMS is calculated. CMS = CMA × ISRMS Minimum secondary AWGS is then calculated from another empirical equation. Secondary calculated wire gauge AWGS is always rounded down to the next integer value which selects the next larger standard wire size. AN-17 AWGS = 9.97 × (5.017 − LOG(CMS )) (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. DIAS = 50 − AWGS 4 × 2 3 1.27 × π 25.4 × 1000 The maximum wire outside diameter ODS (in mm) for a single layer based on number of secondary turns and bobbin width must also be calculated: BW − (2 × M ) ODS = NS 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 INSS (in mm) is the insulation wall thickness rather than the total insulation thickness used in the primary winding calculation. ODS − DIAS INSS = 2 Obviously, if insulation thickness INSS 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, INSS 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 VMAX, an estimated drain clamp voltage term based on VOR , and an estimated voltage term related to typical blocking diode forward recovery. Refer to AN-16 for more detail. Maximum peak inverse voltage PIVS for the output rectifier is determined by transformer primary and secondary number of turns NP and NS, maximum DC input voltage VMAX, and output voltage VO . PIVS = VO + (VMAX × NS ) NP Maximum peak inverse voltage PIVB for the bias rectifier is determined from a similar equation using number of bias turns NB. PIVB = VB + (VMAX × NB ) NP Additional or auxiliary output winding number of turns NX and rectifier diode peak inverse voltage PIVX can be determined from the desired value for auxiliary output voltage VX, auxiliary rectifier diode forward voltage drop VDX, output voltage VO, output rectifier diode forward voltage drop VD, and number of secondary turns NS. NX = VX + VDX × NS VO + VD PIVX = VX + (VMAX × NX ) NP Iteration can now be used to reach a final and acceptable solution for the flyback transformer design. Iterate number of secondary turns NS or primary ripple to peak current ratio KRP until maximum flux density BM is between indicated limits and check that gap length Lg is higher than indicated minimum value. BM will decrease and L g will increase as NS or KRP 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 VDRAIN = VMAX + (1.4 × 1.5 × VOR ) + 20V C 6/96 11 AN-17 References manufacturer needs the following information: Core part number and gapped effective inductance ALG Bobbin part number Wire gauge and insulation style on all windings Safety or Electric strength and Creepage distance specifications Primary Inductance LP Number of turns (NP, NS, NB, 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 VOR and ripple to peak current ratio KRP are now independent variables which make peak current Ip and duty cycle DMAX 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 LP is now calculated from output power PO, KRP, efficiency η, 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 VDRAIN now includes an estimate for the effect of leakage inductance induced voltage spikes on typical primary clamp circuits. 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 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 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 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 APPLICATIONS HOTLINE World Wide 408•523•9260 12 C 6/96 APPLICATIONS FAX Americas 408•523•9361 Europe/Africa 44•(0)•1753•622•209 Japan 81•(0)•45•471•3717 Asia/Oceania 408•523•9364

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