Power-transformer design is the biggest stumbling block in developing switching power supplies. Even more intimidating is developing flyback power supplies, because designers don't use flyback transformers like normal transformers. Energy stores in the core, and the core must be gapped. Current flows in either the primary or secondary winding but never in both windings simultaneously.

Designers use the flyback topology because flyback power supplies require the fewest components. At lower power levels, total component cost is less than with other techniques. However, between 75 and 100W, increasing voltage and current stresses cause flyback-component cost to increase significantly. At these high power levels, topologies with lower voltage- and current-stress levels (such as the forward converter) are 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 less than 10 minutes for a transformer that usually works the first time. This method, which works for both continuous- and discontinuous-mode designs, has three distinct steps:

• Identify and estimate the set of independent variables that depend on the application, transformer core, and TOPSwitch.
• Identify and calculate dependent parameters.
• Iterate specified independent variables until specified dependent parameters fall within defined limits for a practical flyback transformer.

An Excel spreadsheet (Table 1) automates the transformer design method this article details. Depending on the application, the table lists independent variables, beginning with output power and ending at the input filter capacitor. Transformer-core and construction variables are the next listings. Depending on the TOPSwitch (or other PWM circuit), variables include switching frequency, duty cycle, peak primary current, and MOSFET voltage drop.

For a given application and transformer core, calculate or estimate 19 of 22 variables, which will remain fixed during iteration. Only three variables, number of secondary turns, N_S, peak primary current, I_P, and number of primary winding layers, L, will change during the iteration process. Dependent parameters (also in the table) divide into four groups: dc-input voltage, primary-current waveform shape, transformer design, and voltage stress.

During iteration, only four of the 23 dependent parameters are compared to limits. Check primary-ripple to peak-current ratio, K_RP, maximum flux density, B_M, gap length, L_G, and primary current capacity, CMA, with each iteration until all four parameters are within specified limits. The remaining 19 dependent parameters are either intermediate calculations or parameters the manufacturer uses for construction. You need to gain an understanding of the shape of the primary and secondary current waveforms in both continuous and discontinuous operation before beginning transformer design.

Fig 1 shows a typical flyback power supply using the PWR-TOP202 TOPSwitch from Power Integrations Inc (Mountain View, CA, (415) 960-3572). The TOPSwitch combines an integrated high-voltage MOSFET switch with a complete switching power-supply controller and protection circuitry in a single device. In the figure, the power-supply circuit operates from 85 to 265V ac and delivers 15W at 7.5V output. BR1 and C1 (C_IN) rectify and filter ac power to create the high dc voltage applied to the primary winding of T1. The high-voltage MOSFET Q1 within the TOPSwitch drives the other side of the transformer primary. D1 and VR1 clamp voltage spikes that transformer leakage inductance causes. D2, C2, L1, and C3 rectify and filter the power secondary.

D3 and C4, which rectify and filter the bias winding, provide the TOPSwitch bias voltage. EMI-filter components L2, C6, C7, and C8 reduce conducted-emission currents. Bypass-capacitor C5 filters internal MOSFET-gate charge-current spikes and 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 control the duty cycle and output voltage directly. Together with VR2 series impedances and the TOPSwitch, R1 determines the control-loop dc gain. R2 and VR2 provide a slight preload to improve regulation at light loads.

Figs 2a and b show typical voltage and current waveforms taken from the same power supply, delivering 15W from 110V-ac input voltage but with different flyback-transformer primary inductances. Q1 turns on and effectively applies 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 Q1 on time (t_ON).

Peak primary current, I_P, is the final value that occurs as Q1 turns off. Energy proportional to the square of peak current, I_P, stores 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 Q1 is on, output-diode D2 and bias-diode D3 reverse-bias and prevent secondary current flow. When Q1 turns off, the decreasing magnetic field induces an abrupt voltage reversal on all transformer windings, such that the dot side is now at a higher potential than the no-dot side.

Diodes 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. The MOSFET 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, D, is defined as the ratio of Q1 on time, t_ON, to the switching period, T. You can also calculate D from t_ON and switching frequency f_s as shown:

Fig 2a shows MOSFET and diode triangular-current waveforms, which define "discontinuous" mode of operation resulting from low primary inductance. The secondary current linearly decreases to zero before MOSFET Q1 turns on again. The stored energy is completely delivered to the load. The MOSFET drain voltage, V_DRAIN, relaxes and rings back toward the dc bus voltage when no current is flowing in either primary or secondary.

Fig 2b shows trapezoidal current waveforms, which define "continuous" mode of operation resulting from high primary inductance. Secondary current is still flowing when MOSFET Q1 turns on at the beginning of the next cycle. The stored energy isn't completely delivered to the load. Energy (and nonzero magnetic field) remains in the core when MOSFET Q1 turns on again, causing the initial step in MOSFET current. Note that MOSFET drain voltage, V_DRAIN, stays at a high value equal to the sum of the dc input voltage, V_DC, and reflected output voltage, V_OR, until Q1 turns on again.

Current never flows in the primary and secondary winding simultaneously; neither primary nor 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 inductor current continuity defines continuous and discontinuous modes.)

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 prevent transformer saturation; it must also be below the TOPSwitch peak current limit. I_AVG is the average or dc primary current as well as the input current, which is proportional to output power. I_RMS produces power losses due to winding resistance and MOSFET RDS_ON. The ratio, K_RP, of ripple, I_R, to peak current, I_P, defines the continuous waveform. K_RP also simplifies subsequent calculations, such as I_RMS.

Transformers designed for discontinuous operation have a higher peak current and a ripple-to-peak current ratio, K_RP, equal to 1. Practical continuous designs have lower peak currents and a ripple-to-peak current ratio, K_RP, less than 1, but typically greater than 0.33. K_RP is inversely proportional to primary inductance, so a continuous design will have a higher inductance. Continuous-transformer designs have a practical primary-inductance upper limit between five and six times that of a discontinuous design at the same input voltage and output power, which is a result of the difference in peak currents and K_RP ratios.

The primary-current waveforms in Fig 2a and b deliver the same output power and, therefore, must have equal I_AVG current. The discontinuous current waveform has a higher peak value and thus must have a higher rms current value. Discontinuous mode requires less inductance and reduces transformer size but, due to higher rms currents, operates with higher losses and lower efficiency. Continuous mode requires higher inductance and larger transformers but offers improved efficiency and lower power losses. The tradeoff between transformer size and power-supply efficiency depends on the packaging and thermal environment in each application.

Most designers avoid the continuous mode because the feedback control loop is more difficult to analyze. Discontinuous-mode power supplies can be modeled with a single pole response and are simple to stabilize. In continuous mode, a right half-plane zero and complex pole pair that all shift with duty cycle make analysis difficult. Stabilizing the continuous system is quite straightforward with adequate phase margins over all line and load combinations. You can limit right half-plane zero and complex-pole-pair migration with duty cycle by designing for a maximum duty cycle of 50% at low line and heavy load. Improve phase margins by taking into account the effective power path series resistance and capacitor equivalent series resistance. Crossover bandwidths up to 1 kHz are easy to achieve with phase margins of at least 45°.

Before beginning design work, spend time considering transformer-core, winding, and safety issues. 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, which is especially true in ac-mains adapter power supplies that are normally packaged in sealed plastic boxes. Applications allowing at least 0.75 in. 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 applications requiring multiple outputs. When space is not a problem, ETD cores are useful in higher power designs. PQ cores are more expensive but take up slightly less pc-board space and require fewer turns than E cores. Safety isolation requirements make pot cores, RM cores, and toroids generally unsuitable 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 an intended market. For example, information-technology equipment must meet the requirements of IEC950 in Europe and UL1950 in North America. These documents specify distances for creepage and clearance as well as insulation systems used in transformer construction. A 5-mm creepage distance is usually sufficient between primary and secondary (check with appropriate agency and specification). Isolation is usually specified by electric strength and is tested with a voltage of typically 3000V ac applied for 60 sec. Two layers of insulation (basic and supplementary) are appropriate between primary and secondary if each layer exceeds the electric-strength requirement. Use three layers of insulation (reinforced) if all combinations of two layers (out of three total) meet the electric-strength requirement.

Fig 3a 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, or 100 mils in this example). To maintain transformer coupling and reduce leakage inductance, cores and bobbins should be large enough that the actual winding width is at least twice the total creepage distance. 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, separate the primary layers by at least one layer of UL-listed polyester film tape (3m 1298) cut to fit between the margins. Varnish or epoxy impregnation can also improve layer-to-layer insulation and electric strength but do not reduce capacitance. The bias winding then winds over the primary.

Supplementary or reinforced insulation consisting of two or three layers of UL-rated polyester film tape cut to the full width of the bobbin then wraps over the primary and bias windings. Margins are wound again. The secondary winding is wound between the margins. To secure the windings, add another two or three layers of tape. To meet creepage-distance requirements at lead exits, you may need to use insulation sleeving over the leads of one or all windings. To meet safety-agency requirements, use nylon or Teflon sleeving with a minimum wall thickness of 0.41 mm (16 mils). 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 the distance from primary winding (or lead exits) to the core, and the distance from the core to the secondary (or lead exits) must be equal to or greater than required creepage distance.

Figs 3a and b, respectively, show Z and C winding techniques for multiple primary layers. To reduce EMI (common-mode conducted emission currents), the dot side, which connects to the MOSFET, is buried under the second layer for self-shielding. Z winding decreases transformer capacitance, decreases ac MOSFET losses, and improves efficiency but is more difficult and costly to wind. C winding is easier to use and costs less-but at the expense of higher loss and lower efficiency.

Fig 3c shows a new technique using double- or triple-insulated wire on the secondary to eliminate the need for margins . In double-insulated wire, each layer usually meets safety-agency electric-strength requirements. In triple-insulated wire, all three two-layer combinations taken together must meet the electric-strength requirement. Take special care to prevent insulation damage during winding and soldering. This technique reduces transformer size and eliminates the labor cost of adding margins, but it incurs higher material cost and may increase winding costs. The primary winding is wound over the full width of the bobbin flange. If desired, the bias winding can be wound over the primary. To prevent insulated-wire abrasion, use one layer of tape between primary or bias and secondary. The double- or triple-insulated wire is then wound. Add another layer of tape to secure insulated winding.

Fig 3c also shows an alternate position for the bias winding wound directly over the secondary, which improves coupling to the secondary winding and reduces leakage inductance (it im-proves 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.

To begin a flyback-transformer design, you need to specify three groups of independent variables.

Application variables:

Derive output power, P_O, output voltage, V_O, bias voltage, V_B, ac mains frequency, f_L, and minimum and maximum ac mains voltage, V_ACMIN and V_ACMAX, respectively, directly from specifications for each application.

Output-rectifier forward-voltage drop, V_D, depends on output voltage. For output voltages lower than 7.5V, use a Schottky diode (V_D is typically 0.4V). For higher output voltage, use of an ultrafast-recovery PN junction diode is normal, and V_D is typically 0.7V. Bias-winding-diode forward-voltage drop (V_DB) is also typically 0.7V.

For efficiency (n), start with an estimate based on measurements in similar power supplies or use a value of 0.8 if data is unavailable. For input-filter-capacitor C_IN, start with a standard value in microfarads, from two to three times the output power (in watts). For example, 30 to 45 µF is a suitable capacitance range for a 15W supply. A capacitance of 33 µF is the lowest standard value within the range. For bridge-rectifier conduction time, t_C, 2 msec is typical (measure on a similar power supply or set equal to 0 for a conservative first design).

Transformer-core/construction variables:

The following effective parameters are specified by the core and bobbin manufacturer in data sheets: cross-sectional area, A_E (cm2), path length, L_E (CM), ungapped inductance, A_L (specified in either millihenries/(1000 turns)2 or nanohenries/turns2), and physical bobbin-winding width, B_W. Margin-width M, which is determined by the insulation methods and regulatory requirements detailed above, is usually either 0.10 in. or set to 0.

For number of layers, L, one or two layers of primary winding are usually sufficient when switching at 100 kHz or above. Higher layer numbers reduce coupling and increase cost, capacitance, and leakage inductance. Number of secondary turns, N_S, is a key iteration variable. For N_S, one turn per volt of output voltage is a good value with which to begin (for example, start with five turns for a 5V output).

PWM variables:

Switching frequency, f_s, is fixed at 100 kHz for the TOPSwitch. For maximum-duty-cycle D, most flyback power supplies specify a value of 0.5 at the minimum dc input voltage where full-load voltage regulation is required. Under some conditions, for a given TOPSwitch, a higher duty cycle may increase the power level or reduce losses and voltage stress on the output diode. The benefits of higher-duty-cycle operation come at the expense of an increased number of primary turns, as well as higher MOSFET voltage stress and power dissipation.

Primary peak current, I_P, is the other key iteration variable that directly determines current-waveform shape and primary inductance. For universal (85 to 265V-ac) or 100 to 120V-ac input voltage, 50 mA/W of output power is a good starting point for I_P (for example, start with peak current of 500 mA for a 10W output). For 230V-ac input voltage, 25 mA/W of output power is appropriate for peak current, I_P. V_DS is the on-state MOSFET voltage taken from the TOPSwitch or MOSFET data sheet at the specified value for I_P.

Now you can calculate the four groups of dependent parameters.

DC-input-voltage parameters:

Maximum dc input voltage is simply the peak value of the highest ac input voltage, VAC_MAX, expected in the application. Operation from 265V-ac input results in a maximum dc bus voltage, V_MAX, of 375V dc.

Minimum dc input voltage, V_MIN, depends on the ac input voltage, bridge rectifier, and energy-storage capacitor. Fig 4 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 the line frequency. C_IN must supply the entire average primary current during the discharge time between the peaks of the ac input voltage. Derive minimum dc voltage, V_MIN, from the following equation, where P_O is the power-supply output power, n 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 a 60-Hz, 85V-ac input voltage, 0.8 efficiency, 15W output power, 33-µF input filter capacitance, and 2-msec estimated conduction time, V_MIN is 85V dc.

Current-waveform-shape parameters:

Calculate average current from effective primary voltage (the difference between minimum dc input voltage, V_MIN, and drain-source voltage V_DS), output power, P_O, and efficiency, n:

Calculate ripple current from average current, I_AVG, peak primary current, I_P, and maximum duty cycle, D:

Note that ripple-to-peak-current ratio, K_RP, is an important dependent variable to watch during iteration. Peak primary current, I_P, varies to keep K_RP within the limits of 0.33 (heavy continuous) to 1.0 (discontinuous).

Calculate rms current, I_RMS, from maximum duty cycle, D, peak primary current, I_P, and ripple-to-peak ratio, K_RP. You can also calculate I_RMS directly from D, I_PK, and ripple-current I_R.

Primary inductance (in microhenries) is a simple function of ripple current, I_R, effective primary voltage, duty-cycle D, and switching frequency, f_S

The number of primary turns depends on the number of secondary turns, N_S, output voltage, V_O, diode forward-voltage drop, V_D, minimum dc input voltage, V_MIN, the MOSFET, V_DS, and duty cycle, D:

A_LG is the effective inductance for the gapped core in nanohenries/turns2. 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. Also, use A_LG to simplify subsequent calculations. Calculate A_LG from primary inductance, L_P (in µH), and number of primary turns, N_S.

Calculate relative permeability, µ_r, of the ungapped core to estimate the gap length, L_G. Find µ_r from core parameters A_E (cm), L_E (cm), and ungapped-effective-inductance A_L

Effective bobbin width, B_WE, takes into account physical bobbin width, B_W, margins M, and number of layers, L:

Find primary wire diameter, DIA (in mils), from effective bobbin width, B_WE, and number of primary turns, N_P

Maximum flux density, B_M, is a dependent iteration variable to be manipulated between the limits of 2000 and 2500 gauss by varying the number of secondary turns, N_S, which directly varies number of primary turns, N_P, as shown previously. Calculate B_M from peak current, I_P, number of primary turns, N_P, effective gapped inductance, A_LG, and effective core cross-sectional area, A_E. You can also calculate B_M from effective dc input voltage (V_MIN-V_DS), output voltage, V_O, output diode voltage, V_D, and duty cycle, D:

B_AC is the ac-flux density component. The equation gives peak ac-flux density (rather than p-p) to use with core loss curves, which the core vendor provides. Calculate B_AC from maximum flux density, B_M, and ripple-to-peak-current ratio, K_RP. You can also calculate B_AC from effective primary voltage, duty cycle, frequency, effective core cross-sectional area, and number of primary turns, N_S

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 2 mils on L_G. Calculate L_G from the number of primary turns, N_P, core-effective cross-sectional-area, A_E, primary inductance, L_P (in microhenries), core effective path length, L_E, and relative permeability, µ_r:

Magnet wire for transformer winding usually has the cross-sectional area specified in circular mils. Circular mils per amp (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. Calculate CMA, which should range from 200 to 500, from wire diameter DIA (mils) and rms primary current, I_RMS.

You've now completed all calculations necessary for the primary winding. Now you must calculate secondary rms current, secondary minimum and maximum conductor diameter, and number of bias winding turns. Derive secondary rms current, I_SRMS, from duty cycle, D, primary peak current, I_P, primary and secondary turns, N_P and N_S, and ripple-to-peak-current ratio, K_RP (same for primary and secondary):

Determine minimum secondary conductor diameter, DIA_SEC (in mils), based on previously calculated current capacity, CMA, and secondary rms current.

Calculate the maximum wire outside diameter, OD_SEC (in mils), for a single layer based on number of secondary turns and bobbin width:

For magnet-wire secondaries, the minimum conductor diameter, DIA_SEC, should be less than the maximum outside diameter, OD_SEC. Use larger magnet wire with a diameter equal to OD_SEC. For insulated wire secondaries, specify a conductor diameter width equal to or greater than DIA_SEC and an insulated outside diameter less than or equal to OD_SEC. Parallel combinations of wire with half the diameter may be easier to wind and terminate. Finally, calculate the number of bias-winding turns, N_B, from the output voltage, V_O, output diode voltage, V_D, primary and secondary number of turns, N_P and N_S, respectively, target bias voltage, V_B, and bias diode voltage, V_BD

To reduce the number of wire gauges necessary in production, the bias winding is usually wound with the same wire diameter as the primary. You can also use this equation to specify other windings for multiple-output-voltage applications.

Reflected output voltage, V_OR, is the voltage appearing across the primary when the transistor is off and current flows through the output diode. V_OR depends directly on output voltage, V_O, diode voltage, V_D, and transformer primary and secondary number of turns, N_P and N_S, respectively. Calculate V_OR from duty cycle, D, minimum dc input voltage, V_MIN, and MOSFET on-state voltage, V_DS.

Maximum drain voltage (excluding leakage-inductance-induced spikes) is simply the sum of maximum dc input voltage, V_MAX, and reflected output voltage, V_OR

Determine maximum peak inverse voltage, V_PIV, for the output rectifier by transformer primary and secondary numbers of turns, N_P and N_S, respectively, maximum dc input voltage, V_DC, and output voltage, V_O. Calculate V_PIV from minimum dc input voltage, V_MIN, MOSFET on-state voltage, V_DS, output diode voltage, V_D, and duty cycle, D:

Before beginning iteration, check the V_DRAIN voltage and compare with the TOPSwitch-breakdown-voltage rating. TOPS100 series parts should have at least 50V of margin, and TOPS200 series parts should have at least 100V of margin for clamping leading-edge spike voltages that leakage inductance causes. Reduce duty cycle, D, minimum ac input voltage, V_ACMIN, or input capacitor, C_IN, to reduce stress voltage, V_DRAIN.

Use iteration to reach a final and acceptable solution for the flyback-transformer design. Iterate peak current, I_P, until the ripple-to-peak ratio, K_RP, is within indicated limits. K_RP should be 1.0 for discontinuous operation and small transformer size, 0.33 for heavy continuous design and best efficiency, or approximately 0.66 for a good trade-off between the two. K_RP will decrease as peak current, I_P, is reduced.

Iterate number of secondary turns, N_S, until maximum flux density, B_M, falls between indicated limits. Check that the gap length, L_G, is higher than indicated minimum value. B_M will decrease and L_G will increase as the number of secondary turns, N_S, increases.

Examine primary current capacity in 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 and perform new iteration. If CMA is greater than 500, consider using the next smaller core or reducing the number of primary layers.

You've now completed the transformer design. The transformer manufacturer will need 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 electrical-strength and creepage-distance specifications
• Primary inductance, L_P
• Number of turns (N_P, N_S, and N_B) for each winding
• Bobbin pin connections
• Winding-layer placement and winding instructions
• Temperature class of operation (class A, 105øC; class B, 130øC, etc)

Insulated Wire Sources:

Rubudue Wire Co
5150 E LaPalma Ave, Suite 108
Anaheim Hills, CA 92807
(714) 693-5512
fax (714) 693-5515

Fukurawa Electric America Inc
200 Westpark Dr, Suite 190
Peachtree City, GA 30269
(404) 487-1234
fax (404) 487-9910

Brooks R Leman is a senior applications engineer at Power Integrations Inc (Mountain View, CA), where he has worked for six years. He develops low-cost flyback and PFC circuits using highly integrated power-supply devices. Leman has a BSEE and an MSEE from Santa Clara University (Santa Clara, CA) and is a member of the Tau Beta Pi professional society. His hobbies include soccer and skiing.

1. McLyman, C. Transformer and Inductor Design Handbook, Marcel Dekker Inc, 1978.