One Powerful Decade: Keep Core Geometry in Mind When Designing Transformers

Jul 1, 2010 12:00 PM
Charles R. Wild, PE, API Delevan, East Aurora, New York

News & Features From Auto Electronics

Committed to improving hybrid electric cars

New Motors for Hybrid Vehicles

Battery Firms Battle for Hybrid Hegemony

Innovative Bipolar Plates for Fuel Cells

See More Headlines

PET Resources

Buyer's Guide

Conferences

Engineering Jobs

Power Electronics Events

Rent Our Lists

Spotlight on Digital Power

REFERENCES

W. T. McLyman, Transformer and Inductor Design Handbook, 2nd ed. New York; Marcel Dekker, 1988.
E. C. Snelling, Soft Ferrites Properties and Applications, 2nd ed. London,U.K.:Butterworths,1988.
Magnetics Ferrites 2000 Catalog.
N. R. Grossner, Transformers forElectronic Circuits, New York; McGraw Hill, 1967.
R. Lee, Electronic Transformers and Circuits, 3rd ed., New York; John Wiley & Sons, 1988.
J. K. Watson, Applications of Magnetism, Gainesville, FL, Published by the author, 1985.
W. M. Flanagan, Handbook of Transformer Design & Applications, 2nd ed., New York, McGraw Hill, 1993.
A. I. Pressman, Switching and Linear Power Supply, Power Converter Design, Rochelle Park, Hayden Book Company, 1977.

TABLE 2. USING MCLYMAN'S AREA PRODUCT AP APPROACH, RESULTS IN THE BELOW DESIGNS
	POT CORE	E CORE	TOROID	ETD CORE
Output power Po = (Vo + Vd)Io	35.75W	35.75W	35.75W	35.75W
Total power Pt= Po[(20.5/η) + 20.5]	101.8W	101.8W	101.8W	101.8W
Area product Ap= [(Pt×104)/(KfBmfKuKj)]x K= Waveform coefficient Kf= 4 for square waves, = 4.44 for sine waves Ku= Window utilization factor, or the fraction of available space occupied by the winding. Typical values: Ku= 0.25 for toroids, otherwise = 0.4	0.283 cm4	0.366 cm4	0.560 cm4	0.366 cm4
From catalog choose core with closest Ap to calculated value	0.392 cm4	0.421 cm4	0.707 cm4	0.421 cm4
From vendor information, choose appropriate bobbin or coil form (if necessary) and read the actual Mean Length Turn (MLT)	3.76 cm	4.54 cm	2.58 cm	4.09 cm
Actual core area, Ac. Also available from vendor information	0.931 cm2	0.401 cm2	0.374 cm2	0.401 cm2
Actual window area, Wa. Also available from vendor information	0.421 cm2	1.05 cm2	1.89 cm2	1.05 cm2
Actual weight of core, Wtfe. Also available from vendor information	20 grams	15 grams	11.6 grams	15 grams
Approximate transformer surface area At= KsAp0.5	21 cm2	27 cm2	21 cm2	27 cm2
Number of primary turns Np = (Vin ×104)/(KfBmfAc)	16	37	40	37
Primary, input current Ip= Po/(Vinη)	1.45A	1.45A	1.45A	1.45A
Current density allowed for 25°C rise J = KjApy	536 A/cm2	413 A/cm2	432 A/cm2	413 A/cm2
Primary wire area Aw= (0.707Ip)/J (In center tap configuration, Ip is multiplied by 0.707)	0.0019 cm2	0.0025 cm2	0.0024 cm2	0.0025 cm2
Primary wire size from wire table	#24 AWG	#22 AWG	#23 AWG	#22 AWG
Primary Winding Resistance Rp = (MTL)(Np)(µΩ/cm)×10-6	0.0506Ω	0.0895Ω	0.0684Ω	0.0806Ω
Primary copper losses Pp= Ip2Rp	0.106W	0.188W	0.143W	0.169W
Number of secondary turns Ns= (NpVs)/Vp	16	37	40	37
Secondary wire area using output current and allowable current density	0.0018 cm2	0.0024 cm2	0.0023 cm2	0.0025 cm2
Secondary wire size (from wire table)	#24	#22	#23	#22
Secondary winding resistance Rs= (MTL)(Ns)(µΩ/cm)×10-6	0.0506W	0.0895W	0.0684W	0.0806W
Secondary copper losses Ps= Is2Rs	0.096W	0.169W	0.129W	0.152W
Total copper loss Pcu= Pp+Ps	0.202W	0.357W	0.272W	0.321W
Allowable core lossPfe= (Po/η-Po)-Pcu	0.251W	0.096W	0.180W	0.131W