Section 4 – Power Transformer Design Power Transformer Design the volt-seconds per turn applied to the windings and is independent of load current. This Section covers the design of power trans- formers used in buck-derived topologies: forward Undesirable Effects of Energy Storage converter, bridge, half-bridge, and full-wave center- Leakage inductance delays the transfer of current tap. Flyback transformers (actually coupled induc- between switches and rectifiers during switching tors) are covered in a later Section. For more spe- transitions. These delays, proportional to load cur- cialized applications, the principles discussed herein rent, are the main cause of regulation and cross regu- will generally apply. lation problems. Reference (R4) included in this manual explains this in detail. Functions of a Transformer Mutual inductance and leakage inductance energy The purpose of a power transformer in Switch- causes voltage spikes during switching transitions Mode Power Supplies is to transfer power efficiently resulting in EMI and damage or destruction of and instantaneously from an external electrical source switches and rectifiers. Protective snubbers and to an external load. In doing so, the transformer also clamps are required. The stored energy then ends up provides important additional capabilities: as loss in the snubbers or clamps. If the loss is exces- • The primary to secondary turns ratio can be es- sive, non-dissipative snubber circuits (more complex) tablished to efficiently accommodate widely dif- must be used in order to reclaim most of this energy. ferent input/output voltage levels. Leakage and mutual inductance energy is some- • Multiple secondaries with different numbers of times put to good use in zero voltage transition (ZVT) turns can be used to achieve multiple outputs at circuits. This requires caution–leakage inductance different voltage levels. energy disappears at light load, and mutual induc- • Separate primary and secondary windings facili- tance energy is often unpredictable, depending on tate high voltage input/output isolation, especially factors like how well the core halves are mated to- important for safety in off-line applications. gether. Energy Storage in a Transformer Ideally, a transformer stores no energy–all energy Losses and Temperature Rise is transferred instantaneously from input to output. In Transformer loss is sometimes limited directly by practice, all transformers do store some undesired the need to achieve a required overall power supply energy: efficiency. More often, transformer losses are limited • Leakage inductance represents energy stored in by a maximum “hot spot” temperature rise at the core the non-magnetic regions between windings, surface inside the center of the windings. Tempera- caused by imperfect flux coupling. In the ture rise (°C) equals thermal resistance (°C/Watt) equivalent electrical circuit, leakage inductance is times power loss (Watts). in series with the windings, and the stored energy ∆T =×R P is proportional to load current squared. T L • Mutual inductance (magnetizing inductance) rep- Ultimately, the appropriate core size for the ap- resents energy stored in the finite permeability of plication is the smallest core that will handle the re- the magnetic core and in small gaps where the quired power with losses that are acceptable in terms core halves come together. In the equivalent cir- of transformer temperature rise or power supply effi- cuit, mutual inductance appears in parallel with ciency. the windings. The energy stored is a function of 4-1 Temperature Rise Limit with high velocity forced air cooling), and while RI In consumer or industrial applications, a trans- shouldn’t be ignored, it usually is not critically im- former temperature rise of 40-50°C may be accept- portant compared with RE. able, resulting in a maximum internal temperature of External RE is mainly a function of air convection 100°C. However, it may be wiser to use the next size across the surface of the transformer–either natural larger core to obtain reduced temperature rise and convection or forced air. RE with natural convection reduced losses for better power supply efficiency. cooling depends greatly upon how the transformer is mounted and impediments to air flow in its vicinity. Losses A transformer mounted on a horizontal surface and Losses are difficult to predict with accuracy. surrounded by tall components, or mounted in a rela- Core loss data from core manufacturers is not always tively small enclosure will have considerably greater dependable, partly because measurements are made RE than if it were mounted on a vertical surface, under sinusoidal drive conditions. Low frequency benefiting from the “chimney effect”. With forced air winding losses are easy to calculate, but high fre- cooling, RE can be driven down to a very small value, quency eddy current losses are difficult to determine depending on air velocity, in which case internal RI accurately, because of the high frequency harmonic becomes the primary concern. With forced air cool- content of the switched rectangular current wave- ing, thermal resistance and temperature rise often be- shape. Section 3 discusses this problem extensively. come irrelevant, because an absolute loss limit to Computer software can greatly ease the difficulty of achieve power supply efficiency goals becomes calculating the winding losses, including high order dominant. harmonics(1). For the average situation with natural convection Thermal Resistance cooling, a crude “rule of thumb” can be used: Temperature rise depends not only upon trans- former losses, but also upon the thermal resistance, 800° C - cm2 / Watt = ° R (°C/Watt), from the external ambient to the central RE C / Watt T A in cm2 hot spot. Thermal resistance is a key parameter, un- S fortunately very difficult to define with a reasonable Where AS is the total surface area of the trans- degree of accuracy. It has two main components: in- former, excluding the mounting surface. Calculating ternal thermal resistance RI between the heat sources AS is time-consuming, but another rule of thumb sim- (core and windings) and the transformer surface, and plifies this, as well. For a given class of cores, such as the external thermal resistance RE from the surface to E-E cores in the ETD or EC series, the relative pro- the external ambient. portions are quite similar for all core sizes. Thus for Internal thermal resistance depends greatly upon all cores in the ETD or EC series, the usable surface the physical construction. It is difficult to quantify area, AS, is approximately 22 times the winding win- because the heat sources are distributed throughout dow area, AW. Combining this with the equation the transformer. RI from surface to internal hot spot is above enables the window area, AW, from the core not relevant because very little heat is actually gener- data sheet, to be used to directly calculate the exter- ated at that point. Most of the heat generated in the nal thermal resistance: core (other than in toroids) is near the transformer 36 surface. Heat generated within the winding is distrib- =° RE 2 C / Watt uted from the surface to the internal core. Although AW in cm copper has very low thermal resistance, electrical in- For pot cores or PQ cores, window areas are pro- sulation and voids raises the RT within the winding. This is a design area where expertise and experience portionately smaller, and not as consistent. AS/AW is very helpful. Fortunately, internal thermal resis- may range from 25 to 50, so that RE may range from 16/AW to 32/AW °C/W. tance is considerably smaller than external RE (except 4-2 Experience is a great help in minimizing and Ferrite cores: In most ferrite materials used in crudely quantifying thermal resistance. In the final SMPS applications, hysteresis losses dominate up to analysis, an operational check should be conducted 200-300kHz. At higher frequencies, eddy current with a thermocouple cemented at the hot spot near the losses take over, because they tend to vary with fre- middle of the centerpost, with the transformer quency squared (for the same flux swing and wave- mounted in a power supply prototype or mockup. shape). Worst Case Losses Thus, at frequencies up to 200-300kHz, worst Transformer losses should be examined under case is at low VIN and full load because of high worst-case conditions that the power supply is ex- winding losses. Once core eddy current losses be- pected to operate over long periods of time, not under come significant, they rise rapidly with frequency, transient conditions. especially at high VIN. (The increase in eddy current Transformer losses can be put into three major loss with high VIN, small D, is not shown in core categories: core hysteresis losses, core eddy current manufacturer’s loss curves because they assume sinu- losses, and winding losses. soidal waveforms.) Winding losses also rise with fre- Core hysteresis losses are a function of flux quency, especially at low VIN. To maintain a reason- swing and frequency. In all buck-derived applications able RAC/RDC, Litz wire with more strands of finer under steady-state conditions, VIN•D = n•VO. Under wire must be used, raising RDC because increased in- fixed frequency operation, volt-seconds and therefore sulation and voids reduce the copper area. Thus, at flux swing are constant. Hysteresis loss is therefore frequencies where core eddy current losses dominate, constant, regardless of changes in VIN or load cur- core loss worst case is at high VIN, full load. Winding rent. loss worst case is always at low VIN, full load.. Core eddy current loss, on the other hand, is Laminated metal alloy and powdered metal really I2R loss in the core material. If VIN doubles, cores: Core eddy current losses dominate, hence Peak I2R loss quadruples, but since D is halved, aver- worst case is at high VIN, full load.