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Power Transformer & Inductor Design

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Power Transformer & InductorDiamondPOWER SUPPLY TRANSFORMER AND INDUCTOR DESIGN BASIC PRINCIPLES, THEORY, CALCULATION Before going over the numbering of magnetic components for switching power supplies, let me just quickly revisit the vital concepts and definitions. Transformer is a passive device which transfers successive (AC) electric energy from one spin into flipside through electromagnetic induction. It consists of a ferromagnetic cadre and two or increasingly coils (windings). Home Tutorial Topologies SMPS diamond Thermal diamond Software PCB diamond Computer PSU UPSSpinTransformers Formulas EE Reference Inverters Generators Solar A waffly current in the primary winding creates an successive magnetic field in the core. The cadre multiplies this field and couples most of the flux through the secondary windings. This in turn induces successive voltage (electromotive force, or emf) in each of the secondary whorl equal to Faraday's law. Power transformer in SMPS is used to transpiration width of high-frequency pulses by the turns ratio and to provide isolation between circuits. Note that a transformer can't transfer a DC component of a pulse: in a steady state mode net volt-seconds wideness any winding should be zero, otherwise the cadre will soon saturate. DC output voltage can be obtained only by using rectifiers. Nevertheless, an stereotype voltage wideness a real coil's terminals can be non-zero due to non-zero wire resistance. This DC offset can be used for lossless sensing of an stereotype current wideness an inductor or a transformer winding with unidirectional current: if you add an RC network parallel to the coil, the voltage wideness the capacitor will be proportional to the coil's stereotype current. For largest thermal stability the wire can be made of low TCR material, such as a copper alloy. MAGNETICS DESIGNING normally involves trade-offs between size, forfeit and power losses. The main constraint in all cases (except for saturable inductors) is that peak magnetic flux density BMAX should not tideway the cadre material's saturation flux value BSAT. Note that in higher frequencies, cadre loss rather than saturation can wilt the main limiting factor for BMAX. The flux transpiration is a function of the unromantic volt-seconds and the cadre geometry. Excessive volt-seconds unromantic to a whorl rationalization cadre saturation. When it happens, the windings are powerfully shorted out.The table unelevated provides the formulas for BMAX in a steady state operation as function of N×Ac product, unromantic voltage and frequency for worldwide voltage waveforms. Contrary to popular misconception, BMAX does not depend on the magnetic material properties or air gaps. It does not depend on the transferred power neither. That's why in theory the cadre size does not depend on the wattage. However, for efficiency and thermal reasons, we have to limit ohmic losses in the wires. That's why magnetics size increases with power. Most textbooks provide formulas for interpretation of the cadre size based on the product of magnetic cross-section zone by the window zone misogynist for the winding. Unfortunately, this method is not very helpful considering these formulas are based on pretty much wrong-headed selection of current density and on the theorizing of a unrepealable window utilization (fill) factor. In reality, depending on the insulation grade and using requirements, current density in the copper can be selected anywhere between 180 and 500 A/sq.cm. The fill factor likewise can be anywhere between 0.1 and 0.5 depending on the whorl construction and insulation. As the result, if you don't have much wits in practical transformer design, you will need to go through several iterations. Function Waveform BMAX, gauss Sine wave Vrms×108/4.44N×Ac×F Square wave Vpk×108/4N×Ac×F Bipolar pulses with D=Ton/T=Ton×F (0<D<0.5) Vpk×D×108/2N×Ac×F Unipolar pulses with passive reset Br+Vpk×Ton×108/N×Ac In these and other equations: V - voltage (volts), N - coil's turns, Ac - core's cross-sectional zone (sq.cm), F- frequency (hertz), Br - remanence (gauss) Here is a quick simplified transformer diamond procedure: Select the ferrite material based on your operating frequency; Find saturation flux BSAT at maximum operating temperature from the datasheet and pick some derating, such as 75% or so. This will be you target maximum flux BMAX; Determine minimum required N×Ac product for the targeted BMAX for the cadre excitation waveform(see the table to the left);Segregatea cadre size by using typical power handling charts or based on similar designs and find its constructive cross-sectional zone "Ac" from the datasheet; Find minimum required primary turns "N" as required N×Ac product divided by "Ac"; Calculate secondary turns for your output voltage based on a DC transfer function of the selected SMPS topology;Segregatewire size based on your primary and secondary currents, operating frequency, and the misogynist window. When you get an very prototype you can measure the hot spot temperature by placing a thermocouple under the whorl and then retread the diamond if necessary. S.A.Mulder proposed an empirical formula for thermal resistance of a wire-wound transformer measured at the hot spot: Rth≈(53...61)×Ve-0.54 oC/watt, where Ve- cadre volume in cubic centimeters [1990 Phillips App Note]. From this, a "rule of thumb" hot-spot temperature rise in Celsius vs. total losses P(watt) is: Trise≈50×P/sqrt(Ve). Note that the whilom thermal relationship as well as most textbook procedures related to the magnetics thermal management are workable to natural convection cooling. For applications with forced airflow or conduction cooling these procedures results in an over-designed part considering of an overstated temperature rise. In general, platonic SMPS transformers need to transfer all energy instantaneously from one winding to flipside while storing no or little energy in the process. Some topologies do need unrepealable value of energy stored in magnetizing inductance for a proper operation. Conversely, a power inductor is used in SMPS as an energy storage device. It accumulates energy in the magnetic field as current flows through it, and then transfers it into flipside spin during the unorganized part of the switching cycle. In power supplies, the inductors are moreover used for filtering out upper frequency currents (in which specimen they are often tabbed chokes). In power inductors the current rather voltage is controlled. For such "current-driven" coils: B=L×Ipk×108/N×Ac, where L - inductance (in henry), Ipk - peak current in amps, B - flux in gauss. All units and formulas in this page are given in CGS (see CGS to SI unit converter). Once you set BMAX and segregate a cadre size, you can find from the whilom equation the number of turns for the desired inductance L: N=L×Ipk×108/BMAX×Ac. Note that "L" is not constant. If the current keeps increasing, at some point BMAX will be unescapable BSAT and "L" will start dropping. To prevent the magnetic material saturation at a required current, an air gap can be introduced. The length of a net discrete gap: lg≈0.4×π×N×Ipk/BMAX. In practice, the gap may need to be selected slightly larger than the calculated value due to flux fringing. Combining the whilom equations for N and lg yields: lg≈0.4×π×L×Ipk2/(BMAX×Ac). The gap is used not only in inductors. It is moreover often introduced in transformers to increase working flux swing in single-ended topologies, to store increasingly energy in magnetizing inductance, and to stabilize the inductance value. For powder metal materials with a distributed gap and soft saturation curve, the numbering process may take several iterations. In short, you can first pick a powder cadre based on desired L×Ipk2 by using manufacturer's charts. Then determine the turns , where AL - specific inductance in mH/1000 turns (which is nH/turn) from the core's data sheet. Then find peak bias H=0.4×π×N×Ipk/le (Oersted), determine the roll-off in percentage of initial permeability, and correct the turns for the desired L.Unelevatedyou will find increasingly magnetics theory, transformer and inductor diamond information, tutorials, tools and various downloads. FREE INDUCTOR AND POWER TRANSFORMER DESIGN SOFTWARE Transformer turns and wire calculator (includes skin effect) Transformer numbering for various switching regulator topologies Software to diamond electrical inductors with powder cores by Magnetics® Inc. Current transformer diamond software Ferrite magnetic numbering tool (includes skin and proximity effects)Cadreloss calculator for non-sinusoidal waveforms UNITRODE SEMINAR MAGNETICS HANDBOOK (MAG 100A) Introduction and magnetics nuts (design for switching power supplies) Magnetic cadre characteristics Windings data and skin effect Power supply transformer diamond Inductor and flyback transformer diamond Magnetic cadre properties Eddy current losses in transformer windings The effect of leakage inductance Coupled filter inductors MAGNETISM PRINCIPLES, EQUATIONS, TUTORIALS Designing transformers for upper frequency dc-dc converters - pdf downloadCadreselection for flyback and forward converters SMPS transformer diamond procedure and equations Inductor diamond procedure Planar power transformers nuts and diamond guide Electrical transformer: how it works and physical principles- an intoduction for beginners Disclaimer, Disclosure and Terms of Use | Contact Us | About Us | Privacy ©2004-2017 Lazar Rozenblat