## Core Database Basic Transformer Design Tool

Interactive core database (spreadsheet-based) key to a single pass tramsformer design procedure. User enters input specifications from converter design requirements. Type of conductor for windings (round wire, Leitz wire, or rectangular wire or foil) must be made so that copper fill factor kcu is known. Spreadsheet calculates capability of all cores in database and displays smallest size core of each type that meets V- I specification. Also can be designed to calculate (and display as desired)...

## Core Material Performance Factor

Volt-amp (V-A) rating of transformers proportional to f Bac Core materials have different allowable values of Bac at a specific frequency. Bac limted by allowable Pmsp. Most desirable material is one with largest Bac. Choosing best material aided by defining an emperical performance factor PF f Bac. Plots of PF versus frequency for a specified value of Pmsp permit rapid selection of best material for an application. Plot of PF versus frequency at Pmsp 100 mW cm3 for several different ferrites...

## Design of Magnetic Components

Robbins Dept. of Electrical and Computer Engineering University of Minnesota A. Inductor Transformer Design Relationships B. Magnetic Cores and Materials C. Power Dissipation in Copper Windings E. Analysis of Specific Inductor Design G. Analysis of Specific Transformer Design J. Transformer Leakage Inductance K. Transformer Design Procedures

## Details of Interactive Transformer Core Database Calculations

User inputs Vpri, Ipri, turns ratio Ndc Nsec, f, Ts, Ta, and kcu Stored information (static, independent of converter requirements) Core dimensions, Aw, Acore, Vc, Vw, surface area, mean turn length, mean magnetic path length, etc. Quantitative core loss formulas for all materials of interest including approximate temperature dependence. 1. Compute converter-required stored energy value S 2 Vpri Ipri 2. Compute allowable specific power dissipation Psp Ts - Ta R0sa Vc + Vw . R0sa h As or...

## Eddy Currents Increase Winding Losses

AC currents in conductors generate ac magnetic fields which in turn generate eddy currents that cause a nonuniform current density in the conductor . Effective resistance of conductor increased over dc value. dimensions greater than a skin depth. w 2p f, f frequency of ac current m magnetic permeability of conductor m mo for nonmagnetic conductors. s conductivity of conductor material. Numerical example using copper at 100 C Mnimize eddy currents using Leitz wire bundle. Each conductor in...

## Hysteresis Loss in Magnetic Materials

Area encompassed by hysteresis loop equals work done on material during one cycle of applied ac magnetic field. Area times frequency equals power dissipated per unit volume. Typical waveforms of flux density, B(t) versus time, in an inductor. Only Bac contributes to hysteresis loss.

## Inductor Design Example

Peak current 5.6 A, sinewave current, Irms 4 A Stored energy L I Irms (3x1Q-4)(5.6)(4) High frequency operation dictates ferrite material. 3F3 material has highest performance factor PF at 100 kHz. Double-E core chosen for core shape. Double-E core with a 1 cm meets requirements. kcu Jrms B Aw Acore * 0 0125 0 0068 for kcu > 0.3 Database output R0 9.8 C W and Psp 237 mW cm3 Core flux density B 170 mT from database. No Idc, Bpeak 170 mT. Litz wire used, so 0.3. 6 A mm Acu (4 A) (6 A mm2) Q.67...

## Iterative Inductor Design Procedure

Iterative design procedure essentially consists of constructing the core database until a suitable core is found. Choose core material and shape and conductor type as usual. Use stored energy relation to find an initial area product AwAc and thus an Use initial values of Jrms 2-4 A mm2 Use initial core size estimate (value of a in double-E core example) to find corrected values of Jrms and Bac and thus corrected value Compare kcu Jrms B Aw Acore with L I Irms and iterate as needed into proper

## Iterative Transformer Design Procedure

Iterative design procedure essentially consists of constructing the core database until a suitable core is found. Choose core material and shape and conductor type as usual. Use V - I rating to find an initial area product AwAc and thus an initial core size. Use initial values of Jrms 2-4 A mmz Use initial core size estimate (value of a in double-E core example) to find corrected values of Jrms and Bac and thus corrected 2 Vpri Ipri and iterate as needed into proper size is found.

## Magnetic Component Design Problem

Challenge - conversion of component operating specs in converter circuit into component design parameters. Goal - simple, easy-to-use procedure that produces component design specs that result in an acceptable design having a minimum size, weight, and cost. Inductor electrical (e.g.converter circuit) Inductor currents rated peak current I, rated rms current Irms , and rated dc current (if any) Idc Allowable power dissipation in inductor or equivalently maximum surface temperature of the...

## Optimization of Solid Conductor Windings

Locus of minimum total loss 1.5 dc loss Locus of minimum total loss 1.5 dc loss Nomalized power dissipation p' FRRdc Conductor height diameter F copper layer factor F b bo for rectangular conductors F d do for round conductors h effective conductor height Transformer leakage inductance causes overvoltages across power switches at turn-off. Leakage inductance caused by magnetic flux which does not completely link primary and secondary windings. Direction and relative magnitude of leakage...

## Quantitative Description of Core Losses

Eddy current loss plus hysteresis loss core loss. Empirical equation - Pmsp k fa Bac f frequency of applied field. Bac base-to-peak value of applied ac field. k, a, and d are constants which vary from material to material Pm,sp 15x10-6 f13 Bacl2'5 mW cm3 for 3F3 ferrite. (f in kHz and B in mT) Pm,sp 3.2x10-6 f18 Bacl2 mW cm3 METGLAS 2705M (f in kHz and B in mT) Example 3F3 ferrite with f 100 kHz and Bac 100 mT, Pm,sp 60

## Review of Inductor Fundamentals

No core losses or copper winding losses Linearized B-H curve for core with mm > > mo lm > > g and A > > g2 Magnetic circuit approximations (flux uniform over core cross-section, no fringing flux) Hm lm + Hg g N I (Ampere's Law) Bm A Bg A f (Continuity of flux mm Hm Bm (linearized B-H curve)

## Setting DoubleE Core Airgap Length

Set total airgap length Lg so that Bpeak generated at the peak current Ipeak- Lg Ng g Ng number of distributed gaps each of length g. Distributed gaps used to minimize amount of flux fringing into winding and thus causing additional eddy current losses. m,core ' ,xm,gap m,gap - Ag For a double-E core, Ag (a + Tp ) (d + rp ) Ng Ng Ag ad + (a + d) Ng Ng < < a Insertion of expression for Ag(Lg) into expression for Lg(Ag) and solving for Lg yields Above expression for Lg only valid for double-E...

## Simple Nonoptimal Inductor Design Method

Assemble design inputs and compute required LI Ir No Check power dissipation yes and surface temperature. Excessive . No Check power dissipation yes and surface temperature. Excessive . Choose core geometry and core material based on considerations discussed previously. Assume Jrms 2-4 A mm2 and Bac 50-100 mT and use LI Us kcu Jrms Bac Aw Acore to find the required area product Aw Acore and thus the core size. Assumed values of Jrmsand B based on experience. Complete design of inductor as...

## Stored Energy Relation Basis of Inductor Design

Input specifications for inductor design Rated dc current (if any) Idc. Maximum inductor surface temperature Ts and maximum ambient temperature T Design procedure starting point - stored energy relation Selection of core geometric shape and size Winding conductor geometric shape and size Equation relates input specifications (left-hand side) to needed core and winding parameters (right-hand side) A good design procedure will consists of a systematic, single-pass method of selecting kcu, Jrms,...

## Transformer Design Example cont

Three secondary sections requires four primary sections. Two outer primary sections would have 24 6 4 turns each and the inner two sections would have 24 3 8 turns each. Need to determine number of turns per layer and hence number of layers per section. Use four turns per layer. Two interior primary sections have two layers and optimum value of f. Two outer sections have one layer each and f not optimum, but only results in slight increase in loss (4px10-9)(24)2(8)(0.7)(1) (3)(6)2(2)...

## Analysis of a Specific Inductor Design

Maximum current 4 ams rms at 100 kHz Double-E core with a 1 cm using 3F3 ferrite. Distributed air-gap with four gaps, two in series in each leg total gap length Sg 3 mm. Winding - 66 turns of Leitz wire with Acu 0.64 mm2 Inductor surface black with emissivity 0.9 Find inductance L, Ts max effect of a 25 overcurrent on Ts Power dissipation in winding, Pw Vw kcu pcu (Jrms)2 3.2 Watts Vw 12.3 cm3 (table of core characteristics) pcu at 100 C (approx. max. Ts) 2.2x10-8 ohm-m Jrms 4 (.64) 6.25 A mm2...

## Review of Transformer Fundamentals

Assumptions same as for inductor Starting equations H1Lm Nil H2Lm N2 Ampere's Law HmLm H1 - H2 Lm N1I1- N2I2 MmHm Bm linearized B-H curve Faraday's Law Net flux f f 1 - f2 MmHmA Results assuming pm i.e. ideal core Cross-sectional l m mean path ng area of core A Cross-sectional l m mean path ng area of core A

## Proximity Effect Further Increases Winding Losses

Proximity effect - losses due to eddy current generated by the magnetic field experienced by a particular conductor section but generated by the current flowing in the rest of the winding. Design methods for minimizing proximity effect losses discussed later. Pw Pdc Pec Pec eddy current loss. Pw Rdc Rec Irms Rac Irms Rac FR Rdc 1 Rec Rdc Rdc Minimum winding loss at optimum conductor size. High frequencies require small conductor sizes minimize loss. Pdc kept small by putting may small-size...

## Core Database Basic Inductor Design Tool

Interactive core database spreadsheet-based key to a single pass inductor design procedure. User enters input specifications from converter design requirements. Type of conductor for windings round wire, Leitz wire, or rectangular wire or foil must be made so that copper fill factor kcu is known. Spreadsheet calculates capability of all cores in database and displays smallest size core of each type that meets stored energy specification. Also can be designed to calculate and display as desired...