Designation: A772/A772M − 00 (Reapproved 2016)Standard Test Method forAC Magnetic Permeability of Materials Using SinusoidalCurrent1This standard is issued under the fixed designation A772/A772M; the number immediately following the designation indicates the yearof original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval.A superscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method provides a means for determination ofthe impedance permeability (µz) of ferromagnetic materialsunder the condition of sinusoidal current (sinusoidal H) exci-tation. Test specimens in the form of laminated toroidal cores,tape-wound toroidal cores, and link-type laminated coreshaving uniform cross sections and closed flux paths (no airgaps) are used. The method is intended as a means fordetermining the magnetic performance of ferromagnetic striphaving a thickness less than or equal to 0.025 in. [0.635 mm].1.2 This test method shall be used in conjunction with thoseapplicable paragraphs in Practice A34/A34M.1.3 The values and equations stated in customary (cgs-emuand inch-pound) or SI units are to be regarded separately asstandard. Within this standard, SI units are shown in bracketsexcept for the sections concerning calculations where there areseparate sections for the respective unit systems. The valuesstated in each system may not be exact equivalents; therefore,each system shall be used independently of the other. Combin-ing values from the two systems may result in nonconformancewith this standard.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2A34/A34M Practice for Sampling and Procurement Testingof Magnetic MaterialsA340 Terminology of Symbols and Definitions Relating toMagnetic Testing3. Terminology3.1 Definitions—The terms and symbols used in this testmethod are defined in Terminology A340.4. Significance and Use4.1 The permeability determined by this method is theimpedance permeability. Impedance permeability is the ratio ofthe peak value of flux density (Bmax) to the assumed peakmagnetic field strength (Hz) without regard to phase. Ascompared to testing under sinusoidal flux (sinusoidal B)conditions, the permeabilities determined by this method arenumerically lower since, for a given test signal frequency, therate of flux change (dB/dt) is higher.4.2 This test method is suitable for impedance permeabilitymeasurements at very low magnetic inductions at powerfrequencies (50 to 60 Hz) to moderate inductions below thepoint of maximum permeability of the material (the knee of themagnetization curve) or until there is visible distortion of thecurrent waveform. The lower limit is a function of sample area,secondary turns, and the sensitivity of the flux-reading voltme-ter used. At higher inductions, measurements of flux-generatedvoltages that are appreciably distorted mean that the flux hasappreciable harmonic frequency components. The upper limitis given by the availability of pure sinusoidal current, which isa function of the power source. In addition, a large ratio (≥10)of the total series resistance of the primary circuit to theprimary coil impedance is required. With proper test apparatus,this test method is suitable for use at frequencies up to 1 MHz.4.3 This test method is suitable for design, specificationacceptance, service evaluation, quality control, and researchuse.5. Apparatus5.1 The test circuit, which is schematically illustrated in Fig.1, shall consist of the following components.5.2 Power Supply—For power frequency (50- or 60-Hz)testing, a suitable power supply consists of two or three seriesconnected autotransformers of sufficient power rating. This1This test method is under the jurisdiction of ASTM Committee A06 onMagnetic Properties and is the direct responsibility of Subcommittee A06.01 on TestMethods.Current edition approved April 1, 2016. Published April 2016. Originallyapproved in 1980. Last previous edition approved in 2011 as A772/A772M – 00(2011)ɛ1. DOI:10.1520/A0772_A0772M-00R16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1will provide a continuously variable current source to excitethe test specimen. For testing at other than power frequency, anac power source consisting of a low distortion sinusoidal signalgenerator and linear amplifier are required.The use of feedbackcontrol of the power amplifier is permitted.5.3 Isolation/Stepdown Transformer—The use of a lowdistortion isolation/stepdown transformer is highly recom-mended for operator safety and to eliminate any dc bias currentpresent when using electronic power supplies. A combinedisolation/stepdown transformer can provide greater controlwhen testing is done at very low magnetizing currents.5.4 Primary Series Resistor (Z)—A noninductive resistorhaving sufficiently high resistance to maintain sinusoidal cur-rent conditions at the highest magnetizing current and testsignal frequency of interest. In practice, resistance values of 10to 100 Ω are used. If this resistor is used to measure themagnetizing current, the resistance shall be known to betterthan 0.5 % and the resistance shall not increase by more than0.5 % at the rated maximum current of the power supply.5.5 True RMS Ammeter (A)—A true rms ammeter or acombination of a noninductive, precision current viewingresistor and true rms voltmeter shall be used to measure themagnetizing current.The meter shall have an accuracy of betterthan 0.5 % full scale at the test frequency. The current viewingresistor, if used, shall have an accuracy better than 0.5 % andshall have sufficient power rating such that the resistance shallnot vary by more than 0.5 % at the rated maximum current ofthe power supply.5.6 Flux Measuring Voltmeter (V)—The flux shall be deter-mined from the voltage induced in the secondary windingusing one of the following type of voltmeter:(1) an average responding digital voltmeter calibrated toread rms volts for a sine wave, or(2) a true average responding digital voltmeter.The voltmeter shall have input impedance greater than 1 MΩ,a full-scale accuracy of better than 0.5 % at the test frequency,and a crest factor capability of 3 or greater.6. Procedure6.1 Specimen Preparation—After determining the mass anddimensions of the test specimen, it should be enclosed in asuitable insulating case to prevent intimate contact between itand the primary and secondary windings. This will alsominimize the stress introduced by winding. The case shape andsize shall approximate that of the test specimen so that thesecondary winding encloses minimal air flux. All test speci-mens shall have a uniform rectangular cross section.6.1.1 The cross-sectional area and mean magnetic pathlength of the test specimen shall be calculated using theequations in 7.1 and 7.2 or 8.1 and 8.2. To obtain acceptableuniformity of magnetic field strength throughout the specimen,the following dimensional constraints shall be observed:(1) for a toroid the inside diameter to outside diameter ratioshall exceed 0.82, and(2) for the link specimen shown in Fig. 2, the separation (s)shall exceed nine times the radial width (w).6.1.2 A secondary winding (N2) using insulated wire shallbe uniformly distributed over the test specimen using asufficient number of turns so that a measurable voltage will beobtained at the lowest flux density of interest. A uniformlydistributed primary winding (N1) of insulated wire shall beapplied on top of the secondary winding and be of sufficientdiameter to conduct the highest intended magnetizing currentsafely without significant heating. Twisted leads or biconductorcable shall be used to connect the specimen windings to the testapparatus.6.2 Calculation of Test Signals—Testing is done either atspecified values of flux density (Bmax) or magnetic fieldstrength (Hz). Before testing, the rms magnetizing currents orvoltages generated in the secondary shall be calculated usingthe equations found in 7.3 and 7.4 or 8.3 and 8.4.6.3 Demagnetization—After connecting the primary andsecondary windings to the apparatus, the test specimen shall bedemagnetized by applying a magnetizing current sufficientlylarge to create a magnetic field strength greater than ten timesthe coercivity of the test specimen. The magnetizing currentthen shall be slowly and smoothly reduced to zero to demag-netize the test specimen. The frequency used should be thesame as the test frequency.6.4 Measurement—The magnetizing current shall be care-fully increased until the lowest value of either magnetizingcurrent (if measuring at a specified value of magnetic fieldstrength) or flux density (if measuring at a specified value offlux density) is obtained. Both the magnetizing current andsecondary voltage shall be recorded. The magnetizing currentis then increased to the next test point and the process repeateduntil all test points have been measured. It is imperative thatmeasurements be made in order of increasing magnetic fieldstrength or flux density. When a prescribed value of magneticfield strength or flux density has been accidentally exceededduring the test, the specimen must be demagnetized and testingresumed at that point.FIG. 1 Schematic Circuit for Sinusoidal Current Permeability TestFIG. 2 Schematic of Link-Type LaminationA772/A772M − 00 (2016)26.4.1 At the conclusion of testing, the magnetizing currentshall be reduced to zero and the specimen removed from thetest apparatus. The impedance permeability shall be calculatedusing the equations found in 7.5 or 8.5.7. Calculation (Customary Units)7.1 Calculation of Mean Magnetic Path Length, l (assumedto be equal to the mean geometric path):7.1.1 For toroidal cores:l 5π ~D1d!2(1)where:l = mean magnetic path length, cm;D = outside diameter, cm; andd = inside diameter, cm.7.1.2 For link cores of the form shown in Fig. 2:l 5 2L1π~s1w! 5 2L01~π 2 2!s1~π 2 4!w (2)where:l = mean magnetic path length, cm;L0= total length, cm;L = length of parallel sides, cm;s = wall separation, cm; andw = radial width, cm.7.2 Calculation of Cross-Sectional Area, A:7.2.1 For either toroidal or link-type cores, the cross-sectional area is calculated from the mass and mean magneticpath length as:A 5mlδ(3)where:A = cross-sectional area, cm2;m = specimen mass, gm;l = mean magnetic path length, cm; andδ = specimen density, g/cm3.Note that the core height or lamination stacking factor is notrequired in the preceding equation.7.3 Calculation of the Assumed Peak Magnetic FieldStrength, Hz—The assumed peak magnetic field strength iscalculated from the rms value of magnetizing current as:Hz50.4π=2N1Iml(4)where:Hz= assumed peak magnetic field strength, Oe;N1= number of primary turns;Im= rms magnetizing current, A; andl = mean magnetic path length of specimen, cm.7.4 Calculation of Peak Flux Density, Bmax7.4.1 The peak flux density when using an average respond-ing voltmeter calibrated to yield rms values for a sine wave iscalculated as:Bmax5108Ef=2πfN2A(5)7.4.2 The peak flux density when using a true averageresponding voltmeter is calculated as:Bmax5108Eavg4fN2A(6)where:Bmax= peak flux density (induction), gauss;Ef= flux voltage measured across secondary winding, V;Eavg= average voltage measured across secondary winding,V;f = test frequency, Hz;N2= number of secondary turns; andA = cross-sectional area of test specimen, cm2.7.5 Calculation of Impedance Permeability, µz7.5.1 The impedance permeability is calculated as the ratioof Bmaxto Hzor:µz5BmaxHz(7)8. Calculation (SI Units)8.1 Calculation of Mean Magnetic Path Length, l (assumedto be equal to the mean geometric path):8.1.1 For toroidal cores:l 5π ~D1d!2(8)where:l = mean magnetic path length, m;D = outside diameter, m; andd = inside diameter, m.8.1.2 For link cores of the form shown in Fig. 2:l 5 2L1π~s1w! 5 2L01~π 2 2!s1~π 2 4!w (9)where:l = mean magnetic path length, m;L0= total length, m;L = length of parallel sides, m;s = wall separation, m; andw = radial width, m.8.2 Calculation of Cross-Sectional Area, A8.2.1 For either toroidal or link type cores, the cross-sectional area is calculated from the mass and mean magneticpath length as:A 5mlδ(10)where:A = cross-sectional area, m2;m = specimen mass, kg;l = mean magnetic path length, m; andδ = specimen density, kg/m3.Note that the core height or lamination stacking factor is notrequired in the preceding equation.8.3 Calculation of the Assumed Peak Magnetic FieldStrength, Hz—The assumed peak magnetic field strength iscalculated from the rms value of magnetizing current as:A772/A772M − 00 (2016)3Hz5=2N1Iml(11)where:Hz= assumed peak magnetic field strength, A/m;N1= number of primary turns;lm= rms magnetizing current, A; andl = mean magnetic path length of specimen, m.8.4 Calculation of Peak Flux Density, Bmax8.4.1 The peak flux density when using an average respond-ing voltmeter calibrated to yield rms values for a sine wave iscalculated as:Bmax5Ef=2πfN2A(12)8.4.2 The peak flux density when using a true averageresponding voltmeter is calculated as:Bmax5Eavg4fN2A(13)where:Bmax= peak flux density (induction), tesla;Ef= flux voltage measured across secondary winding, V;Eavg= average voltage measured across secondary winding,V;f = test frequency, Hz;N2= number of secondary turns; andA = cross-sectional area of test specimen, m2.8.5 Calculation of Impedance Permeability, µz8.5.1 In the SI system of units, the ratio of Bmaxto Hzis theabsolute impedance permeability. A more useful form is therelative impedance permeability which is the ratio of theabsolute permeability to the permeability of free space or:µz5BmaxΓmHz(14)Γm= magnetic constant equal to 4π ×10–7H/m.9. Precision and Bias9.1 The precision and bias of this test method have not beenestablished by interlaboratory study. However, it is estimatedthat the precision of measurement is no worse than 65%.10. Keywords10.1 magnetic field strength; magnetic flux density; mag-netic induction; permeability; sinusoidal current; toroidal coreASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed e