Designation: A893/A893M − 03 (Reapproved 2015)Standard Test Method forComplex Dielectric Constant of Nonmetallic MagneticMaterials at Microwave Frequencies1This standard is issued under the fixed designation A893/A893M; 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 covers the measurement of the com-plex dielectric constant of isotropic ferrites for extremelyhigh-frequency applications.1.2 The values stated in either SI units or inch-pound unitsare to be regarded separately as standard. The values stated ineach system may not be exact equivalents; therefore, eachsystem shall be used independently of the other. Combiningvalues from the two systems may result in non-conformancewith the standard. Within this standard, SI units are shown inbrackets.1.3 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. Summary of Test Method2.1 In an isotropic dielectric medium with a steady electricfield, E, the electric displacement, D, is given by the equation:D 5 kε0E (1)where:ε0= permittivity of free space andk = dielectric constant. If the medium is subjected to analternating electric field, the electric displacement is notnecessarily in phase with the field. This fact may beexpressed mathematically by taking k as a complexquantity. If we write k = k −jk“, the imaginary part, k“,determines the dissipation in the medium.2.2 This test method uses a cavity perturbation technique asa means of separating electric from magnetic effects. Quanti-ties that must be measured are the resonance frequency, f,ofthe cavity with and without the sample, the loaded Q of thecavity with and without the specimen, and the cavity andspecimen dimensions.2.3 The specimen is in the form of a rod and is placedparallel to the microwave electric field in a region of substan-tially uniform electric and zero microwave magnetic fields.The perturbation theory requires that the diameter of thesample rod be small compared to one quarter of the wavelengthof the microwave radiation in the specimen. Estimation of thiswavelength requires knowledge of the permittivity, ε = kε0, andpermeability, µ, of the specimen under the conditions ofmeasurement. The wavelength, λ, in the specimen is given bythe equation:λ 5 1/f ~µε!1/2(2)For many ferrites, µ may be taken equal to µ0, the perme-ability of empty space, without serious error. The permittivity,ε, is determined by measurement as described below; afterobtaining a value of ε, it is necessary to ascertain with the aidof Eq 1 that the sample diameter is sufficiently small.2.4 This test method is not suitable for materials with losstangents ≥0.1, with the loss tangent defined as tan δ = k“⁄k .2.5 The results of the perturbation theory calculation may beexpressed in the form:δf/f 5 @2~k 2 1! ?MivsEoEidv#/2?Mivc~Eo!2dv (3)where:f = f +jf ⁄2Q;Q = loaded Q of the cavity;vs= specimen volume contained within the cavity,in.3[mm3];vc= cavity volume, in.3[mm3]; andE = microwave electric field strength.The superscript o refers to fields in the empty cavity and thesuperscript i refers to fields inside the specimen.2.6 A specific cavity suitable for this test method is a TE10nrectangular cavity,2where n is odd. With the rod running1This 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, 2015. Published April 2015. Originallyapproved in 1963. Last previous edition approved in 2008 as A893/A893M–03(2008). DOI: 10.1520/A0893_A0893M-03R15.2See, for example, Montgomery, C. G., Ed., Technique of MicrowaveMeasurements, McGraw-Hill Book Co., Inc., New York, 1947, pp. 294–295;Bronwell and Beam , Theory and Application of Microwaves, McGraw-Hill BookCo., Inc., 1947, pp. 368–337.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1completely across the cavity at the center, Eq 2 for δf/f can bereduced to the following:δf /f 522~k 21!~vs/vc!; δ ~1/Q! 5 4k “~vs/vc! (4)δf and δ(1/Q) are, respectively, the difference in the cavityresonant frequency with and without the specimen and thedifference in the reciprocal Q of the cavity with and without thespecimen, and f is the resonant frequency of the empty cavity.2.7 In many cases it is convenient to describe the dissipativeproperties of the medium by alternative notation. An effectiveresistivity at the frequency f =θ⁄2π may be defined by theequation:ρ 5 1/ωk “εo(5)3. Significance and Use3.1 This test method can be used to evaluate batch type orcontinuous production of material for use in microwaveapplications. It may be used to determine the loss factors ofmicrowave ferrites or help evaluate absorption materials foruse in microwave ovens and other shielding applications.3.2 The values obtained by use of this practice can be usedas quality assurance information for process control, or both,when correlated to the chemistry or process for manufacturingthe material.4. Apparatus4.1 Fig. 1 is a schematic diagram of the equipment requiredfor the measurement. Power from a suitable unmodulated oramplitude modulated microwave source, A, is run through avariable attenuator, D, and kept at a constant level throughoutthe measurement with the aid of a directional coupler, E,acrystal detector, and a power-indicating meter, F. This constantpower is run through a precision variable attenuator, G,tothecavity, H, and the cavity output power is detected and indicatedon a suitable meter, I.5. Test Specimen and Cavity5.1 The specimen shall be in the form of a rod. It is insertedin a transmission-type cavity so that the axis of the rod is alonga line of constant microwave electric field and zero microwavemagnetic field. The ends of the rod shall pass through holes inboth cavity walls.5.2 The rod diameter shall be 0.041 + 0.000, − 0.002 in.[0.10 + 0.00, − 0.05 mm] at X-band unless this violates theconditions of 2.3.5.3 The input and output lines of this cavity shall be madeto appear as matched loads by the appropriate use of pads orisolators.5.4 The TE10ncavity (n odd and 3 or greater) shall beresonant between 9000 and 10 000 MHz for the X-bandmeasurement. The loaded Q of the empty cavity shall begreater than 2000 (Note 1). The holes through which the ferritepasses shall be 0.042 + 0.002, − 0.000 in. [0.11 + 0.05, − 0.00mm] in diameter. The dimensions of a typical cavity, operatingin the TE103mode, are shown in Fig. 2.NOTE 1—High Qs are obtainable by using waveguide and end plates ofoxygen-free high-conductivity copper or by silver plating.6. Procedure6.1 Introduce an attenuation of 3 dB with the precisionattenuator. Without the specimen in the cavity, adjust themicrowave frequency to cavity resonance, as indicated bymaximum power output with respect to frequency variation.Note the indication of the output power level and measure theresonant frequency, f , with a wavemeter or other suitablemeans at B. Remove the 3 dB of attenuation and locate the twofrequencies at which the output power is the same as at cavityresonance with the 3-dB attenuation in. Determine the separa-tion in frequency of these two half-power points at B by aheterodyning technique using a frequency stabilized source, C.The loaded Q of the cavity is then given by f ⁄∆f 1⁄2 where ∆f 1⁄2 is the frequency separation of the half-power points.6.2 Alternatively, instead of the 3 dB of attenuation speci-fied above, a larger amount, α decibels, may be used. If ∆f isthe separation of the two frequencies at which the output powerwithout attenuation is the same as the output power at cavityresonance with the α decibels of attenuation inserted, the Q isgiven by the equation:FIG. 1 Schematic Diagram of Equipment Required for Measurement of Complex Dielectric ConstantA893/A893M − 03 (2015)2Q 5 ~f /∆f ! =10α/102 1 (6)6.3 By choosing a value of α sufficiently large, it is possibleto make the measurement of δf with a precision wavemeter,eliminating the need of the heterodyning technique.6.4 Position the specimen in the cavity and then repeat themeasurements of f and Q. The change in f (a negativequantity) is the desired δf , and the change in 1/Q is the desiredδ (1/Q). Nonzero microwave magnetic field at the specimencan introduce magnetic loss into this measurement. A suitablemagnetic bias can be applied to the ferrite to avoid this losscontribution. The measurement of dielectric loss tangent mustbe independent of the applied magnetic field.6.5 The recommended standard test temperature is 25 65°C.7. Calculation7.1 Calculate the values of k and k“ by means of Eq 3.Obtain the loss tangent, as defined in 2.4, from these values ofk and k“.8. Report8.1 The report shall include the following:8.1.1 Values of k and loss tangent,8.1.2 Temperature of the material during the measurement,8.1.3 Frequency at which the measurement was made,8.1.4 Specimen diameter, and8.1.5 Unique identity of the specimen.9. Precision and Bias9.1 The bias of the measurements shall be such that the errorcontributed to k will be within 63 % and the error contributedto the loss tangent will be within 60.001 or 65 %, whicheveris greater.10. Keywords10.1 absorption; dielectric; dielectric constant; ferrimag-netic; ferrite; loss factor; loss tangent; microwave; permittivity;shieldingASTM 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 every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or

[email protected] (e-mail); or through the ASTM website(www.astm.org). Permission rights to photocopy the standard may also be secured from the Copyright Clearance Center, 222Rosewood Drive, Danvers, MA 01923, Tel: (978) 646-2600; http://www.copyright.com/in.[mm]0.002[0.05]0.028[0.71]0.200[5.08]1.350[34.29]2.700[68.58]FIG. 2 Typical Cavity for Measurement of Dieletric Constant at9300 MHzA893/A893M − 03 (2015)3