Standard Active Last Updated: Oct 18, 2022 Track Document
ASTM D7449/D7449M-22a

# Standard Test Method for Measuring Relative Complex Permittivity and Relative Magnetic Permeability of Solid Materials at Microwave Frequencies Using Coaxial Air Line

Standard Test Method for Measuring Relative Complex Permittivity and Relative Magnetic Permeability of Solid Materials at Microwave Frequencies Using Coaxial Air Line D7449_D7449M-22A ASTM|D7449_D7449M-22A|en-US Standard Test Method for Measuring Relative Complex Permittivity and Relative Magnetic Permeability of Solid Materials at Microwave Frequencies Using Coaxial Air Line Standard new BOS Vol. 10.02 Committee D09
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Significance and Use

5.1 Design calculations for radio frequency (RF), microwave, and millimetre-wave components require the knowledge of values of complex permittivity and permeability at operating frequencies. This test method is useful for evaluating small experimental batch or continuous production materials used in electromagnetic applications. Use this method to determine complex permittivity only (in non-magnetic materials), or both complex permittivity and permeability simultaneously.

5.2 Relative complex permittivity (relative complex dielectric constant), , is the proportionality factor that relates the electric field to the electric flux density, and which depends on intrinsic material properties such as molecular polarizability, charge mobility, and so forth:

 where: ε0 = permittivity of free space
 = electric flux density vector, and
 = electric field vector.

Note 1: In common usage the word “relative” is frequently dropped. The real part of complex relative permittivity ( ) is often referred to as simply relative permittivity, permittivity, or dielectric constant. The imaginary part of complex relative permittivity ( ) is often referred to as the loss factor. In anisotropic media, permittivity is described by a three dimensional tensor.

Note 2: For the purposes of this test method, the media is considered to be isotropic and, therefore, permittivity is a single complex number at each frequency.

5.3 Relative complex permeability, , is the proportionality factor that relates the magnetic flux density to the magnetic field, and which depends on intrinsic material properties such as magnetic moment, domain magnetization, and so forth:

 where: μ0 = permeability of free space,
 = magnetic flux density vector, and
 = magnetic field vector.

Note 3: In common usage the word “relative” is frequently dropped. The real part of complex relative permeability ( ) is often referred to as relative permeability or simply permeability. The imaginary part of complex relative permeability ( ) is often referred to as the magnetic loss factor. In anisotropic media, permeability is described by a three dimensional tensor.

Note 4: For the purposes of this test method, the media is considered to be isotropic, and therefore permeability is a single complex number at each frequency.

5.4 Relative permittivity ((relative dielectric constant) (SIC) κ′(εr)) is the real part of the relative complex permittivity. It is also the ratio of the equivalent parallel capacitance, Cp, of a given configuration of electrodes with a material as a dielectric to the capacitance, Cυ, of the same configuration of electrodes with vacuum (or air for most practical purposes) as the dielectric:

Note 5: In common usage the word “relative” is frequently dropped.

Note 6: Experimentally, vacuum must be replaced by the material at all points where it makes a significant change in capacitance. The equivalent circuit of the dielectric is assumed to consist of Cp, a capacitance in parallel with conductance. (See Fig. 3 of Test Methods D150.)

Note 7: Cx is taken to be Cp, the equivalent parallel capacitance as shown in Fig. 3 of Test Methods D150.

Note 8: The series capacitance is larger than the parallel capacitance by less than 1 % for a dissipation factor of 0.1, and by less than 0.1 % for a dissipation factor of 0.03. If a measuring circuit yields results in terms of series components, the parallel capacitance must be calculated from Eq 5 of Test Methods D150 before the corrections and permittivity are calculated.

Note 9: The permittivity of dry air at 23 °C and standard pressure at 101.3 kPa is 1.000536. Its divergence from unity, κ′ − 1, is inversely proportional to absolute temperature and directly proportional to atmospheric pressure. The increase in permittivity when the space is saturated with water vapor at 23 °C is 0.00025, and varies approximately linearly with temperature expressed in degrees Celsius, from 10 °C to 27 °C. For partial saturation the increase is proportional to the relative humidity.

Scope

1.1 This test method covers a procedure for determining relative complex permittivity (relative dielectric constant and loss) and relative magnetic permeability of isotropic, reciprocal (non-gyromagnetic) solid materials. If the material is nonmagnetic, it is acceptable to use this procedure to measure permittivity only.

1.2 This measurement method is valid over a frequency range of approximately 1 GHz to over 20 GHz. These limits are not exact and depend on the size of the specimen, the size of coaxial air line used as a specimen holder, and on the applicable frequency range of the network analyzer used to make measurements. The size of specimen dimension is limited by test frequency, intrinsic specimen electromagnetism properties, and the request of algorithm. For a given air line size, the upper frequency is also limited by the onset of higher order modes that invalidate the dominant-mode transmission line model and the lower frequency is limited by the smallest measurable phase shift through a specimen. Being a non-resonant method, the selection of any number of discrete measurement frequencies in a measurement band would be suitable. The coaxial fixture is preferred over rectangular waveguide fixtures when broadband data are desired with a single sample or when only small sample volumes are available, particularly for lower frequency measurements.

1.3 The values stated in either SI units of in inch-pound units are to be regarded separately as standard. The values stated in each system are not necessarily exact equivalents; therefore each system shall be used independently of the other. Combining values from the two systems is likely to result in non conformance with the standard. The equations shown here assume an e+jωt harmonic time convention.

1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.

1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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