The two-transmission method is an improved method of determining, from microwave measurements, the complex permeability and complex permittivity of a sample of a material typified by a lossy dielectric or a magnetic radar absorbing material. The two-transmission method is so named because it involves two microwave transmission- measurement runs: one on the sample alone and one on a two-layer stack comprising the sample plus a layer of an acrylic material that has known permittivity and permeability. The name of the two-transmission method also serves to distinguish it from a prior method that involves microwave-reflection measurements with which errors have been associated.

A Focus Arch can be used in the frequency domain in a prior method or in either the frequency or time domain in the present improved method.
The two-transmission method admits of frequency-domain and time-domain variants and is applicable to measurements made in either a waveguide laboratory setup or a free-space laboratory setup called a "focus arch." The frequency-domain variant in both the prior and present methods involves the use of a network analyzer to obtain measurements from which are calculated the scattering parameters ["S-parameters" (four standard parameters used to quantify reflectance and transmittance)].

In the frequency-domain variants in the waveguide laboratory setup, it is necessary to perform a through-reflect-line calibration of the waveguide apparatus that includes a holder in which the sample or the sample/acrylic stack is to be placed. The sample or the sample/ acrylic stack must be accurately machined to fill the holder to ensure that only the dominant waveguide mode is present. The S-parameters of the sample or the sample/acrylic stack are obtained from the network-analyzer measurements. Then the complex permittivity and permeability are extracted from the S-parameters by means of a suitable algorithm, which is typically based on equations known as the NRW formulas [wherein "NRW" signifies the surnames (Nicolson, Ross, and Weir) of the originators of the equations] that are well known to specialists in this art. The NRW formulas require transmission and reflection measurements. If, as in the two-transmission method, the NRW formulas cannot be used, then an iterative method such as a Newton two-dimensional root search is used.

A reflection measurement can entail a path-length difference that can give rise to a large error. A position-correction factor can be used in conjunction with both forward and reverse measurements to account for this error. However, the use of transmission measurements (as in the two-transmission method) that are independent of the position of the sample eliminates this source of error and the need for a correction factor, thus leading to more accurate results.

The process for characterizing a sample in a focus arch differs somewhat from that in a waveguide setup. In the frequency-domain variants, a focus arch (see figure) includes two wideband antennas, a network analyzer for making the S-parameter measurements, a sample holder, and two dielectric lenses that collimate the beams from the antennas in the region that contains the sample holder. As in the waveguide setup, a calibration must be performed, and the complex permittivity and permeability are extracted from the S-parameters. Error is introduced if the sample is not properly positioned and oriented at the reference plane.

Unlike in the waveguide setup, the process of extracting the complex permittivity and permeability from the S-parameters includes a frequency windowing subprocess to knock down side-lobes that occur in another subprocess in which data are transformed to the time domain. This frequency windowing causes a loss of accuracy at the edges of the frequency band represented by the window. In the time domain, the data are time-gated to remove unwanted sample/antenna interactions. Finally, the data are transformed back into the frequency domain, and the applicable algorithm for extracting the complex permittivity and permeability are applied.

For the focus arch, the process can be simplified if the measurements are made in the time domain. For this purpose, the network analyzer is replaced with a digital oscilloscope that includes a time-domain reflection/time-domain transmission (TDR/TDT) module. Making measurements in the time domain eliminates the need for frequency windowing and transforming to the time domain, thereby making it possible to retain the accuracy of data at the window frequency-band edges. The direct time-domain measurements are gated as described above and then transformed to the frequency domain for extraction of the complex permeability and permittivity as described above.

This work was done by Kirt J. Cassell of the Air Force Institute of Technology for the Air Force Research Laboratory.

AFRL-0093


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Improvements in Measurement of Permeability and Permittivity

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This article first appeared in the August, 2008 issue of Defense Tech Briefs Magazine.

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