Nicolson–Ross–Weir Method
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Nicolson–Ross–Weir method is a
measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to ...
technique for determination of complex permittivities and permeabilities of material samples for
microwave Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...
frequencies. The method is based on insertion of a material sample with a known thickness inside a
waveguide A waveguide is a structure that guides waves by restricting the transmission of energy to one direction. Common types of waveguides include acoustic waveguides which direct sound, optical waveguides which direct light, and radio-frequency w ...
, such as a
coaxial cable Coaxial cable, or coax (pronounced ), is a type of electrical cable consisting of an inner Electrical conductor, conductor surrounded by a concentric conducting Electromagnetic shielding, shield, with the two separated by a dielectric (Insulat ...
or a rectangular waveguide, after which the
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns * Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variat ...
data is extracted from the resulting
scattering parameters Scattering parameters or S-parameters (the elements of a scattering matrix or S-matrix) describe the electrical behavior of linear electrical networks when undergoing various steady state stimuli by electrical signals. The parameters are useful ...
. The method is named after A. M. Nicolson and G. F. Ross, and W. B. Weir, who developed the approach in 1970 and 1974, respectively. The technique is one of the most common procedures for material characterization in
microwave engineering Microwave engineering pertains to the study and design of microwave circuits, components, and systems. Fundamental principles are applied to analysis, design and measurement techniques in this field. The short wavelengths involved distinguish this ...
.


Method

The method uses
scattering parameters Scattering parameters or S-parameters (the elements of a scattering matrix or S-matrix) describe the electrical behavior of linear electrical networks when undergoing various steady state stimuli by electrical signals. The parameters are useful ...
of a material sample embedded in a waveguide, namely S_ and S_, to calculate permittivity and permeability data. S_ and S_ correspond to the cumulative
reflection Reflection or reflexion may refer to: Science and technology * Reflection (physics), a common wave phenomenon ** Specular reflection, mirror-like reflection of waves from a surface *** Mirror image, a reflection in a mirror or in water ** Diffuse r ...
and
transmission coefficient The transmission coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered. A transmission coefficient describes the amplitude, intensity, or total power of a transmitt ...
of the sample that are referenced to the each sample end, respectively: these parameters account for the multiple internal reflections inside the sample, which is considered to have a thickness of d. The reflection coefficient of the bulk sample is: :\Gamma=X \pm \sqrt where :X=\frac The sign of the root for the reflection coefficient is chosen appropriately to ensure its passivity (, \Gamma, \leq 1). Similarly, the transmission coefficient of the bulk sample can be written as: :T=\frac Thus, the effective permeability (\mu^*) and permittivity (\varepsilon^*) of the material can be written as: :\mu^*=\frac \left( \frac \right) :\varepsilon^*=\frac where :\frac=-\left \frac ln\frac \right2 and *\lambda_0 is the free-space
wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
. *\lambda_ is the guided mode wavelength of the unfilled transmission line. *\lambda_ is the
cutoff wavelength In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced ( attenuated or reflected) rather than ...
of the unfilled transmission line The constitutive relation for \Lambda admits an infinite number of solutions due to the
branches A branch, also called a ramus in botany, is a stem that grows off from another stem, or when structures like veins in leaves are divided into smaller veins. History and etymology In Old English, there are numerous words for branch, includi ...
of the
complex logarithm In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following, which are strongly related: * A complex logarithm of a nonzero complex number z, defined to be ...
. The ambiguity regarding its result can be resolved by taking the
group delay In signal processing, group delay and phase delay are functions that describe in different ways the delay times experienced by a signal’s various sinusoidal frequency components as they pass through a linear time-invariant (LTI) system (such as ...
into account.


Limitations and extensions

In the case of low material loss, the Nicolson–Ross–Weir method is known to be unstable for sample thicknesses at
integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
multiples of one half wavelength due to
resonance Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...
phenomenon. Improvements over the standard algorithm have been presented in engineering literature to alleviate this effect. Furthermore, complete filling of a waveguide with sample material may pose a particular challenge: presence of gaps during the filling of the waveguide section would excite higher-order modes, which may yield errors in scattering parameter results. In such cases, more advanced methods based on the rigorous
modal analysis Modal analysis is the study of the dynamic properties of systems in the frequency domain. It consists of mechanically exciting a studied component in such a way to target the Normal mode, modeshapes of the structure, and recording the vibration ...
of partially-filled waveguides or
optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfiel ...
methods can be used. A modification of the method for single-port measurements was also reported. In addition to homogenous materials, the extension of the method was developed to obtain constitutive parameters of isotropic and bianisotropic
metamaterial A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is a type of material engineered to have a property, typically rarely observed in naturally occu ...
s.


See also

*
Fourier-transform spectroscopy Fourier-transform spectroscopy (FTS) is a measurement technique whereby Spectrum (physics), spectra are collected based on measurements of the coherence (physics), coherence of a Radiation, radiative source, using time-domain or space-domain meas ...
*
Microwave radiometer A microwave radiometer (MWR) is a radiometer that measures energy emitted at one millimeter-to-metre wavelengths (frequencies of 0.3–300 GHz) known as microwaves. Microwave radiometers are very sensitive receivers designed to measure thermally ...
*
Reflection seismology Reflection seismology (or seismic reflection) is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflection (physics), reflected seismic waves. The method requir ...
*
Spectroscopy Spectroscopy is the field of study that measures and interprets electromagnetic spectra. In narrower contexts, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum. Spectro ...
*
Time-domain reflectometer A time-domain reflectometer (TDR) is an electronic instrument used to determine the characteristics of electrical lines by observing reflected pulses. It can be used to characterize and locate faults in metallic cables (for example, twisted pai ...
* Vector network analyzer


References


Further reading

* Microwave technology Spectroscopy Electric and magnetic fields in matter {{DEFAULTSORT:Nicolson-Ross-Weir method