Nicolson–Ross–Weir method

Nicolson–Ross–Weir method is a measurement technique for determination of complex permittivities and permeabilities of material samples for microwave frequencies.

The method is based on insertion of a material sample with a known thickness inside a waveguide, such as a coaxial cable or a rectangular waveguide, after which the dispersion data is extracted from the resulting scattering parameters.

[3] The method uses scattering parameters of a material sample embedded in a waveguide, namely

Similarly, the transmission coefficient of the bulk sample can be written as: Thus, the effective permeability (

admits an infinite number of solutions due to the branches of the complex logarithm.

[2] In the case of low material loss, the Nicolson–Ross–Weir method is known to be unstable for sample thicknesses at integer multiples of one half wavelength due to resonance phenomenon.

Improvements over the standard algorithm have been presented in engineering literature to alleviate this effect.

[4][5][6] 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.

[11] In addition to homogenous materials, the extension of the method was developed to obtain constitutive parameters of isotropic and bianisotropic metamaterials.