Microwave measurements of the complex permittivities and permeabilities of magnetodielectrics

Abstract

A method is proposed for determining complex permittivities e* and permeabilities I~* by analyzing the interaction of a plane electromagnetic wave with a plane-parallel sample in free space. Results of the method are presented.Difficulties arise when measuring the complex permittivity e* and permeability /z* of materials at microwave frequencies in free space because of the necessity to jointly determine e* and/~* from a system of complex transcendental equations with consequent ambiguity of the result obtained. At the same time, such measurements are preferred for solving a whole class of special problems (developing electromagnetic wave absorbers for electronics and microwave technology, absorbing coatings and screens for various purposes, etc.).We now demonstrate the possibility of developing an impedance method for determining permittivities and permeabilities [1] at microwave frequencies. The interaction of a plane electromagnetic wave of wavelength )~ with a sample of investigated material located in free space was previously considered in [2]. The sample was made in the form of a plane-parallel plate of thickness d mounted perpendicularly to the direction of propagation of the electromagnetic wave. The relationship was found between e ~ and/~* of the investigated material and the reflection coefficients: E;-* =1+ 4r~ e l-l-r; -I-r; r;--3r 2 ;":," ~ [,+r; (4r;)],t~ i.t*8*= arc tanh t--+r~ ~-~ (t-,~ p ---r-I +r 2 '(1)where rl* and r2* are the complex reflection coefficients of the sample for reflection from the magnetodielectric sample respectively on a metal screen and without a screen; j is the square root of minus one. Thus, according the system (1), the determination of e* and/z* can be reduced to measuring the complex reflection coefficients rl* and r2* and then solving the system of equations (1). Expression (1) defines in the most general form the dependence of the required parameters e* and/.t ~ on the experimentally measured quantities r[ and r2*. The range of application is limited only if the quasisteady-state conditions at the medium--sample interface are violated or if there is high attenuation of the microwave energy in the sample. Figure 1 shows a functional schematic diagram of an apparatus for determining the coPplex reflection coefficients in free space. The microwave signal radiated by a horn antenna 6 is converted into a plane electromagnetic wave by a lens 7. The wave reflected from the investigated sample 8 is returned into the waveguide line. A directional coupler 5 separates out signals proportional to the powers of the reflected and incident waves and feeds them to detectors whose outputs enter a ratio meter 4 giving an output voltage which is proportional to the square of the modulus of the coefficient of reflection from sample 8: