Analytical expressions for electrodynamic parameters of the shielded microstrip line

On the basis of an electrodynamic model of a screened microstrip line, built on the basis of the projection method using the Chebyshev basis, which explicitly takes into account the edge features of the field, a mathematical model of a microstrip line with a strip conductor was developed. The line width does not exceed the height of the substrate. In this case, the current density on the strip conductor is approximated by only one basis function. Analytical expressions are presented in the form of a sum of slowly and rapidly converging series to determine the main electrodynamic parameters of the line – wave resistance and deceleration coefficient. Due to logarithmic features, slowly converging series are summed up and transformed into rapidly converging power series. In addition, limit expressions in the form of improper integrals are given for the main electrodynamic parameters of an open microstrip line in the quasi-static approximation. Due to the logarithmic features, these integrals are also converted to rapidly converging power series. As a result, simple approximate formulas were obtained. They allow calculating the deceleration coefficient and wave impedance of the line with an error not exceeding 1%, when the width of the strip conductor is less than twice the thickness of the substrate. The results of calculating the electrodynamic parameters obtained on the basis of the developed mathematical model and on the basis of the projection method with an accuracy of up to 5 significant digits are presented. These results make it possible to establish the limits of applicability of the quasi-static approximation and to determine the error in calculating the deceleration coefficient and wave resistance using the obtained analytical expressions. The error does not exceed 0.1%, if the width of the strip conductor is less than twice the thickness of the substrate in a wide range of changes in the substrate dielectric constant and frequency.

A Wideband Termination Based on Laser-Scribed Lossy Microstrip Line Structures

Laser-direct writing has become an alternative method to fabricate microwave devices. We present a laser-scribed wideband open-end termination that relies on conductor loss of the microstrip line structure to obtain effective absorption. The proposed design consists of a resistive film overlapped on a strip conductor, providing an enlarged sheet-resistance range (20 Ω/□ ~ 1.2 kΩ/□) of the resistive film to reduce the fabrication difficulties. The resistive film is in tapered shape to enable small gradual changes in impedance, yielding minimized reflections (|S11|). The prototype is demonstrated utilizing the laser-direct writing technique, with a measured |S11| over −15 dB from 6 GHz to at least 30 GHz. The termination can also be used for attenuation over a −10 dB attenuation level (>8.5 GHz) with a low reflection level better than −15 dB (>2.0 GHz). This study can be employed for the applications where cheap wideband planar terminations are needed and promote fast, flexible, and low-cost prototyping or modification of the existing microwave circuits.

Теория ленточной антенны, расположенной на плоской границе раздела одноосного магнитного метаматериала и изотропной среды

A study is made of the electrodynamic characteristics of an antenna having the form of an infinitesimally thin, perfectly conducting narrow strip located at the plane interface of a uniaxial magnetic metamaterial and an isotropic magnetodielectric medium. The antenna is perpendicular to the anisotropy axis of the metamaterial and is excited by a time-harmonic given voltage. Singular integral equations for the antenna current are obtained in the case of an infinitely long strip conductor. Based on the solution of these equations, the current distribution and input impedance of the antenna are found and analyzed. The limits of applicability of an approximate method based on the transmission line theory for determining the antenna characteristics are established. Within the framework of this method, the results obtained are generalized to the case of a finite-length strip antenna.

Experimental investigation of magnetic field near strip conductors with rectangle cut-out

A theoretical distribution of magnetic field generated by strip conductors of different widths close to a rectangular cutout is derived. An experimental investigation of strip conductor magnetic field with magnetoresistive and Hall sensors based devices is presented. The experimental results fit the theoretical calculations. A method of conductor defect detection using appliances based on the sensors was developed.