KEY FACTORS AFFECTING THE DISCONNECTION OF EXPERIMENTAL AND MODEL CURVES IN MODELING P–N-TRANSITION ON PULSE BROADBAND SIGNALS

The article discusses the key factors influencing the discrepancy between the experimental and model curves when simulating a p – n junction on pulsed broadband signals. The reason for the discrepancy lies in the quasi-static representation of the forward and backward reconstruction of the p – n junction in the standard SPICE model. The quasi-static approximation does not take into account the transient processes in the p – n junction, which are associated with the transit time of minority charge carriers and the series resistance of losses.

Covariant density and velocity perturbations of the quasi-Newtonian cosmological model in f(T) gravity

We investigate classes of shear-free cosmological dust models with irrotational fluid flows within the framework of f(T) gravity. In particular, we use the $$1 + 3$$ 1 + 3 covariant formalism and present the covariant linearised evolution and constraint equations describing such models. We then derive the integrability conditions describing a consistent evolution of the linearised field equations of these quasi-Newtonian universes in the f(T) gravitational theory. Finally, we derive the evolution equations for the density and velocity perturbations of the quasi-Newtonian universe. We explore the behaviour of the matter density contrast for two models – $$f(T)= \mu T_{0}(T/T_{0})^{n}$$ f ( T ) = μ T 0 ( T / T 0 ) n and the more generalised case, where $$f(T)= T+ \mu T_{0} (T/T_{0})^{n}$$ f ( T ) = T + μ T 0 ( T / T 0 ) n , with and without the application of the quasi-static approximation. Our numerical solutions show that these f(T) theories can be suitable alternatives to study the background dynamics, whereas the growth of energy density fluctuations change dramatically from the expected $$\Lambda $$ Λ CDM behaviour even for small deviation from the general relativistic limits of the underlying f(T) theory. Moreover, applying the so-called quasi-static approximation yields exact-solution results that are orders of magnitude different from the numerically integrated solutions of the full system, suggesting that these approximations are not applicable here.

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.

Interaction of acoustic waves with moving boundary surfaces

A quasi-static approximation is considered for the interaction of a probing ultrasonic beam with a vibrating boundary surface. The model is considered in the form of a boundary value problem, presented in the form of d'Alembert. The method of successive approximations was used for the solution. The error arising from this interaction is established. Keywords: quasi-static approximation, boundary value problem, d'Alembert form, Doppler effect, rheological medium. [email protected]; [email protected]

The Investigation of Coupling between Matching Circuit and Input Resonators of Channels in a Microstrip Diplexer

This paper deals with investigation of the coupling coefficients between the matching circuit and the input resonators of channels in a microstrip diplexer. Diplexer channels are two-section filters, and matching circuit is regular non-resonant segment of a microstrip line placed between input resonators of channels. The common port is connected to outer end of the segment and its second end is opened. Research was carried out theoretically using a computer program developed on the basis of mathematical expressions obtained by means of one-dimensional models and quasi-static approximation. The results show that a value of coupling is quite large and the use of the matching circuit in a form of a non-resonant segment of a microstrip line allows to design diplexers with wide fractional bandwidth of the channels

Cloaking Using the Anisotropic Multilayer Sphere

We studied a Spherically Radially Anisotropic (SRA) multilayer sphere with an arbitrary number of layers. Within each layer permittivity components are different from each other in radial and tangential directions. Under the quasi-static approximation, we developed a more generalized mathematical model that can be used to calculate polarizability of the SRA multilayer sphere with any arbitrary number of layers. Moreover, the functionality of the SRA multilayer sphere as a cloak has been investigated. It has been shown that by choosing a suitable contrast between components of the permittivity, the SRA multilayer sphere can achieve threshold required for invisibility cloaking.