Inductive Coupling Coefficients Research Articles

Generalized Theory of PT-Symmetric Radio-Frequency Systems With Divergent Exceptional Points

The emergence of exceptional point (EP) and its divergent form, so-called divergent EP (DEP), in parity-time (PT)-symmetric trimer opens a new pathway for making radio frequency (RF) telemetric sensor systems with unprecedented sensitivity. Here, we put forward a rigorous and formally exact analysis for PT -symmetric electronic multimers, shedding light on the lower bound of the inductive coupling coefficient required to achieve DEPs. One clear observation is that there exists a subtle compromise among the degree of diverging bifurcation, critical inductive coupling strength, and spectral noises arising from modal interferences. We conclude that an electronic PT -symmetric trimer, although not sufficient to work at the lowest inductive coupling strength, may be the simplest structure that enables the emergence of DEPs. Our findings may provide the theoretical underpinnings and open avenues for various RF telemetry and wireless sensing systems.

Comparative Study of Achievable Efficiency Between Three- and Four-Coil Wireless Power Transfer Systems

In magnetic resonant wireless power transfer (WPT), intermediate resonant coils (i-RCs) can be deployed between a transmitter and a receiver as a means of improving performance, but this entails a high additional cost. In the search for a cost-effective strategy for the use of additional components of WPT, we provide a comparative analysis of the achievable transmission efficiency (TE) between three-coil (3C) and four-coil (4C) systems. In particular, we find optimal control parameters, e.g., load resistance and inductive coupling coefficient, to derive the achievable TE for each system in closed-form expressions. In comparing the achievable TEs of the two systems, we also remark on the effective use of additional coils in two main ways. First, by optimizing the load resistance, the position of the i-RC is determined to be close to the transmitter or the receiver in a 3C system for improving the achievable TE depending on the strength difference between inductive and resonant couplings. Moreover, if the i-RC is placed near the transmitter, the 3C system shows the same achievable TE as the 4C system. Second, by optimizing the inductive coupling coefficient, the achievable TE of the 3C system is not affected by the location of the i-RC, whether it is placed nearer to the transmitter or the receiver, and the 4C system always outperforms the 3C system. Through a series of experiments conducted in a variety of environments, we verify both the validity of these observations and the accuracy of the theoretical analysis.

Choosing the Optimal Power Coils Using Open-Source k-Oriented Design Automation.

Wireless power coils have found important use in implantable medical devices for safe and reliable wireless power transfer. Designing coils for each specific application is a complex process with many interdependent design variables; determining the most optimal design parameters for each pair is challenging and time-consuming. In this paper, we develop an automated design method for planar square-spiral coils that generates the idealized design parameters for maximum power transfer efficiency according to the input design requirements. Computational complexity is first reduced by isolating the inductive coupling coefficient, k, from other design parameters. A simplified but accurate equivalent circuit model is then developed, where skin effect, proximity effect, and parasitic capacitive coupling are iteratively considered. The proposed method is implemented in an open-source software which accounts for the input fabrication limitations and application specific requirements. The accuracy of the estimated power transfer efficiency is validated via finite element method simulation. Using the presented approach, the coil design process is fully automated and can be done in few minutes.

High‐performance differentially fed coupled‐line directional couplers realised in inhomogeneous medium

In this study, a generalised approach for the design of high-performance differentially fed coupled-line directional couplers in inhomogeneous medium is presented for the first time. Conditions for the realisation of ideal coupled-line section under differential excitation are provided and it is shown that generally in such medium couplers feature different capacitive and inductive coupling coefficients, which significantly deteriorate circuits' performance. Therefore, the compensation technique is proposed allowing for equalisation of the differential coupling coefficients by adding appropriate compensating elements to the per-unit-length capacitance and inductance matrices of the coupled-line section. The proposed approach allows for realisation of quasi-ideal differential coupled-line couplers designed in arbitrarily chosen dielectric stack-up, and almost for arbitrarily chosen coupling. The provided theoretical analysis and resulting design methodology are verified experimentally with a 3-dB differential coupler operating at f 0 = 1.5 GHz and realised in suspended microstrip technique. Moreover, a combination of laminate and additive manufacturing technologies was used for higher design flexibility and low-cost manufacturing.

Pulse Train Controlled Single-Input Dual-Output Buck Converter With Coupled Inductors

The pulse train (PT) controlled switching dc/dc converters possess the benefits of simple structure, fast dynamic response, and good robustness. However, PT controlled converters also give the drawbacks of undesirable low-frequency oscillation phenomenon as operated in continuous conduction mode. In this paper, a single-input dual-output buck converter based on the coupled inductor is newly proposed with the ability to suppress the low-frequency oscillation. The inductor of the conventional buck converter is replaced by the primary side of the coupled inductor, and the secondary side of the coupled inductor connected in series with a diode is paralleled to a capacitor as an equivalent power source for the extra load. By rational allocation of inductance coupling coefficient and the equivalent power supply voltage, low-frequency oscillation of output voltage can be suppressed and the fast response speed is achieved. A hardware prototype of 48 V/16 V converter is built and tested to validate the practicability of the proposed converter.

Design of low-loss directional couplers with compensated coupled-line sections in suspended microstrip technique

Design of coupled line 3dB directional couplers realized in suspended microstrip technique has been presented. The main goal was to minimize the insertion losses of the coupler, what has been achieved by a proper choice of the realization technique. As the chosen coupled line geometry is asymmetric to achieve good electrical performance of the resulting coupler, capacitive compensation technique has been utilized to equalize capacitive and inductive coupling coefficients. Furthermore, a distributed-element approach has been investigated for realization of compensation capacitances, due to their physical size resulting from the dielectric structure. The proposed coupler has been designed in two versions, having center frequencies equal to 0.89 and 1.1 GHz, manufactured and measured. The measurement results show good agreement with electromagnetic analyses and prove the correctness and usefulness of the presented design method. The manufactured couplers exhibit insertion losses as low as 0.08 dB at the center frequency.

Numerical studies of the electromagnetic reciprocal influences of symmetric communication cable

The reciprocal influences between chains of symmetric communication cables is considered based on mathematical simulations of electromagnetic processes. It is assumed that the electric- and magnetic-field force lines are situated in the plane perpendicular to the cable axis and, therefore, the mathematical models describing the electric-potential distribution and components of the vector magnetic potential of alternating currents in a complex form can be presented in a two-dimensional setting. Differential equations written in the Cartesian coordinate system and describing the electric and magnetic potential distributions are solved by the finite-element method. The electromagnetic processes are studied numerically for the UTP Cat 5e LAN cable used in the structured cable networks. Such an approach allows one to determine electric- and magnetic-field distributions and calculate the coefficients of capacitive and inductive coupling in the cross section of a symmetric cable for a preset position of twisted pairs. The main way to reduce the reciprocal influences in unshielded symmetric communication cables is appropriate selection of twist pitches. The twist pitch in each chain should be chosen such that the integral of the capacitive and inductive coupling coefficients over a length of the symmetry section between all the cable chains tends to zero.

Theory of Image Impedance Matching for Inductively Coupled Power Transfer Systems

The optimum design of an inductively coupled power transfer system is accomplished by applying the Roberts's theory on conjugate image impedance. The input and output ports' impedance and the loading capacitances for maximum power transfer are obtained as functions of the self-inductances, the mutual inductance, the copper losses, and the iron loss, which are used to define the figure-of-merit of the system. It is found that the loading capacitances necessarily satisfy the resonance conditions individually in the input and output circuits. The capacitors may be connected in series or in parallel. The equivalent transform formulas between the series and parallel topologies are given for the capacitances and for the port impedances. The port impedance in the series (parallel) topology is proportional (approximately inversely proportional) to the inductive coupling coefficient. The image impedances of the lossless symmetric systems are real or pure imaginary depending on the frequency, and the image impedance patterns are classified as “Hill”, “Valley”, and “Waterfall". The reactance network approach for such lossless systems gives in-depth insight into the system behaviors and facilitates the practical design.

Approach to the Design of Asymmetric Coupled-Line Directional Couplers With the Maximum Achievable Impedance-Transformation Ratio

A novel approach to the design of asymmetric coupled-line impedance-transforming directional couplers with the maximum achievable impedance-transformation ratio is proposed. It is shown that the couplers in which one conductor is completely shielded from the other can be represented by two uncoupled transmission lines, which significantly simplifies the design procedure. Furthermore, the proposed approach of the directional couplers' analysis has been utilized for the derivation of a general condition describing the maximum impedance transformation ratio that can be achieved for directional couplers designed in inhomogeneous media. It has been also shown that impedance-transforming directional couplers, in which the capacitive coupling coefficient differs from the inductive coupling coefficient feature limited isolation, and that such couplers can be represented by two uncoupled lines having different electrical lengths. Subsequently, it has been shown that this isolation can be improved when the electrical lengths of the two uncoupled lines are equal, which corresponds to the equalization of capacitive and inductive coupling coefficients. The theoretical analyses have been confirmed by the measurements of two different 3-dB impedance-transforming directional couplers designed with the use of the proposed simplified approach.

Generalized Methods for the Design of Quasi-Ideal Symmetric and Asymmetric Coupled-Line Sections and Directional Couplers

Generalized methods for the design of quasi-ideal symmetric and asymmetric coupled-line sections have been proposed. Two cases of coupled-line sections, in which the inductive coupling coefficient is either greater or smaller than the capacitive coupling coefficient, have been separately considered. To compensate for the coupling coefficients' inequality, a combination of lumped capacitors and short coupled-line sections has been introduced into the coupled-line section. The proposed methods allow for designing quasi-ideal coupled-line sections in nearly arbitrarily chosen dielectric media and for arbitrarily chosen coupling. The theoretical analyses have been verified by the design and measurement of three compensated coupled-line directional couplers illustrating application of the proposed methods in different dielectric structures.

Number-Phase Quantization and Deriving Energy-Level Gap of Two LC Circuits with Mutual-Inductance

For two LC circuits with mutual-inductance, we introduce a new quantization scheme in the context of number-phase quantization through the standard Lagrangian formalism. The commutative relation between the charge operator and the magnetic flux operator is derived. Then we use the Heisenberg equation of motion to obtain the current and voltage equation across the inductance and capacity. The results clearly show how the current and voltage in a single LC circuit are affected by the circuit parameters and inductance coupling coefficient. In addition, adopting invariant eigen-operator method the energy-level gap of the dynamic Hamiltonian which describes two LC circuits with mutual-inductance is obtained.

Determination of the Parameters of High- T C RF SQUID from Its Small Signal Voltage-Frequency Characteristics

The present study is the extension of a recent theory of high-TC RF SQUIDs, operating in the presence of large thermal fluctuations. First, the explicit analytical expressions for the amplitudes of higher harmonics of the current circulating in a SQUID loop which are necessary for the determination of the junction critical current IC and the inductive coupling coefficient of the SQUID loop to its tank circuit, k2 , are found. Second, in order to find the junction resistance R with acceptable accuracy, the solution of Fokker–Plank equation to first order in parameter q = ωL/R, where ω is a bias frequency, L is a loop inductance, is obtained. These results allow one to derive the simple expressions for the determination of the junction critical current IC, its normal resistance R, and the inductive coupling coefficient of the SQUID loop to its tank circuit, k2 , from the experimental measured small signal voltage-frequency characteristics.

Quench development in superconducting cable having insulated strands with high resistive matrix. I. Experiment

The process of quench development in two- and six-strand cables was investigated in detail. Different types of quenches were found. The increase of the starting current level led to a change in the nature of the quench, from current redistribution, to a quench in all strands, to multi-quench with acceleration of the process from step to step, and to fast quench. Strand currents never achieved the critical current value under DC conditions. It is concluded that the cause of fast quench in AC cables is a specific mechanism of the electromagnetic development of quench. It is caused by a rapid redistribution of currents between the strands, which leads to a multi-quench process with acceleration of the normal zone propagation after each quench of the strand. The cause of the fast redistribution is the high inductive coupling coefficient between strands.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Normal-Mode Parameters of Microstrip Coupled Lines of Unequal Width (Short Paper)

Empirical relations for the capacitive and inductive coupling coefficients have been used to compute normal-mode parameters of non-identical microstrip coupled lines. The computed values of mode velocities and mode impedances are compared with available results from the literature and experimental results on nonidentical microstrip couplers to test the applicability of the empirical relations.

Empirical Relations for Capacitive and Inductive Coupling Coefficients of Coupled Microstrip Lines

Empirical relations for inductive and capacitive coupling coefficients are proposed. The functional relationships are based on the physical mechanism of coupling in microstrip lines. Values of coupling coefficients computed from even- and odd-mode impedances and phase velocities, available in the literature, are compared with those computed from the proposed relations. Microstrip couplers have been designed on the basis of coupling coefficients to meet the desired coupling and isolation.