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The paper aims to propose several new approaches for the discrete‐time integration of stiff non‐linear differential equations.

The proposed approaches build on a method developed by the authors involving Padé approximates about each function sample. Both single‐ and multi‐step methods are suggested. The use of Richardson extrapolation is recommended for increasing efficiency.

The efficacy of the methods is shown using two examples and results are compared to a standard integration technique.

The paper shows that the methods are suitable for application in any field of science requiring efficient and accurate numerical solution of stiff differential equations.

To provide an efficient and accurate model for interconnect networks characterised by frequency‐domain scattering or admittance parameters. The parameters are derived from measurements or rigorous full‐wave simulation.

Initially, Hilbert transform relationships are enforced to ensure causality. A reverse Fourier series representation of the discrete data is then converted to the z‐domain and from this a state‐space formulation is determined. This enables the application of a judiciously chosen model reduction algorithm to obtain an efficient time‐domain representation of the network.

Sample results from both simulated and measured data indicate the efficacy of the proposed modelling strategy. For successful implementation of the strategy, it is necessary to employ the Hilbert transform to ensure that a causal impulse response is obtained.

The method is applicable to the interconnect networks for which the analytical models cannot be obtained due to the complexity and inhomogeneity of the geometries involved.

The work combines in a novel manner aspects from several existing techniques proposed for network simulation and model reduction. The end result is a highly efficient causal, stable and passive representation of the network in question for implementation in a time‐domain circuit simulator.

Radio-frequency circuits often possess a multi-rate behavior. Slow changing baseband signals and fast oscillating carrier signals often occur in the same circuit. Frequency modulated signals pose a particular challenge. The paper aims to discuss these issues.

The ordinary circuit differential equations are first rewritten by a system of (multi-rate) partial differential equations in order to decouple the different time scales. For an efficient simulation the paper needs an optimal choice of a frequency-dependent parameter. This is achieved by an additional smoothness condition.

By incorporating the smoothness condition into the discretization, the paper obtains a non-linear system of equations complemented by a minimization constraint. This problem is solved by a modified Newton method, which needs only little extra computational effort. The method is tested on a phase locked loop with a frequency modulated input signal.

A new optimal frequency sweep method was introduced, which will permit a very efficient simulation of multi-rate circuits.

The purpose of this paper is to analyse a novel technique for an efficient numerical approximation of systems of highly oscillatory ordinary differential equations (ODEs) that arise in electronic systems subject to modulated signals.

The paper combines a Filon‐type method with waveform relaxation techniques for nonlinear systems of ODEs.

The analysis includes numerical examples to compare with traditional methods such as the trapezoidal rule and Runge‐Kutta methods. This comparison shows that the proposed approach can be very effective when dealing with systems of highly oscillatory differential equations.

The present paper constitutes a preliminary study of Filon‐type methods applied to highly oscillatory ODEs in the context of electronic systems, and it is a starting point for future research that will address more general cases.

The proposed method makes use of novel and recent techniques in the area of highly oscillatory problems, and it proves to be particularly useful in cases where standard methods become expensive to implement.

The aim of this paper is to provide the theoretical conceptualization of a bandpass (BP) negative group delay (NGD) microstrip circuit. The main objective is to provide a theorization of the particular geometry of the microstrip circuit with experimental validation of the NGD effect.

The methodology followed in this work is organized in three steps. A theoretical model is established of equivalent S-parameters model using Y-matrix analysis. The GD analysis is also presented by showing that the circuit presents a possibility to generate NGD function around certain frequencies. To validate the theoretical model, as proof-of-concept (POC), a microstrip prototype is designed, fabricated and tested.

This work clearly highlighted the modelled (analytical design model), simulated (ADS simulation tool) and measured results are in good correlation. Relying on the proposed theoretical, numerical and experimental models, the BP NGD behaviour is validated successfully with GD responses specified by the NGD centre frequency: it is observed around 2.35 GHz, with an NGD value of about −2 ns.

It is to be noticed the proposed GD analysis requires limitations of the theoretical NGD model. It is depicted and validated through a POC demonstrating that the circuit presents a possibility to generate NGD function around certain frequencies (assuming constraints around usable frequency and bandwidth).

The NGD O-shape topology developed in this work could be exploited in the future in the microwave and radiofrequency context. Thus, it is expected to develop GD equalization technique for radiofrequency and microwave filters, GD compensation of oscillators, filters and communication systems, design of broadband switch-less bi-directional amplifiers, efficient enhancement of feedforward amplifiers, design method of frequency independent phase shifters with negligible delay, synthesis method of arbitrary-angle beamforming antennas. The BP NGD behavior may also be successfully used for the reduction of resonance effect for the electronic compatibility (EMC) of electronic devices.

The non-conventional NGD O-circuit theoretical development and validation through experimental POC could be exploited by academic and industrial developers in the area of wireless communications including, but not restricted to, 5-generation communication systems. The use of the remarkable NGD effect is also useful for the mitigation of electromagnetic interferences between electronic devices and more and more complex electromagnetic environment (current development of Internet of Things[ IoT]).

The originality of this work relies on the new NGD design proposed in this work including the extraction of S-matrix parameters of the microstrip novel structure designed. The validation process based upon an experimental POC showed very interesting levels of NGD O-circuit (nanosecond-GD duration).