Linear circuit

Summary

A linear circuit is an electronic circuit which obeys the superposition principle. This means that the output of the circuit F(x) when a linear combination of signals ax1(t) + bx2(t) is applied to it is equal to the linear combination of the outputs due to the signals x1(t) and x2(t) applied separately: :F(ax_1 + bx_2) = aF(x_1) + bF(x_2), It is called a linear circuit because the output voltage and current of such a circuit are linear functions of its input voltage and current. This kind of linearity is not the same as that of straight-line graphs. In the common case of a circuit in which the components' values are constant and don't change with time, an alternate definition of linearity is that when a sinusoidal input voltage or current of frequency f is applied, any steady-state output of the circuit (the current through any component, or the voltage between any two points) is also sinusoidal with frequency f. A linear circuit with constant

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https://en.wikipedia.org/wiki/Linear_circuit

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Compact, spatial-mode-interaction-free, ultralow-loss, nonlinear photonic integrated circuits

Jijun He, Xinru Ji, Tobias Kippenberg, Junqiu Liu, Zheru Qiu, Rui Ning Wang

Multi-mode waveguides are ubiquitously used in integrated photonics. Although interaction among different spatial waveguide eigenmodes can induce novel nonlinear phenomena, spatial mode interaction is typically undesired. Adiabatic bends, such as Euler bends, have been favoured to suppress spatial mode interaction. Here, we adapt and optimize Euler bends to build compact racetrack microresonators based on ultralow-loss, multi-mode, silicon nitride photonic integrated circuits. The racetrack microresonators feature a footprint of only 0.21 mm(2) for 19.8 GHz free spectral range, suitable for tight photonic integration. We quantitatively investigate the suppression of spatial mode interaction in the racetrack microresonators with Euler bends. We show that the low optical loss rate (15.5 MHz) is preserved, on par with the mode interaction strength (25 MHz). This results in an unperturbed microresonator dispersion profile. We further generate a single dissipative Kerr soliton of 19.8 GHz repetition rate without complex laser tuning schemes or auxiliary lasers. The optimized Euler bends and racetrack microresonators can be building blocks for integrated nonlinear photonic systems, as well as linear circuits for programmable processors or photonic quantum computing. Adiabatic bends are used to reduce the optical loss of waveguides for integrated optics, but quantitative analysis of their adiabaticity have not been reported. Here, racetrack microresonators with circular and Euler bends are compared quantitatively, showing that the adiabatic Euler bends can preserve low optical loss and avoid spatial mode interaction in multimode waveguides.

NATURE PORTFOLIO2022

, ,

We report the development of the frequency-modulation (FM) method for measuring electron spin resonance (ESR) absorption in the 210- to 420 GHz frequency range. We demonstrate that using a high-frequency ESR spectrometer without resonating microwave components enables us to overcome technical difficulties associated with the FM method due to nonlinear microwave-elements, without sacrificing spectrometer performance. FM was achieved by modulating the reference oscillator of a 13 GHz Phase-Locked Dielectric Resonator Oscillator, and amplifying and frequency-multi plying the resulting millimeter-wave radiation up to 210, 315 and 420 GHz. ESR spectra were obtained in reflection mode by a lock-in detection at the fundamental modulation frequency, and also at the second and third harmonic. Sensitivity of the setup was verified by conduction electron spin resonance measurement in KC60. (c) 2008 Elsevier Inc. All rights reserved.

2008

Computing upper and lower bounds for linear outputs of elasticity by the smoothed finite element method

Toni Mikael Lassila, Alfio Quarteroni, Gianluigi Rozza

Verification of the computation of local quantities of interest, e.g. the displacements at a point, the stresses in a local area and the stress intensity factors at crack tips, plays an important role in improving the structural design for safety. In this paper, the smoothed finite element method (SFEM) is used for finding upper and lower bounds on the local quantities of interest that are outputs of the displacement field for linear elasticity problems, based on bounds on strain energy in both the primal and dual problems. One important feature of SFEM is that it bounds the strain energy of the structure from above without needing the solutions of different subproblems that are based on elements or patches but only requires the direct finite element computation. Upper and lower bounds on two linear outputs and one quadratic output related with elasticity – the local reaction, the local displacement, and the J-integral – are computed by the proposed method in two different examples. Some issues with SFEM that remain to be resolved are also discussed.

2010