One-dimensional Transmission Line Research Articles

An assessment of a conical horn waveguide to represent the human eardrum

This study examined a model of the acoustic input impedance of the ear that includes a waveguide model of the eardrum. The eardrum was modeled as a lossless conical-horn with rigid walls. The ear canal was modeled as a one-dimensional lossy transmission line. The output impedance of the eardrum, the middle ear, and the cochlea, was modeled as a circuit analog. The model was fit to acoustic input impedance data from human ears using a nonlinear least-squares fit. The impact of a conical-horn shape for the eardrum was quantified by comparison with the eardrum modeled as a near-flat surface. The model provided a good match to the data over the frequency range examined. A conical-horn model of the human eardrum provided gain at high frequencies, most notably above 1–2 kHz, with a broader middle-ear frequency response. This finding may suggest that eardrum shape plays an important role in sound transmission to the cochlea.

Self-induced topological protection in nonlinear circuit arrays

The interplay between topology and many-body physics has been a topic of strong interest in condensed matter physics for several years. For electronic systems, research has so far focused on linear topological phenomena due to the lack of a proper experimental platform and, in classical systems, due to the weak nature of nonlinear phenomena. Recently, it has been shown, however, that nonlinear effects can lead to unique phenomena, including self-induced topological states. Here we report nonlinear circuit arrays that exhibit self-induced topological protection. Our arrays are based on one-dimensional transmission-line circuits that emulate the Su–Schrieffer–Heeger model. We show that these nonlinear circuit arrays can exhibit self-induced topological transitions as a function of the input intensity, leading to topologically robust edge states that are immune to the presence of defects. The emergence of these topological states could lead to the design of electronic, optical and acoustic devices with functionalities that are highly tolerant to fabrication imperfections and unwanted parasitic effects. Nonlinear circuit arrays can exhibit self-induced topological transitions as a function of input intensity and topological immunity against defects and disorder.

PSpice Modeling of a Sandwich Piezoelectric Ceramic Ultrasonic Transducer in Longitudinal Vibration

Sandwiched piezoelectric transducers are widely used, especially in high power applications. For more convenient analysis and design, a PSpice lossy model of sandwiched piezoelectric ultrasonic transducers in longitudinal vibration is proposed by means of the one-dimensional wave and transmission line theories. With the proposed model, the resonance and antiresonance frequencies are obtained, and it is shown that the simulations and measurements have good consistency. For the purpose of further verification the accuracy and application of the PSpice model, a pitch-catch setup and an experimental platform are built. They include two sandwiched piezoelectric ultrasonic transducers and two aluminum cylinders whose lengths are 20 mm and 100 mm respectively. Based on this pitch-catch setup, the impedance and transient analysis are performed. Compared with the measured results, it is shown that the simulated results have good consistency. In addition, the conclusion can be drawn that the optimal excitation frequency for the pitch-catch setup is not necessarily the resonance frequency of ultrasonic transducers, because the resonance frequency is obtained under no load. The proposed PSpice model of the sandwiched piezoelectric transducer is more conveniently applied to combine with other circuits such as driving circuits, filters, amplifiers, and so on.

Photonic Kondo-like model

Here we introduce and study a photonic analogue of the Kondo model. The model is defined as a far detuned regime of photonic scattering off a three-level emitter in a $\Lambda$-type configuration coupled to a one-dimensional transmission line with linear dispersion. We characterize this system by studying the dynamics of a local system (emitter) driven by a coherent field pulse as well as the first- and second-order correlation functions of the scattered light. Various polarization-dependent correlation effects including entanglement between the emitter and transmitted photons are quantified by the purity of the emitter's state. We also show that statistical properties of the scattered light are very sensitive to the polarization of the incoming coherent pulse.

Two‐dimensional distributed amplifier by 2D‐LC lattice

In this study a new configuration for distributed amplifiers (DAs) is presented for the first time. Using two-dimensional (2D) LC lattices instead of one-dimensional transmission lines leads to 2D wave propagation. This configuration can cover the traditional problem of increasing conventional DA stages by decreasing the distance of power sources to the load. This new additive gain mechanism uses an electrical funnel to add the drain powers. Gain and noise relations are extracted and a broad band, high gain, low noise DA with reasonable DC power consumption is designed. Circuit layout is presented and all inductors and connections are simulated by advanced design system electromagnetic simulator with TSMC 0.18 CMOS layout specifications. Good agreements between post layout simulation results and the presented relations are achieved. The final design shows a 21.8 dB gain along 0.7 to 43.9 GHz band width. The circuit consumes only 183 mw DC power and it shows noise figure less than 7.8 dB. The output power of this circuit at 1-dB output compression point (OP1dB) is more than 8.1 dBm. The proposed technique yields excellent performance in comparison with other design techniques.

Inductive intrinsic localized modes in a one-dimensional nonlinear electric transmission line.

The experimental properties of intrinsic localized modes (ILMs) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest-neighbor intersite potentials. Here it is shown for a one-dimensional lumped electrical transmission line that a nonlinear inductive component in an otherwise linear parallel capacitor lattice makes possible a new kind of ILM outside the plane wave spectrum. To simplify the analysis, the nonlinear inductive current equations are transformed to flux transmission line equations with analog onsite hard potential nonlinearities. Approximate analytic results compare favorably with those obtained from a driven damped lattice model and with eigenvalue simulations. For this mono-element lattice, ILMs above the top of the plane wave spectrum are the result. We find that the current ILM is spatially compressed relative to the corresponding flux ILM. Finally, this study makes the connection between the dynamics of mass and force constant defects in the harmonic lattice and ILMs in a strongly anharmonic lattice.

Crosstalk-insensitive method for simultaneously coupling multiple pairs of resonators

In a circuit consisting of two or more resonators, the inter-cavity crosstalk is inevitable, which could create some problems, such as degrading the performance of quantum operations and the fidelity of various quantum states. The focus of this work is to propose a crosstalk-insensitive method for simultaneously coupling multiple pairs of resonators, which is important in large-scale quantum information processing and communication in a network consisting of resonators or cavities. In this work, we consider 2N resonators of different frequencies, which are coupled to a three-level quantum system (qutrit). By applying a strong pulse to the coupler qutrit, we show that an effective Hamiltonian can be constructed for simultaneously coupling multiple pairs of resonators.~The main advantage of this proposal is that the effect of inter-resonator crosstalks is greatly suppressed by using resonators of different frequencies. In addition, by employing the qutrit-resonator dispersive interaction, the intermediate higher-energy level of the qutrit is virtually excited and thus decoherence from this level is suppressed. This effective Hamiltonian can be applied to implement quantum operations with photonic qubits distributed in different resonators. As one application of this Hamiltonian, we show how to simultaneously generate multiple EPR pairs of photonic qubits distributed in 2N resonators. Numerical simulations show that it is feasible to prepare two high-fidelity EPR photonic pairs using a setup of four one-dimensional transmission line resonators coupled to a superconducting flux qutrit with current circuit QED technology.

Digital filter-based 1D TLM model of dispersive anisotropic conductivity panel

One-dimensional (1D) Transmission Line Matrix (TLM) method with Z-transforms, is applied in the paper to allow for an efficient time-domain simulation of thin anisotropic conductive panel of dispersive behavior. It uses a digital filter model to incorporate the scattering coefficients of the panel at two TLM cells interface in order to avoid a fine meshing of panel thickness. Model validation is done for a panel made of carbon-fibre material whose electric conductivity is anisotropic and assumed to be frequency dependent according to the Drude model. Fine TLM mesh results are used to verify the model accuracy.

Wave propagation in two‐dimensional left‐handed non‐linear transmission line metamaterials

Recent research on harmonic generations in one-dimensional (1D) left-handed non-linear transmission line (LH NLTL) metamaterials has shown that the fundamental wave and its higher harmonics can realise quasi-phase matching, which in turn ensures the high conversion efficiency of the harmonics. In this study, the authors first present the electromagnetic (EM) theory to describe the generation and propagation of both second-harmonic (SH) and third-harmonic (TH) waves in a 2D non-linear transmission line metamaterial. Then, with the aid of the microwave circuit simulations, they fabricate a 2D LH NLTL metamaterial and demonstrate that an EM wave propagation in such medium has three states: left-handed (LH), right-handed (RH), and non-propagation. Furthermore, the response of the medium to applied field intensity shows that it can realise self-tuning between LH and RH states for the TH waves.

P-Spice Modeling Three-Dimensional Propagation of Ultrasound Diffraction Considering a Gaussian Beam Approach

In this paper, we propose a new method for simulating three-dimensional (3D) ultrasonic wave propagation using P-Spice like simulator. We use a one-dimensional transmission line model to implement the diffraction losses. In order to simulate the beam pattern considering axial and radial orientations, we calculate the diffraction losses in 3D space. First, we express the radiated field using a set of Gaussian beams. Calculating the average pressure over the receiver surface allows us to determine the diffraction losses. These losses are then incorporated into the P-Spice model via the G parameter which is axial and radial orientations dependent. Comparison between P-Spice simulation and analytical model results shows good agreements.

Analytical study of dynamics of matter-wave solitons in lossless nonlinear discrete bi-inductance transmission lines

We consider a lossless one-dimensional nonlinear discrete bi-inductance electrical transmission line made of N identical unit cells. When lattice effects are considered, we use the reductive perturbation method in the semidiscrete limit to show that the dynamics of modulated waves can be modeled by the classical nonlinear Schrödinger (CNLS) equation, which describes the modulational instability and the propagation of bright and dark solitons on a continuous-wave background. Our theoretical analysis based on the CNLS equation predicts either two or four frequency regions with different behavior concerning the modulational instability of a plane wave. With the help of the analytical solutions of the CNLS equation, we investigate analytically the effects of the linear capacitance CS on the dynamics of matter-wave solitons in the network. Our results reveal that the linear parameter CS can be used to manipulate the motion of bright, dark, and kink soliton in the network.

Mathematical solutions of comprehensive variations of a transmission-line model of the theoretical impedance of porous electrodes

Mathematical solutions were obtained for the impedance of one-dimensional transmission-line (TML) models with all possible variations of the boundary conditions and connections to an external circuit. First, three types of connection (Z-type, T-type, and E-type) were considered. A more generalized connection that includes the characteristics of both Z-type and T-type (universal-type) was also considered. All four of the resulting general solutions were versatile, but quite complicated. Next, comprehensive variations of the general solutions depending on specific boundary conditions, which are generally simpler, were also considered. Finally, an equivalent transform from a three-terminal TML model to a simple Y-circuit was calculated. This enables calculation of the serial connection of multiple TML models with different parameters, which represents a multi-layered electrode.

The -type four-particle entangled state generated by using superconducting artificial atoms with broken symmetry

We propose a scheme for generating a genuine -type four-particle entangled state of superconducting artificial atoms with broken symmetry by using one-dimensional transmission line resonator as a data bus. With the help of the Circuit quantum electrodynamics system composed of -type three-level artificial atoms and transmission line resonator, our scheme also has long coherence time and storage time. Meanwhile, the -type three-level artificial atom used in the scheme is different from natural atom and has cyclic transitions. Furthermore, our scheme is easy to control and flexible. Through a suitable choice of the Rabi frequencies and detunings of the classical fields, we can use this system to implement the selective coupling between two arbitrary qubits. After suitable interaction time and simple operations, the desired entangled state can be obtained. Since artificial atomic excited states and photonic states are adiabatically eliminated, our scheme is robust against the spontaneous emissions of artificial atoms and the decays of transmission line resonator. We also analyze the performance and the experimental feasibility of the scheme, and show that our scheme is feasible under existing experimental conditions.

Scattering of two photons from two distant qubits: exact solution.

We consider the inelastic scattering of two photons from two qubits separated by an arbitrary distance R and coupled to a one-dimensional transmission line. We present an exact, analytical solution to the problem, and use it to explore a particular configuration of qubits that is transparent to single-photon scattering, thus highlighting non-Markovian effects of inelastic two-photon scattering: strong two-photon interference and momentum dependent photon (anti)bunching. This latter effect can be seen as an inelastic generalization of the Hong-Ou-Mandel effect.

Generating multipartite entangled states of qubits distributed in different cavities

Cavity-based large-scale quantum information processing (QIP) needs a large number of qubits and placing all of them in a single cavity quickly runs into many fundamental and practical problems such as the increase of cavity decay rate and decrease of qubit-cavity coupling strength. Therefore, future QIP most likely will require quantum networks consisting of a large number of cavities, each hosting and coupled to multiple qubits. In this work, we propose a way to prepare a $W$-class entangled state of spatially-separated multiple qubits in different cavities, which are connected to a coupler qubit. Because no cavity photon is excited, decoherence caused by the cavity decay is greatly suppressed during the entanglement preparation. This proposal needs only one coupler qubit and one operational step, and does not require using a classical pulse, so that the engineering complexity is much reduced and the operation is greatly simplified. As an example of the experimental implementation, we further give a numerical analysis, which shows that high-fidelity generation of the $W$ state using three superconducting phase qubits each embedded in a one-dimensional transmission line resonator is feasible within the present circuit QED technique. The proposal is quite general and can be applied to accomplish the same task with other types of qubits such as superconducting flux qubits, charge qubits, quantum dots, nitrogen-vacancy centers and atoms.

INHOMOGENEOUS MICROWAVE LENS BASED ON PERIODICALLY LOADED TRANSMISSION LINES

A new design for a low-re∞ection inhomogeneous microwave lens based on periodically loaded one-dimensional transmission lines is proposed and experimentally tested. The inhomogeneous efiective refractive index of this ∞at-proflle lens is achieved by loading the transmission lines comprising the lens with difierent inductive elements.

Entanglement generation and quantum information transfer between spatially-separated qubits in different cavities

The generation and control of quantum states of spatially-separated qubits distributed in different cavities constitute fundamental tasks in cavity quantum electrodynamics (QED). An interesting question in this context is how to prepare entanglement and realize quantum information transfer between qubits located at different cavities, which are important in large-scale quantum information processing. In this paper, we consider a physical system consisting of two cavities and three qubits. Two of the qubits are placed in two different cavities while the remaining one acts as a coupler, which is used to connect the two cavities. We propose an approach for generating quantum entanglement and implementing quantum information transfer between the two spatially-separated inter-cavity qubits. The quantum operations involved in this proposal are performed by a virtual photon process; thus the cavity decay is greatly suppressed during operations. In addition, to complete these tasks, only one coupler qubit and one operation step are needed. Moreover, there is no need to apply classical pulses, so that the engineering complexity is much reduced and the operation procedure is greatly simplified. Finally, our numerical results illustrate that high-fidelity implementation of this proposal using superconducting phase qubits and one-dimensional transmission line resonators is feasible for current circuit QED implementations. This proposal can also be applied to other types of superconducting qubits, including flux and charge qubits.

Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms

We study the collective effects that emerge in waveguide quantum electrodynamics where several (artificial) atoms are coupled to a one-dimensional superconducting transmission line. Since single microwave photons can travel without loss for a long distance along the line, real and virtual photons emitted by one atom can be reabsorbed or scattered by a second atom. Depending on the distance between the atoms, this collective effect can lead to super- and subradiance or to a coherent exchange-type interaction between the atoms. Changing the artificial atoms transition frequencies, something which can be easily done with superconducting qubits (two levels artificial atoms), is equivalent to changing the atom-atom separation and thereby opens the possibility to study the characteristics of these collective effects. To study this waveguide quantum electrodynamics system, we extend previous work and present an effective master equation valid for an ensemble of inhomogeneous atoms driven by a coherent state. Using input-output theory, we compute analytically and numerically the elastic and inelastic scattering and show how these quantities reveal information about collective effects. These theoretical results are compatible with recent experimental results using transmon qubits coupled to a superconducting one-dimensional transmission line [A.~F.~van Loo {\it et al.}].

An Analysis of the Acoustic Input Impedance of the Ear

Ear canal acoustics was examined using a one-dimensional lossy transmission line with a distributed load impedance to model the ear. The acoustic input impedance of the ear was derived from sound pressure measurements in the ear canal of healthy human ears. A nonlinear least squares fit of the model to data generated estimates for ear canal radius, ear canal length, and quantified the resistance that would produce transmission losses. Derivation of ear canal radius has application to quantifying the impedance mismatch at the eardrum between the ear canal and the middle ear. The length of the ear canal was found, in general, to be longer than the length derived from the one-quarter wavelength standing wave frequency, consistent with the middle ear being mass-controlled at the standing wave frequency. Viscothermal losses in the ear canal, in some cases, may exceed that attributable to a smooth rigid wall. Resistance in the middle ear was found to contribute significantly to the total resistance. In effect, this analysis "reverse engineers" physical parameters of the ear from sound pressure measurements in the ear canal.

Generation place of the long- and short-latency components of transient-evoked otoacoustic emissions in a nonlinear cochlear model

Time-domain numerical solutions of a nonlinear active cochlear model forced by click stimuli are analyzed with a time-frequency wavelet technique to identify the components of the otoacoustic response associated with different generation mechanisms/places. Previous experimental studies have shown evidence for the presence of at least two components in the transient otoacoustic response: A long-latency response, growing compressively with increasing stimulus level, and a shorter-latency response, characterized by faster growth. The possible mechanisms for the generation of the two components are discussed using the results of the numerical simulations. The model is a one-dimensional (1-D) transmission line model with nonlinear and nonlocal active terms representing the anti-damping action of the "cochlear amplifier." The dependence on the stimulus level of latency and level was measured for the different components of the response. The generation mechanisms/places of the different components were identified by varying the stimulus level and by turning off the cochlear roughness in well-defined cochlear regions. The results suggest that reflections from roughness coming from basal regions of the cochlea may give a relevant contribution to the early otoacoustic response, whereas nonlinear mechanisms seem to produce a much smaller additional contribution.