With soaring work frequency and decreasing feature sizes, VLSI circuits with RLC parasitic components are more like analog circuits and should be carefully analyzed in physical design. However, the number of extracted...With soaring work frequency and decreasing feature sizes, VLSI circuits with RLC parasitic components are more like analog circuits and should be carefully analyzed in physical design. However, the number of extracted RLC components is typically too large to be analyzed efficiently by using present analog circuit simulators like SPICE. In order to speedup the simulations without error penalty, this paper proposes a novel methodology to compress the time-descritized circuits resulted from numerical integration approximation at every time step. The main contribution of the methodology is the efficient structure-level compression of DC circuits containing many current sources, which is an important complement to present circuit analysis theory. The methodology consists of the following parts： 1） An approach is proposed to delete all intermediate nodes of RL branches. 2） An efficient approach is proposed to compress and back-solve parallel and serial branches so that it is error-free and of linear complexity to analyze circuits of tree topology. 3） The Y to πtransformation method is used to error-free reduce and back-solve the intermediate nodes of ladder circuits with the linear complexity. Thus, the whole simulation method is very accurate and of linear complexity to analyze circuits of chain topology. Based on the methodology, we propose several novel algorithms for efficiently solving RLC-model transient power/ground （P/G） networks. Among them, EQU-ADI algorithm of linear-complexity is proposed to solve RLC P/G networks with mesh-tree or mesh-chain topologies. Experimental results show that the proposed method is at least two orders of magnitude faster than SPICE while it can scale linearly in both time- and memory-complexity to solve very large P/G networks.展开更多
In this paper,we propose an RLC equivalent circuit model theory which can accurately predict the spectral response and resonance characteristics of metamaterial absorption structures,extend its design,and characterize...In this paper,we propose an RLC equivalent circuit model theory which can accurately predict the spectral response and resonance characteristics of metamaterial absorption structures,extend its design,and characterize the parameters of the model in detail.By employing this model,we conducted computations to characterize the response wavelength and bandwidth of variously sized metamaterial absorbers.A comparative analysis with Finite Difference Time Domain(FDTD)simulations demonstrated a remarkable level of consistency in the results.The designed absorbers were fabricated using micro-nano fabrication processes,and were experimentally tested to demonstrate absorption rates exceeding 90%at a wavelength of 9.28μm.The predicted results are then compared with test results.The comparison reveals good consistency in two aspects of the resonance responses,thereby confirming the rationality and accuracy of this model.展开更多
In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for ...In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.展开更多
According to the physical mechanism of the generation of the resistance or the electron phonon interaction, a new method is proposed to quantize the RLC electric circuit. Calculations show that the quantum fluctuatio...According to the physical mechanism of the generation of the resistance or the electron phonon interaction, a new method is proposed to quantize the RLC electric circuit. Calculations show that the quantum fluctuations under this new quantization are smaller than those by the traditional effective Hamiltonian method. And squeezed states can be generated if the inductance and capacity are time dependent. Meanwhile, the shortcoming of the traditional method that the electric charge and current will vanish in the long time limit is overcome.展开更多
Based on the scheme of damped harmonic oscillator quantization and thermo-field dynamics （TFD）, the quantization of mesoscopic damped double resonance RLC circuit with mutual capacitance-inductance coupling is propo...Based on the scheme of damped harmonic oscillator quantization and thermo-field dynamics （TFD）, the quantization of mesoscopic damped double resonance RLC circuit with mutual capacitance-inductance coupling is proposed. The quantum fluctuations of charge and current of each loop in a squeezed vacuum state are studied in the thermal excitation case. It is shown that the fluctuations not only depend on circuit inherent parameters, but also rely on excitation quantum number and squeezing parameter. Moreover, due to the finite environmental temperature and damped resistance, the fluctuations increase with the temperature rising, and decay with time.展开更多
By virtue of the generalized Hellmann-Feynman theorem for the ensemble average, we obtain the internal energy and average energy consumed by the resistance R in a quantized resistance-inductance-capacitance （RLC） el...By virtue of the generalized Hellmann-Feynman theorem for the ensemble average, we obtain the internal energy and average energy consumed by the resistance R in a quantized resistance-inductance-capacitance （RLC） electric circuit. We also calculate the entropy-variation with R. The relation between entropy and R is also derived. By the use of figures we indeed see that the entropy increases with the increment of R.展开更多
Based on the maximum entropy principle, we present a density matrix of mesoscopic RLC circuit to make it possible to analyze the connection of the initial condition with temperature. Our results show that the quantum ...Based on the maximum entropy principle, we present a density matrix of mesoscopic RLC circuit to make it possible to analyze the connection of the initial condition with temperature. Our results show that the quantum state evolution is closely related to the initial condition, and that the system evolves to generalized coherent state if it is in ground state initially, and evolves to squeezed state if it is in excited state initially.展开更多
With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamilt...With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamiltonian operator is obtained. Then the evolution of the charge number and phase difference across the capacity are obtained. It is shown that the number-phase analysis is useful to tackle the quantization of some mesoscopic circuits and dynamical equations of the corresponding operators.展开更多
The invariants for a mesoscopic RLC circuit with a power source are studied and used to construct the squeezed states and squeezed number states for the system. The quantum fluctuations of the mesoscopic RLC circuit i...The invariants for a mesoscopic RLC circuit with a power source are studied and used to construct the squeezed states and squeezed number states for the system. The quantum fluctuations of the mesoscopic RLC circuit in the squeezed states and squeezed number states are also investigated.展开更多
Using the path integral method we derive quantum wave function and quantum fluctuations of charge andcurrent in the mesoscopic RLC circuit. We find that the quantum fluctuation of charge decreases with time, oppositel...Using the path integral method we derive quantum wave function and quantum fluctuations of charge andcurrent in the mesoscopic RLC circuit. We find that the quantum fluctuation of charge decreases with time, oppositely,the quantum fluctuation of current increases with time monotonously. Therefore there is a squeezing effect in the circuit.If some more charge devices are used in the mesoscopic-damped circuit, the quantum noise can be reduced. We also findthat uncertainty relation of charge and current periodically varies with the period π/2 in the under-damped case.展开更多
This paper presents an efficient algorithm for reducing RLC power/ground network complexities by exploitation of the regularities in the power/ground networks. The new method first builds the equivalent models for man...This paper presents an efficient algorithm for reducing RLC power/ground network complexities by exploitation of the regularities in the power/ground networks. The new method first builds the equivalent models for many series RLC-current chains based on their Norton＇s form companion models in the original networks,and then the precondition conjugate gradient based iterative method is used to solve the reduced networks,which are symmetric positive definite. The solutions of the original networks are then back solved from those of the reduced networks.Experimental results show that the complexities of reduced networks are typically significantly smaller than those of the original circuits, which makes the new algorithm extremely fast. For instance, power/ground networks with more than one million branches can be solved in a few minutes on modern Sun workstations.展开更多
A convenient method to exactly solve the quantum-nonautonomous systems with non-Hermitian Hamiltonians is proposed. It is shown that a nonadiabatic complete biorthonormal set can be easily obtained by the gauge transf...A convenient method to exactly solve the quantum-nonautonomous systems with non-Hermitian Hamiltonians is proposed. It is shown that a nonadiabatic complete biorthonormal set can be easily obtained by the gauge transformation method in which the algebraic structure of systems has been used. The nonunitary evolution operator is also found by choosing a special gauge function. All auxiliary parameters introduced in the present approach are only determined by some algebraic equations. The dynamics of two quantum-nonautonomous systems ruled by non-Hermitian Hamiltonians, including a two-photon ionization process involving two-state only and a mesoscopic RLC circuit with a source, are treated as the demonstration of our general approach.展开更多
Through-silicon vias （TSVs） have provided an attractive solution for three-dimensional （3D） integrated devices and circuit technologies with reduced parasitic losses and power dissipation, higher input-output （I/...Through-silicon vias （TSVs） have provided an attractive solution for three-dimensional （3D） integrated devices and circuit technologies with reduced parasitic losses and power dissipation, higher input-output （I/O） den- sity and improved system performance. This paper investigates the propagation delay and average power dissipation of single-walled carbon nanotube bundled TSVs having different via radius and height. Depending on the physical configuration, a comprehensive and accurate analytical model of CNT bundled TSV is employed to represent the via （vertical interconnect access） line of a driver-TSV-load （DTL） system. The via radius and height are used to estimate the bundle aspect ratio （AR） and the cross-sectional area. For a fixed via height, the delay and the power dissipation are reduced up to 96.2% using a SWCNT bundled TSV with AR = 300 ： 1 in comparison to AR = 6：1.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.60476014)the State"973"Key Basic Research Program(Grant No.2005CB321604)the UC Senate Research Fund.
文摘With soaring work frequency and decreasing feature sizes, VLSI circuits with RLC parasitic components are more like analog circuits and should be carefully analyzed in physical design. However, the number of extracted RLC components is typically too large to be analyzed efficiently by using present analog circuit simulators like SPICE. In order to speedup the simulations without error penalty, this paper proposes a novel methodology to compress the time-descritized circuits resulted from numerical integration approximation at every time step. The main contribution of the methodology is the efficient structure-level compression of DC circuits containing many current sources, which is an important complement to present circuit analysis theory. The methodology consists of the following parts： 1） An approach is proposed to delete all intermediate nodes of RL branches. 2） An efficient approach is proposed to compress and back-solve parallel and serial branches so that it is error-free and of linear complexity to analyze circuits of tree topology. 3） The Y to πtransformation method is used to error-free reduce and back-solve the intermediate nodes of ladder circuits with the linear complexity. Thus, the whole simulation method is very accurate and of linear complexity to analyze circuits of chain topology. Based on the methodology, we propose several novel algorithms for efficiently solving RLC-model transient power/ground （P/G） networks. Among them, EQU-ADI algorithm of linear-complexity is proposed to solve RLC P/G networks with mesh-tree or mesh-chain topologies. Experimental results show that the proposed method is at least two orders of magnitude faster than SPICE while it can scale linearly in both time- and memory-complexity to solve very large P/G networks.
基金Supported by the National Natural Science Foundation of China(62174092)the Open Fund of State Key Laboratory of Infrared Physics(SITP-NLIST-ZD-2023-04)the Strategic Priority Research Program of the Chinese Academy of Sciences(XDB0580000)。
文摘In this paper,we propose an RLC equivalent circuit model theory which can accurately predict the spectral response and resonance characteristics of metamaterial absorption structures,extend its design,and characterize the parameters of the model in detail.By employing this model,we conducted computations to characterize the response wavelength and bandwidth of variously sized metamaterial absorbers.A comparative analysis with Finite Difference Time Domain(FDTD)simulations demonstrated a remarkable level of consistency in the results.The designed absorbers were fabricated using micro-nano fabrication processes,and were experimentally tested to demonstrate absorption rates exceeding 90%at a wavelength of 9.28μm.The predicted results are then compared with test results.The comparison reveals good consistency in two aspects of the resonance responses,thereby confirming the rationality and accuracy of this model.
基金Taif University Researchers Supporting Project number(TURSP-2020/275),Taif University,Taif,Saudi Arabia.
文摘In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.
文摘According to the physical mechanism of the generation of the resistance or the electron phonon interaction, a new method is proposed to quantize the RLC electric circuit. Calculations show that the quantum fluctuations under this new quantization are smaller than those by the traditional effective Hamiltonian method. And squeezed states can be generated if the inductance and capacity are time dependent. Meanwhile, the shortcoming of the traditional method that the electric charge and current will vanish in the long time limit is overcome.
基金Project supported by the Natural Science Foundation of Heze University of Shandong Province, China （Grant No XY05WL01）, the University Experimental Technology Foundation of Shandong Province, China （Grant No S04W138）, the Natural Science Foundation of Shandong Province, China （Grant No Y2004A09） and the National Natural Science Foundation of China （Grant No 10574060）.
文摘Based on the scheme of damped harmonic oscillator quantization and thermo-field dynamics （TFD）, the quantization of mesoscopic damped double resonance RLC circuit with mutual capacitance-inductance coupling is proposed. The quantum fluctuations of charge and current of each loop in a squeezed vacuum state are studied in the thermal excitation case. It is shown that the fluctuations not only depend on circuit inherent parameters, but also rely on excitation quantum number and squeezing parameter. Moreover, due to the finite environmental temperature and damped resistance, the fluctuations increase with the temperature rising, and decay with time.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10775097 and 10874174)the Research Foundation of the Education Department of Jiangxi Province of China (Grant No.GJJ10097)
文摘By virtue of the generalized Hellmann-Feynman theorem for the ensemble average, we obtain the internal energy and average energy consumed by the resistance R in a quantized resistance-inductance-capacitance （RLC） electric circuit. We also calculate the entropy-variation with R. The relation between entropy and R is also derived. By the use of figures we indeed see that the entropy increases with the increment of R.
基金Open Fund of Jiangxi Center of Test and Control Engineering
文摘Based on the maximum entropy principle, we present a density matrix of mesoscopic RLC circuit to make it possible to analyze the connection of the initial condition with temperature. Our results show that the quantum state evolution is closely related to the initial condition, and that the system evolves to generalized coherent state if it is in ground state initially, and evolves to squeezed state if it is in excited state initially.
文摘With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamiltonian operator is obtained. Then the evolution of the charge number and phase difference across the capacity are obtained. It is shown that the number-phase analysis is useful to tackle the quantization of some mesoscopic circuits and dynamical equations of the corresponding operators.
基金The project supported by National Natural Science Foundation of China under Grant No.10174066
文摘The invariants for a mesoscopic RLC circuit with a power source are studied and used to construct the squeezed states and squeezed number states for the system. The quantum fluctuations of the mesoscopic RLC circuit in the squeezed states and squeezed number states are also investigated.
文摘Using the path integral method we derive quantum wave function and quantum fluctuations of charge andcurrent in the mesoscopic RLC circuit. We find that the quantum fluctuation of charge decreases with time, oppositely,the quantum fluctuation of current increases with time monotonously. Therefore there is a squeezing effect in the circuit.If some more charge devices are used in the mesoscopic-damped circuit, the quantum noise can be reduced. We also findthat uncertainty relation of charge and current periodically varies with the period π/2 in the under-damped case.
文摘This paper presents an efficient algorithm for reducing RLC power/ground network complexities by exploitation of the regularities in the power/ground networks. The new method first builds the equivalent models for many series RLC-current chains based on their Norton＇s form companion models in the original networks,and then the precondition conjugate gradient based iterative method is used to solve the reduced networks,which are symmetric positive definite. The solutions of the original networks are then back solved from those of the reduced networks.Experimental results show that the complexities of reduced networks are typically significantly smaller than those of the original circuits, which makes the new algorithm extremely fast. For instance, power/ground networks with more than one million branches can be solved in a few minutes on modern Sun workstations.
文摘A convenient method to exactly solve the quantum-nonautonomous systems with non-Hermitian Hamiltonians is proposed. It is shown that a nonadiabatic complete biorthonormal set can be easily obtained by the gauge transformation method in which the algebraic structure of systems has been used. The nonunitary evolution operator is also found by choosing a special gauge function. All auxiliary parameters introduced in the present approach are only determined by some algebraic equations. The dynamics of two quantum-nonautonomous systems ruled by non-Hermitian Hamiltonians, including a two-photon ionization process involving two-state only and a mesoscopic RLC circuit with a source, are treated as the demonstration of our general approach.
文摘Through-silicon vias （TSVs） have provided an attractive solution for three-dimensional （3D） integrated devices and circuit technologies with reduced parasitic losses and power dissipation, higher input-output （I/O） den- sity and improved system performance. This paper investigates the propagation delay and average power dissipation of single-walled carbon nanotube bundled TSVs having different via radius and height. Depending on the physical configuration, a comprehensive and accurate analytical model of CNT bundled TSV is employed to represent the via （vertical interconnect access） line of a driver-TSV-load （DTL） system. The via radius and height are used to estimate the bundle aspect ratio （AR） and the cross-sectional area. For a fixed via height, the delay and the power dissipation are reduced up to 96.2% using a SWCNT bundled TSV with AR = 300 ： 1 in comparison to AR = 6：1.
