The goal of this paper is to prove, by means of calculations the existence of the ω-limit cycle of a simple circuit where a resistor, a capacitor and a square-wave-type voltage source are in series.
The paper considers the response to the accumulated energy in the resistor (R)-capacitor (C) circuit. In the (RC) circuit, the capacitor C is initially charged with the “capacitive” voltage U0. At that moment t=0, t...The paper considers the response to the accumulated energy in the resistor (R)-capacitor (C) circuit. In the (RC) circuit, the capacitor C is initially charged with the “capacitive” voltage U0. At that moment t=0, the P circuit switch turns on. By using Kirchhoff’s laws on the elements, a homogeneous differential equation of the first order with constant coefficients is obtained with the initial condition UC(0)=U0. The solution of the differential equation is presented in exponential form UC(t)=U0⋅e−t/τ. Qualitative analysis RC of the circuit gives a phase portrait on the line. From the phase portrait on the line, it can be seen that the charge UC(t)→UC∗=0when t→∞stabilizes, regardless of the initial conditions. It is shown that from UC(t)=U0⋅e−t/τa dynamic system defined by the function φ(t,UC)=UC⋅e−t/τcan be formed from. It has also been shown that, from the formed dynamic system, an autonomous system (circuit equation RC) can be found whose solution describes the formed dynamic system. It is also shown that the dynamic system φ(t,UC)=UC⋅e−t/τhas one attractive fixed point UC=0.展开更多
The Balanced Truncation Method (BTM) is applied to an even distributed RC interconnect case by using Wang's closed-forms of even distributed RC interconnect models. The results show that extremely high order RC in...The Balanced Truncation Method (BTM) is applied to an even distributed RC interconnect case by using Wang's closed-forms of even distributed RC interconnect models. The results show that extremely high order RC interconnect can be high-accurately approximated by only third order balanced model. Related simulations are executed in both time domain and frequency domain. The results may be applied to VLSI interconnect model reduction and design.展开更多
移相全桥ZVS变换器副边整流二极管电压应力较高,需要设计缓冲电路来保证系统性能。然而,加入RC缓冲电路的变换器在某种工作模式下近似为LCL三阶谐振系统,导致接近开关频率的谐振甚至在整流二极管两侧产生更高的电压应力。通过建立移相全...移相全桥ZVS变换器副边整流二极管电压应力较高,需要设计缓冲电路来保证系统性能。然而,加入RC缓冲电路的变换器在某种工作模式下近似为LCL三阶谐振系统,导致接近开关频率的谐振甚至在整流二极管两侧产生更高的电压应力。通过建立移相全桥ZVS变换器在能量传输模式期间的等效电路模型,揭示RC缓冲电路对系统稳定性产生影响机理及电路参数对振荡的影响规律,通过分析选取合理的RC缓冲电路参数,不仅有效降低整流二极管电压应力,同时抑制由缓冲电路带来的振荡问题,进而提高系统的效率。设计了一个3.2 k W(10 A,320 V)的实验样机,验证了理论分析的正确性。展开更多
文摘The goal of this paper is to prove, by means of calculations the existence of the ω-limit cycle of a simple circuit where a resistor, a capacitor and a square-wave-type voltage source are in series.
文摘The paper considers the response to the accumulated energy in the resistor (R)-capacitor (C) circuit. In the (RC) circuit, the capacitor C is initially charged with the “capacitive” voltage U0. At that moment t=0, the P circuit switch turns on. By using Kirchhoff’s laws on the elements, a homogeneous differential equation of the first order with constant coefficients is obtained with the initial condition UC(0)=U0. The solution of the differential equation is presented in exponential form UC(t)=U0⋅e−t/τ. Qualitative analysis RC of the circuit gives a phase portrait on the line. From the phase portrait on the line, it can be seen that the charge UC(t)→UC∗=0when t→∞stabilizes, regardless of the initial conditions. It is shown that from UC(t)=U0⋅e−t/τa dynamic system defined by the function φ(t,UC)=UC⋅e−t/τcan be formed from. It has also been shown that, from the formed dynamic system, an autonomous system (circuit equation RC) can be found whose solution describes the formed dynamic system. It is also shown that the dynamic system φ(t,UC)=UC⋅e−t/τhas one attractive fixed point UC=0.
基金Supported in part by the National Science Foundation (US) under Grant CCR 0098275
文摘The Balanced Truncation Method (BTM) is applied to an even distributed RC interconnect case by using Wang's closed-forms of even distributed RC interconnect models. The results show that extremely high order RC interconnect can be high-accurately approximated by only third order balanced model. Related simulations are executed in both time domain and frequency domain. The results may be applied to VLSI interconnect model reduction and design.
文摘移相全桥ZVS变换器副边整流二极管电压应力较高,需要设计缓冲电路来保证系统性能。然而,加入RC缓冲电路的变换器在某种工作模式下近似为LCL三阶谐振系统,导致接近开关频率的谐振甚至在整流二极管两侧产生更高的电压应力。通过建立移相全桥ZVS变换器在能量传输模式期间的等效电路模型,揭示RC缓冲电路对系统稳定性产生影响机理及电路参数对振荡的影响规律,通过分析选取合理的RC缓冲电路参数,不仅有效降低整流二极管电压应力,同时抑制由缓冲电路带来的振荡问题,进而提高系统的效率。设计了一个3.2 k W(10 A,320 V)的实验样机,验证了理论分析的正确性。
