| Project/Area Number |
60550268
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
計算機工学
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| Research Institution | Tokushima University |
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Principal Investigator |
USHIDA A. Faculty of Engineering, The University of Tokushima, 工学部, 教授 (20035611)
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| Co-Investigator(Kenkyū-buntansha) |
OKUMURA K. Faculty of Engineering, Kyoto University, 工学部, 講師 (50026241)
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| Project Period (FY) |
1985 – 1986
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| Project Status |
Completed (Fiscal Year 1986)
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| Budget Amount *help |
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1986: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1985: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | Variable step-size homotopy method / Interval method for nonlinear equation / 非線形代数方程式の区間解析法 / 周波数領域での振動解析 / ニュートン緩和法 / 多入力非線形システムの解法 / 非同期発振回路の解析 |
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| Research Abstract |
Many kinds of computer simulation programs have been proposed that can calculate dc-solution, transient responses and ac-responses of electronic circuits. However, they are not so efficient for the special problems such as steady-state responses of nonlinear circuits and dc-analysis of nonlinear algebraic systems having multiple solutions. Hence, object of our project is to obtain efficient algorithms to the special problems on the nonlinear circuit simulations.
For the dc-analysis of nonlinear electronic circuits, we obtained two efficient algorithms that can calculate multiple solutions of nonlinear equations. The first is homotopy method that traces the solution curve and gets all the solutions on it, where we introduced a new variable step-size method that can trace the curve efficiently. The second is an iterval method that can find all the solutions of the nonlinear equation.
Many communication circuits such as modulator and mixer are usually driven by multi-frequency components. I
… More
t is difficult to solve these systems because they have never period and many combination frequency components. Two basic approaches have been used for determining the steady-state response; namely, frequency-domain approach and time-domain approach. Volterra series and perturbation technique are practical frequency-domain methods that can be applied only weakly nonlinear circuits. While the least-square harmonic balance method can be used when the nonlinearity is strong, the number of nonlinear equations to be solved is generally very large.
We get an efficient substitution algorithm that can calculate the steady-state responses of nonlinear circuits driven by multi-frequency signals. The algorithm also can be applied to the analysis of non-synchronous oscillations in autonomous and forced oscillator systems. Our algorithm is a sort of Newton method whose variational value is estimated by a relaxation method, where a given nonlinear circuit is separated into two parts: a linear multi-port and a nonlinear subnetwork. The steady-state is obtained by finding the substitution sources such that both subnetworks give the same responses. Then, the equivalent circuit at each iteration is reduced to a time-invariant circuit and the variational value is calculated by solving it for the residual error. Thus, our substitution algorithm is very simple and can be applied many kind of electronic circuits. Less
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