L. Chua, P. Lin [1975], Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques, Prentice-Hall Inc., 1975.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....representations of the solutions of autonomous systems can be found by efficient numerical methods. 4 The Warped Multirate Partial Differential Equation (WaMPDE) We consider a nonlinear system modelled using vector differentialalgebraic equations (DAEs) a description adequate for circuits [CL75] and many other applications: d dt q(x(t) f (x(t) b(t) 12) In the circuit context, x(t) is a vector of node voltages and branch currents; q( and f ( are nonlinear functions describing the charge flux and resistive terms, respectively. b(t) is a vector forcing term consisting of ....

L.O. Chua and P-M. Lin. Computer-aided analysis of electronic circuits : algorithms and computational techniques. Prentice-Hall, Englewood Cliffs, N.J., 1975.

....is a common engineering technique for calculating the effect on system performance due to variations in system parameters. In other words, comparative analysis is a qualitative version of sensitivity analysis. The sensi tivity of a quantity T, to perturbations in a parameter X, is defined [1] as the product: OT X OX T Because of its important application to design, considerable work has been done on efficient methods for calculating sensitivities. Approaches include numerical and symbolic differentiation, construction of an incremental network, and analysis of an adjoint network ....

....[1] as the product: OT X OX T Because of its important application to design, considerable work has been done on efficient methods for calculating sensitivities. Approaches include numerical and symbolic differentiation, construction of an incremental network, and analysis of an adjoint network [1]. Compared to DQ analysis, these methods have a major advantage they generate a quantitative value for sensitivity. But sensitivity analysis has two limitations: it does not generate explanations, and it requires an explicit equation for the desired quantity T. Thus sensitivity analysis could ....

L. Chua and P. Lin. Computer Aided Analysis of Electronic Circuits: Algorithms and Techniques. Prentice Hall, Englewood Cliffs, N J, 1975.

....an equivalent DC circuit problem. III. A SIMPLE EXAMPLE OF RCM Let us consider the simple dynamic circuit of Figure 1. R C v( t) Figure 1: A simple first order dynamic circuit In order to create a RCM equivalent of the circuit we need to define the discrete time equivalent of the capacitor [3 4]. The voltage current relation in a capacitor can be written as: dt dv C i c c = We can now discretize the equation solving the derivative using the trapezoidal algorithm: 1( 2 ) 1 ( k i k i C T k v k v c c c c c where Tc is the simulation step. Solving for the current in ....

Leon O. Chua, Pen-Min Lin, "Computer aided analysis of electronic circuits: algorithms and computational techniques", Prentice-Hall Inc., New Jersey

....network[BS65] Figure 53) The parameters are defined by extracting two voltage CHAPTER 5. MOMENT COMPUTATION 74 (b) 2 v v e t p2 t p1 1 e 5 (a) Figure 52: Transistor capacitor tree. v 2 i 2 1 v 1 Figure 53: Three terminal network model. ports, one from each terminal to ground[CL75] 5 2 4 i 1 i 2 3 5 = 2 4 y 11 y 12 y 21 y 22 3 5 2 4 v 1 v 2 3 5 2 4 i s1 i s2 3 5 (57) Figure 54 gives a physical interpretation of the six parameters of the admittance formulation. y 2 v 12 1 s1 v 11 y s2 1 21 v y i v y 22 2 Figure 54: Circuit ....

Leon O. Chua and Pen-Min Lin. Computer Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1975.

....substitution. The LU decomposition will maintain the sparse structure of the original matrix, which property is essential to solve large problems. The new matrices have a nonzero entry for each original nonzero entry, and a number of new nonzero entries called fill ins. As is shown earlier (Chua and Lin 1975; van Stiphout 1990) it is possible to order the rows and columns of the matrix in 3.3 The LU decomposition 39 such a way, that for an electric circuit the number of fill ins in the L and U matrices is in general less than the number of original elements. Algorithm 7.2: The LU decomposition. ....

CHUA, L.O., and P.M. LIN, 1975, Computer--Aided Analysis of Electronic Circuits: Algorithms & Computational Techniques, Prentice--Hall, Englewood Cliffs, N.J.

.... ffl Component linearization at ideal bias conditions, ffl Linearized component insertion into interconnection network, ffl Network solving for new bias conditions V , ffl Optional step: Sensitivity computation of V with respect to all elements in the interconnect using adjoint techniques[7]. ffl Bias change (from ideal bias conditions) computation, V Gamma Vo , on linearized components. ffl Changes (sensitivity) of V propagation to changes (sensitivity) of behavioral model parameters W , and then to changes (sensitivity) of system performance S. The advantage of the new approach ....

L. O. Chua and Pen-Min Lin. Computer aided analysis of electronic circuits: algorithms & computational techniques. Prentice-hall, 1975.

....dynamics of the map should correspond closely to the dynamics of the differential equation. From the Runge Kutta family of algorithms come arguably the most well known and used methods for numerical integration (see, for example, Henrici [1962] Gear [1971] Lambert [1973] Stetter [1973] Chua Lin [1975] , Hall Watt [1976] Butcher [1987] Press et al. 1988] Parker Chua [1989] or Lambert [1991] Thus we choose to look at Runge Kutta methods to investigate what pitfalls there may be in the integration of nonlinear and chaotic systems. We examine here the initial value problem; the ....

Chua, L. O. & Lin, P. M. [1975] Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques (Prentice-Hall).

.... when the equivalent network of the power or ground bus is represented by a resistive network, the vector of voltage drops appearing at its nodes (V ) is related to the corresponding vector of contact point currents (I) as follows : Y V = I (2) where Y is the node admittance matrix of the network [15]. When the bus is represented by an RC network, the following relationship holds Y V = I Gamma C V (3) where C is the diagonal matrix of node capacitances. By calculating the LU factors of the Y matrix and quantizing time, the above equations are solved by forward and backward substitutions ....

....by an RC network, the following relationship holds Y V = I Gamma C V (3) where C is the diagonal matrix of node capacitances. By calculating the LU factors of the Y matrix and quantizing time, the above equations are solved by forward and backward substitutions or by numerical integration [15]. Once the voltage drop waveforms at various nodes in the network (V i ; 1 i n) are known, the maximum voltage drop is calculated by finding the maximum of the voltage drops: Max V D = max 1in; t0 V i (t) 4) 5.6 Implementation Details The above approach has been implemented in a program in ....

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L. O. Chua and P.-M. Lin, Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques. Englewood Cliffs, NJ: Prentice-Hall, 1975.

.... perturbed coefficients, singular perturbations (Saxena, O Reilly and Kokotovic, 1984) noncausal systems (Bernhard, 1982) identification (Adams, Levy and Willsky, 1984) economic systems (Luenberger, 1977) interconnected systems (Rosenbrock and Pugh, 1974) and modeling of electronic circuits (Chua and P. M. Lin, 1975). A system described by (1.4) is said to be non singular if E has full rank and singular otherwise. The zeros of a non singular GSS system are identical to those of the corresponding standard state space system described by x(t) E Gamma1 Ax(t) E Gamma1 Bu(t) y(t) Cx(t) Du(t) ....

Chua, L.O. and P.-M. Lin (1975). Computer Aided Analysis of Electronic Circuits: Algorithms & Computational Techniques. Prentice Hall, Englewood Cliffs, NJ.

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L. Chua, P. Lin [1975], Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques, Prentice-Hall Inc., 1975.

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L.-O. Chua, P.-M. Lin: "Computer Aided analysis of electronic circuits: Algorithms and computational techniques", Prentice-Hall, 1975

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L. Chua, P. Lin [1975], Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques, Prentice-Hall Inc., 1975.

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