An Efficient Homotopy Method That Can Be Easily Implemented on SPICE

An Effective Embed Algorithm for Newton Fixed-Point Homotopy Method in MOS Transistor Circuits

“…The Proposed "Embed" Implementation Algorithm In this work, the MOS Newton fixed-point homotopy method is implemented using the source code implementation method, which is developed by directly adding and modifying some programs on the SPICE3F5simulator. Comparing with the net list implementation method [8], this source code implementation method is more useful and has higher flexibility for the reason that the Jacobian matrix scale in this implementation method does not be enlarged and the higher efficiency can be obtained.…”

An Effective Implementation of the Nonlinear Homotopy Method for MOS Transistor Circuits

“…where ( ) is the drain current of additional MOS diode in initial homotopy circuit [16].  If is not a MOS transistor branch, then ̃ The solution curve of the homotopy equation can be traced by the BDF curve-tracing algorithm [7,9]. In the BDF algorithm, the solution curve is parameterized by its arc-length and the following system of differential-algebraic equations…”

“…In this paper, the idea of SPICE-oriented numerical methods [7,18] is extended to MOS transistor circuits and an effective netlist implementation method for the MOS NLH method is proposed. In this netlist implementation method, the equations ( 16) and ( 17) will be described by some circuits.…”

“…To overcome this non-convergence problem, many computer-aided design (CAD) researchers have long studied the globally convergent homotopy methods from various viewpoints [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. These studies are divided into three categories.…”

“…The first one is how to construct a homotopy function. For example, Newton homotopy, Fixed-point homotopy, Nonlinear homotopy, Variable gain homotopy and other homotopy methods have been proposed in [4][5][6][7][8]. The second one is how to numerically trace a solution curve.…”