TY - JOUR
T1 - A practical approach for the fixed-point homotopy method using a solution-tracing circuit
AU - Inoue, Yasuaki
AU - Kusanobu, Saeko
AU - Yamamura, Kiyotaka
PY - 2002/1
Y1 - 2002/1
N2 - Finding DC operating-points of nonlinear circuits is an important and difficult task. The Newton-Raphson method employed in the SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. The fixed-point homotopy method is one of the excellent methods. However, from the viewpoint of implementation, it is important to study it further so that the method can be easily and widely used by many circuit designers. This paper presents a practical method to implement the fixed-point homotopy method. A special circuit called the solution-tracing circuit for the fixed-point homotopy method is proposed. By using this circuit, the solution curves of homotopy equations can be traced by performing the SPICE transient analysis. Therefore, no modification to the existing programs is necessary. Moreover, it is proved that the proposed method is globally convergent. Numerical examples show that the proposed technique is effective and can be easily implemented. By the proposed technique, many SPICE users can easily implement the fixed-point homotopy method.
AB - Finding DC operating-points of nonlinear circuits is an important and difficult task. The Newton-Raphson method employed in the SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. The fixed-point homotopy method is one of the excellent methods. However, from the viewpoint of implementation, it is important to study it further so that the method can be easily and widely used by many circuit designers. This paper presents a practical method to implement the fixed-point homotopy method. A special circuit called the solution-tracing circuit for the fixed-point homotopy method is proposed. By using this circuit, the solution curves of homotopy equations can be traced by performing the SPICE transient analysis. Therefore, no modification to the existing programs is necessary. Moreover, it is proved that the proposed method is globally convergent. Numerical examples show that the proposed technique is effective and can be easily implemented. By the proposed technique, many SPICE users can easily implement the fixed-point homotopy method.
KW - Circuit simulation
KW - DC operating-point
KW - Fixed-point homotopy
KW - Homotopy method
KW - SPICE
UR - http://www.scopus.com/inward/record.url?scp=0036458730&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036458730&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0036458730
VL - E85-A
SP - 222
EP - 233
JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
SN - 0916-8508
IS - 1
ER -