An efficient algorithm for finding multiple DC solutions based on the SPICE-oriented Newton homotopy method
It is a very important, but difficult, task to calculate the multiple dc solutions in circuit simulations. In this paper, we show a very simple SFICE-oriented Newton homotopy method which can efficiently find out the multiple de solutions. In the paper, we show our solution curve-tracing algorithm b...
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| Veröffentlicht in: | IEEE transactions on computer-aided design of integrated circuits and systems 2002-03, Vol.21 (3), p.337-348 |
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| container_end_page | 348 |
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| container_title | IEEE transactions on computer-aided design of integrated circuits and systems |
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| creator | Ushida, A. Yamagami, Y. Nishio, Y. Kinouchi, I. Inoue, Y. |
| description | It is a very important, but difficult, task to calculate the multiple dc solutions in circuit simulations. In this paper, we show a very simple SFICE-oriented Newton homotopy method which can efficiently find out the multiple de solutions. In the paper, we show our solution curve-tracing algorithm based on the arc-length method and the Newton homotopy method. We will also prove an important theorem about how many variables should be chosen to implement our algorithm. It verifies that our simulator can be efficiently applied even if the circuit scales are relatively large. In Section III, we show that our Newton homotopy method is implemented by the transient analysis of SPICE. Thus, we do not need to formulate a troublesome circuit equation or the Jacobian matrix. Finally, applying our method to solve many important benchmark problems, all the solutions for the transistor circuits could be found on each homotopy path. Thus, our simulator can be efficiently applied to calculate the multiple dc solutions and perhaps all the solutions. |
| doi_str_mv | 10.1109/43.986427 |
| format | Article |
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In this paper, we show a very simple SFICE-oriented Newton homotopy method which can efficiently find out the multiple de solutions. In the paper, we show our solution curve-tracing algorithm based on the arc-length method and the Newton homotopy method. We will also prove an important theorem about how many variables should be chosen to implement our algorithm. It verifies that our simulator can be efficiently applied even if the circuit scales are relatively large. In Section III, we show that our Newton homotopy method is implemented by the transient analysis of SPICE. Thus, we do not need to formulate a troublesome circuit equation or the Jacobian matrix. Finally, applying our method to solve many important benchmark problems, all the solutions for the transistor circuits could be found on each homotopy path. 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In this paper, we show a very simple SFICE-oriented Newton homotopy method which can efficiently find out the multiple de solutions. In the paper, we show our solution curve-tracing algorithm based on the arc-length method and the Newton homotopy method. We will also prove an important theorem about how many variables should be chosen to implement our algorithm. It verifies that our simulator can be efficiently applied even if the circuit scales are relatively large. In Section III, we show that our Newton homotopy method is implemented by the transient analysis of SPICE. Thus, we do not need to formulate a troublesome circuit equation or the Jacobian matrix. Finally, applying our method to solve many important benchmark problems, all the solutions for the transistor circuits could be found on each homotopy path. Thus, our simulator can be efficiently applied to calculate the multiple dc solutions and perhaps all the solutions.</description><subject>Algorithms</subject><subject>Analog circuits</subject><subject>Application software</subject><subject>Circuit simulation</subject><subject>Circuits</subject><subject>Computer simulation</subject><subject>Direct current</subject><subject>Flip-flops</subject><subject>Jacobian matrices</subject><subject>Jacobian matrix</subject><subject>Large-scale systems</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Nonlinear equations</subject><subject>Piecewise linear techniques</subject><subject>SPICE</subject><subject>Studies</subject><subject>Transient analysis</subject><subject>Transistor circuits</subject><issn>0278-0070</issn><issn>1937-4151</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2002</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp90TtPwzAQAGALgUR5DKxMFgOIIcWvxvZYhfKQECABc2Scc-uSxCV2hPrvSVXEwMB00t13dzodQieUjCkl-krwsVa5YHIHjajmMhN0QnfRiDCpMkIk2UcHMS4JoWLC9Ah9TFsMznnroU3Y1PPQ-bRosAsddr6tfDvHTV8nv6oBXxc4hrpPPrQRv5sIFQ4tTgvAL8_3xSwbeocpQ_YRvtJQWYQmpLBa4wbSIlRHaM-ZOsLxTzxEbzez1-Iue3i6vS-mD5kVXKaMazphXFnmSK6MtsQwwti7yisjuQRjnKoUNVTnRgmtqK4s4Qxs7ixoLRQ_RBfbuasufPYQU9n4aKGuTQuhj6UmUudCSz7I838lkxMpdL6BZ3_gMvRdO1xRKiWEZDnZ7L3cItuFGDtw5arzjenWJSXl5jul4OX2O4M93VoPAL_up_gNAkCJVg</recordid><startdate>20020301</startdate><enddate>20020301</enddate><creator>Ushida, A.</creator><creator>Yamagami, Y.</creator><creator>Nishio, Y.</creator><creator>Kinouchi, I.</creator><creator>Inoue, Y.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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In this paper, we show a very simple SFICE-oriented Newton homotopy method which can efficiently find out the multiple de solutions. In the paper, we show our solution curve-tracing algorithm based on the arc-length method and the Newton homotopy method. We will also prove an important theorem about how many variables should be chosen to implement our algorithm. It verifies that our simulator can be efficiently applied even if the circuit scales are relatively large. In Section III, we show that our Newton homotopy method is implemented by the transient analysis of SPICE. Thus, we do not need to formulate a troublesome circuit equation or the Jacobian matrix. Finally, applying our method to solve many important benchmark problems, all the solutions for the transistor circuits could be found on each homotopy path. 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| subjects | Algorithms Analog circuits Application software Circuit simulation Circuits Computer simulation Direct current Flip-flops Jacobian matrices Jacobian matrix Large-scale systems Mathematical analysis Mathematical models Nonlinear equations Piecewise linear techniques SPICE Studies Transient analysis Transistor circuits |
| title | An efficient algorithm for finding multiple DC solutions based on the SPICE-oriented Newton homotopy method |
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