Details
| Original language | English |
|---|---|
| Article number | 8370180 |
| Pages (from-to) | 4272-4284 |
| Number of pages | 13 |
| Journal | IEEE Transactions on Circuits and Systems I: Regular Papers |
| Volume | 65 |
| Issue number | 12 |
| Early online date | 31 May 2018 |
| Publication status | Published - Dec 2018 |
Abstract
In this paper, a procedure for the analysis and design of nonlinear circuits based on the Carleman linearization is presented. Since this procedure starts with the general network equations which are derived by Kirchhoff's law, it can be used for a variety of circuits. The proposed procedure is applied for oscillator and RF mixer circuits which are a crucial part of every wireless communication system. Based on the general network equations, a transformation into equivalent polynomial differential equations is performed using the not widely known method of Kerner. This polynomial differential equation is further transformed into an equivalent infinite-dimensional system of linear differential equations. Since the infinite-dimensional linear system cannot be solved in general, an approximation by a finite one is performed using a self-consistent technique. The obtained finite linear system is used for the approximation of the infinite-dimensional linear system on a predefined interval. The approximation is utilized for the design and analysis process of the circuit, which is a challenging problem until now.
Keywords
- Carleman, circuits, linearization, Nonlinear, oscillator, RF mixer, self-consistent
ASJC Scopus subject areas
- Engineering(all)
- Electrical and Electronic Engineering
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In: IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 65, No. 12, 8370180, 12.2018, p. 4272-4284.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Analysis and Design of Nonlinear Circuits with a Self-Consistent Carleman Linearization
AU - Weber, Harry
AU - Mathis, Wolfgang
N1 - Publisher Copyright: © 2004-2012 IEEE. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/12
Y1 - 2018/12
N2 - In this paper, a procedure for the analysis and design of nonlinear circuits based on the Carleman linearization is presented. Since this procedure starts with the general network equations which are derived by Kirchhoff's law, it can be used for a variety of circuits. The proposed procedure is applied for oscillator and RF mixer circuits which are a crucial part of every wireless communication system. Based on the general network equations, a transformation into equivalent polynomial differential equations is performed using the not widely known method of Kerner. This polynomial differential equation is further transformed into an equivalent infinite-dimensional system of linear differential equations. Since the infinite-dimensional linear system cannot be solved in general, an approximation by a finite one is performed using a self-consistent technique. The obtained finite linear system is used for the approximation of the infinite-dimensional linear system on a predefined interval. The approximation is utilized for the design and analysis process of the circuit, which is a challenging problem until now.
AB - In this paper, a procedure for the analysis and design of nonlinear circuits based on the Carleman linearization is presented. Since this procedure starts with the general network equations which are derived by Kirchhoff's law, it can be used for a variety of circuits. The proposed procedure is applied for oscillator and RF mixer circuits which are a crucial part of every wireless communication system. Based on the general network equations, a transformation into equivalent polynomial differential equations is performed using the not widely known method of Kerner. This polynomial differential equation is further transformed into an equivalent infinite-dimensional system of linear differential equations. Since the infinite-dimensional linear system cannot be solved in general, an approximation by a finite one is performed using a self-consistent technique. The obtained finite linear system is used for the approximation of the infinite-dimensional linear system on a predefined interval. The approximation is utilized for the design and analysis process of the circuit, which is a challenging problem until now.
KW - Carleman
KW - circuits
KW - linearization
KW - Nonlinear
KW - oscillator
KW - RF mixer
KW - self-consistent
UR - http://www.scopus.com/inward/record.url?scp=85047971577&partnerID=8YFLogxK
U2 - 10.1109/TCSI.2018.2837677
DO - 10.1109/TCSI.2018.2837677
M3 - Article
AN - SCOPUS:85047971577
VL - 65
SP - 4272
EP - 4284
JO - IEEE Transactions on Circuits and Systems I: Regular Papers
JF - IEEE Transactions on Circuits and Systems I: Regular Papers
SN - 1549-8328
IS - 12
M1 - 8370180
ER -