Analysis of nonlinear termination networks for coupled lossy and dispersive transmission lines

George W. Pan; Gaofeng Wang; Barry K. Gilbert

doi:10.1109/22.223758

Analysis of nonlinear termination networks for coupled lossy and dispersive transmission lines

George W. Pan
, Gaofeng Wang
, Barry K. Gilbert

Physiology & Biomedical Engineering

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Based upon an algorithm described in a separate paper [1], multiple transmission lines with skin effect losses and dispersive characteristics were analyzed by the volume equivalent principle, and the scattering matrix [Sω] and characteristic impedance matrix [z_0ω] of the transmission lines were obtained. The [Sω] and [Z₀(w)] were then transformed by the inverse FFT into the time domain. The scattering matrix representation is multiplicative in nature, which leads to the time domain formulation as a set of convolution integrals. Instead of attempting to solve a set of coupled convolution integral equations by the multivariable Newton-Raphson method, which may occasionally be unstable, we generated a set of object functions and applied a multivariable optimization technique, referred to as the modified Levenberg-Marquardt algorithm, to attain the solutions. The new method, which is quite general, reduces to the special cases derived in many previous publications.

Original language	English (US)
Pages (from-to)	531-535
Number of pages	5
Journal	IEEE Transactions on Microwave Theory and Techniques
Volume	41
Issue number	3
DOIs	https://doi.org/10.1109/22.223758
State	Published - Mar 1993

ASJC Scopus subject areas

Radiation
Condensed Matter Physics
Electrical and Electronic Engineering

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Cite this

@article{0b331bd526504daf97cddd5c242d3081,

title = "Analysis of nonlinear termination networks for coupled lossy and dispersive transmission lines",

abstract = "Based upon an algorithm described in a separate paper [1], multiple transmission lines with skin effect losses and dispersive characteristics were analyzed by the volume equivalent principle, and the scattering matrix [Sω] and characteristic impedance matrix [z0ω] of the transmission lines were obtained. The [Sω] and [Z0(w)] were then transformed by the inverse FFT into the time domain. The scattering matrix representation is multiplicative in nature, which leads to the time domain formulation as a set of convolution integrals. Instead of attempting to solve a set of coupled convolution integral equations by the multivariable Newton-Raphson method, which may occasionally be unstable, we generated a set of object functions and applied a multivariable optimization technique, referred to as the modified Levenberg-Marquardt algorithm, to attain the solutions. The new method, which is quite general, reduces to the special cases derived in many previous publications.",

author = "Pan, \{George W.\} and Gaofeng Wang and Gilbert, \{Barry K.\}",

note = "Funding Information: Gu et a/. [lo] improved the S-parameter approach, discarded the negative networks and eliminated the fixed reference impedance. These authors discussed general cases of coupled lossy and dispersive transmission lines with nonlinear loads. Nevertheless, the (semiempirical) dispersion formula (Equation 15 in [lo], which has been verified to be accurate to the terahertz range [ 1 I]), is valid only for a single microstrip line, and the Newton-Raphson method as employed in [lo] may be. unstable, particularly when multiple variables are involved. Recently, Mehalic and Mittra [12] expanded the S-parameter approach in conjunction with an iteration-perturbation method [13] so that multiple lines can be treated. However, because resistive Manuscript received December 5, 1991; revised July 27. 1992. This work was supported under contract N66001-89-C-0104 from the Naval Ocean Systems Center. The authors are with the Mayo Foundation, Special Purpose Processor Development Group, Rochester, MN 55905. IEEE Log Number 9205468.",

year = "1993",

month = mar,

doi = "10.1109/22.223758",

language = "English (US)",

volume = "41",

pages = "531--535",

journal = "IEEE Transactions on Microwave Theory and Techniques",

issn = "0018-9480",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "3",

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T1 - Analysis of nonlinear termination networks for coupled lossy and dispersive transmission lines

AU - Pan, George W.

AU - Wang, Gaofeng

AU - Gilbert, Barry K.

N1 - Funding Information: Gu et a/. [lo] improved the S-parameter approach, discarded the negative networks and eliminated the fixed reference impedance. These authors discussed general cases of coupled lossy and dispersive transmission lines with nonlinear loads. Nevertheless, the (semiempirical) dispersion formula (Equation 15 in [lo], which has been verified to be accurate to the terahertz range [ 1 I]), is valid only for a single microstrip line, and the Newton-Raphson method as employed in [lo] may be. unstable, particularly when multiple variables are involved. Recently, Mehalic and Mittra [12] expanded the S-parameter approach in conjunction with an iteration-perturbation method [13] so that multiple lines can be treated. However, because resistive Manuscript received December 5, 1991; revised July 27. 1992. This work was supported under contract N66001-89-C-0104 from the Naval Ocean Systems Center. The authors are with the Mayo Foundation, Special Purpose Processor Development Group, Rochester, MN 55905. IEEE Log Number 9205468.

PY - 1993/3

Y1 - 1993/3

N2 - Based upon an algorithm described in a separate paper [1], multiple transmission lines with skin effect losses and dispersive characteristics were analyzed by the volume equivalent principle, and the scattering matrix [Sω] and characteristic impedance matrix [z0ω] of the transmission lines were obtained. The [Sω] and [Z0(w)] were then transformed by the inverse FFT into the time domain. The scattering matrix representation is multiplicative in nature, which leads to the time domain formulation as a set of convolution integrals. Instead of attempting to solve a set of coupled convolution integral equations by the multivariable Newton-Raphson method, which may occasionally be unstable, we generated a set of object functions and applied a multivariable optimization technique, referred to as the modified Levenberg-Marquardt algorithm, to attain the solutions. The new method, which is quite general, reduces to the special cases derived in many previous publications.

AB - Based upon an algorithm described in a separate paper [1], multiple transmission lines with skin effect losses and dispersive characteristics were analyzed by the volume equivalent principle, and the scattering matrix [Sω] and characteristic impedance matrix [z0ω] of the transmission lines were obtained. The [Sω] and [Z0(w)] were then transformed by the inverse FFT into the time domain. The scattering matrix representation is multiplicative in nature, which leads to the time domain formulation as a set of convolution integrals. Instead of attempting to solve a set of coupled convolution integral equations by the multivariable Newton-Raphson method, which may occasionally be unstable, we generated a set of object functions and applied a multivariable optimization technique, referred to as the modified Levenberg-Marquardt algorithm, to attain the solutions. The new method, which is quite general, reduces to the special cases derived in many previous publications.

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Analysis of nonlinear termination networks for coupled lossy and dispersive transmission lines

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