First Order Approximation of the Exact Solution of Arbitrary Nonuniform Transmission Lines: Application in High Speed Integrated Circuits

Ahmad CHELDAVI; Mahmoud KAMAREI; Safieddin SAFAVI-NAEINI

First Order Approximation of the Exact Solution of Arbitrary Nonuniform Transmission Lines: Application in High Speed Integrated Circuits

Ahmad CHELDAVI, Mahmoud KAMAREI, Safieddin SAFAVI-NAEINI

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An efficient procedure is presented to determine the implicit exact solution of an arbitrary nonuniform transmission line (NTL), and its first order approximation (F. O. A. ) as an explicit expression. The method of the solution is based on the steplines approximation of the nonuniform transmission lines and quasi-TEM assumptions. Using steplines approximation the NTL is subdivided into a large number of uniform line segments (steps). Using time-domain approach and invoking the boundary conditions at the discontinuities of the adjacent steps, each step is modeled as continuous time domain linear filter characterized by a transfer function. The frequency domain transfer function of this filter is then obtained for linear termination networks. For very large number of steplines this transfer function approaches transfer function of the NTL. In the next step a F. O. A. , as an explicit expression of the exact response will be obtained. This F. O. A. is more suitable for very short transmission lines which is often the case in integrated circuits and some of printed circuit boards. Then, the F. O. A. of the ABCD matrix will be obtained.

Publication: IEICE TRANSACTIONS on Electronics Vol.E82-C No.12 pp.2248-2254

Publication Date: 1999/12/25

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Type of Manuscript: PAPER

Category: Microwave and Millimeter Wave Technology

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Ahmad CHELDAVI, Mahmoud KAMAREI, Safieddin SAFAVI-NAEINI, "First Order Approximation of the Exact Solution of Arbitrary Nonuniform Transmission Lines: Application in High Speed Integrated Circuits" in IEICE TRANSACTIONS on Electronics, vol. E82-C, no. 12, pp. 2248-2254, December 1999, doi: .
Abstract: An efficient procedure is presented to determine the implicit exact solution of an arbitrary nonuniform transmission line (NTL), and its first order approximation (F. O. A. ) as an explicit expression. The method of the solution is based on the steplines approximation of the nonuniform transmission lines and quasi-TEM assumptions. Using steplines approximation the NTL is subdivided into a large number of uniform line segments (steps). Using time-domain approach and invoking the boundary conditions at the discontinuities of the adjacent steps, each step is modeled as continuous time domain linear filter characterized by a transfer function. The frequency domain transfer function of this filter is then obtained for linear termination networks. For very large number of steplines this transfer function approaches transfer function of the NTL. In the next step a F. O. A. , as an explicit expression of the exact response will be obtained. This F. O. A. is more suitable for very short transmission lines which is often the case in integrated circuits and some of printed circuit boards. Then, the F. O. A. of the ABCD matrix will be obtained.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e82-c_12_2248/_p

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@ARTICLE{e82-c_12_2248,
author={Ahmad CHELDAVI, Mahmoud KAMAREI, Safieddin SAFAVI-NAEINI, },
journal={IEICE TRANSACTIONS on Electronics},
title={First Order Approximation of the Exact Solution of Arbitrary Nonuniform Transmission Lines: Application in High Speed Integrated Circuits},
year={1999},
volume={E82-C},
number={12},
pages={2248-2254},
abstract={An efficient procedure is presented to determine the implicit exact solution of an arbitrary nonuniform transmission line (NTL), and its first order approximation (F. O. A. ) as an explicit expression. The method of the solution is based on the steplines approximation of the nonuniform transmission lines and quasi-TEM assumptions. Using steplines approximation the NTL is subdivided into a large number of uniform line segments (steps). Using time-domain approach and invoking the boundary conditions at the discontinuities of the adjacent steps, each step is modeled as continuous time domain linear filter characterized by a transfer function. The frequency domain transfer function of this filter is then obtained for linear termination networks. For very large number of steplines this transfer function approaches transfer function of the NTL. In the next step a F. O. A. , as an explicit expression of the exact response will be obtained. This F. O. A. is more suitable for very short transmission lines which is often the case in integrated circuits and some of printed circuit boards. Then, the F. O. A. of the ABCD matrix will be obtained.},
keywords={},
doi={},
ISSN={},
month={December},}

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TY - JOUR
TI - First Order Approximation of the Exact Solution of Arbitrary Nonuniform Transmission Lines: Application in High Speed Integrated Circuits
T2 - IEICE TRANSACTIONS on Electronics
SP - 2248
EP - 2254
AU - Ahmad CHELDAVI
AU - Mahmoud KAMAREI
AU - Safieddin SAFAVI-NAEINI
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E82-C
IS - 12
JA - IEICE TRANSACTIONS on Electronics
Y1 - December 1999
AB - An efficient procedure is presented to determine the implicit exact solution of an arbitrary nonuniform transmission line (NTL), and its first order approximation (F. O. A. ) as an explicit expression. The method of the solution is based on the steplines approximation of the nonuniform transmission lines and quasi-TEM assumptions. Using steplines approximation the NTL is subdivided into a large number of uniform line segments (steps). Using time-domain approach and invoking the boundary conditions at the discontinuities of the adjacent steps, each step is modeled as continuous time domain linear filter characterized by a transfer function. The frequency domain transfer function of this filter is then obtained for linear termination networks. For very large number of steplines this transfer function approaches transfer function of the NTL. In the next step a F. O. A. , as an explicit expression of the exact response will be obtained. This F. O. A. is more suitable for very short transmission lines which is often the case in integrated circuits and some of printed circuit boards. Then, the F. O. A. of the ABCD matrix will be obtained.
ER -