Boundary Induced Inductive Delay in Transmission of Electromagnetic Signals

Affiliation(s)

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School of Electrical Engineering & Computer Science, Peking University, Beijing, China..

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School of Electrical Engineering & Computer Science, Peking University, Beijing, China..

Abstract

When an electromagnetic signal transmits through a coaxial cable, it propagates at speed determined by the dielectrics of insulator between the cooper core wire and the metallic shield. However, we demonstrate here that, once the shielding layer of the coaxial cable is cut into two parts leaving a small gap, while the copper core wire is still perfectly connected, a remarkable transmission delay immediately appears in the system. We have revealed by both computational simulation and experiments that, when the gap spacing between two parts of the shielding layer is small, this delay is mostly determined by the overall geometrical parameters of the conductive boundary which connects two parts of the cut shielding layer. A reduced analytic formula for the transmission delay related with geometrical parameters, which is based on an inductive model of the transmission system, matches well with the fitted formula of the simulated delay. This above structure is analog to the situation that an interconnect is between two inter-modules in a circuit. The results suggest that for high speed circuits and systems, parasitic inductance should be taken into full consideration, and compact conductive packaging is favorable for reducing transmission delay of inter-modules, therefore enhancing the performance of the system.

When an electromagnetic signal transmits through a coaxial cable, it propagates at speed determined by the dielectrics of insulator between the cooper core wire and the metallic shield. However, we demonstrate here that, once the shielding layer of the coaxial cable is cut into two parts leaving a small gap, while the copper core wire is still perfectly connected, a remarkable transmission delay immediately appears in the system. We have revealed by both computational simulation and experiments that, when the gap spacing between two parts of the shielding layer is small, this delay is mostly determined by the overall geometrical parameters of the conductive boundary which connects two parts of the cut shielding layer. A reduced analytic formula for the transmission delay related with geometrical parameters, which is based on an inductive model of the transmission system, matches well with the fitted formula of the simulated delay. This above structure is analog to the situation that an interconnect is between two inter-modules in a circuit. The results suggest that for high speed circuits and systems, parasitic inductance should be taken into full consideration, and compact conductive packaging is favorable for reducing transmission delay of inter-modules, therefore enhancing the performance of the system.

Cite this paper

Y. Yang, M. Li, Y. Sun, D. Pei and S. Xu, "Boundary Induced Inductive Delay in Transmission of Electromagnetic Signals,"*Journal of Electromagnetic Analysis and Applications*, Vol. 4 No. 4, 2012, pp. 156-161. doi: 10.4236/jemaa.2012.44020.

Y. Yang, M. Li, Y. Sun, D. Pei and S. Xu, "Boundary Induced Inductive Delay in Transmission of Electromagnetic Signals,"

References

[1] A. D. Yaghjian, “An Overview of Near-Field Antenna Measurements,” IEEE Transactions on Antennas and Propagation, Vol. 34, No. 1, 1986, pp. 30-45.
doi:10.1109/TAP.1986.1143727

[2] IEEE Antennas and Propagation Society, “Special Issue on Near-Field Scanning Techniques,” IEEE Transactions on Antennas and Propagation, Vol. 36, No. 6, 1988, pp. 727-901.

[3] D. Slater, “Near-Field Antenna Measurements,” Artech House, Boston, 1991.

[4] C. Gennarelli, G. Riccio, F. D’Agostino and F. Ferrara, “Near-Field - Far-Field Transformation Techniques,” CUES, Salerno, 2004.

[5] C. A. Balanis, “Modern Antenna Handbook,” John Wiley & Sons, Inc., Hoboken, 2008.
doi:10.1002/9780470294154

[6] R. G. Yaccarino, Y. R. Samii and L. I. Williams, “The Bi- Polar Planar Near-Field Measurement Technique, Part II: Near-Field to Far-Field Transformation and Holographic Imaging Methods,” IEEE Transactions on Antennas and Propagation, Vol. 42, No. 2, 1994, pp. 196-204.
doi:10.1109/8.277213

[7] P. F. Wacker, “Non-Planar Near-Field Measurements: Sphe- rical Scanning,” National Bureau of Standards, Boulder, 1975.

[8] F. H. Larsen, “Probe Correction of Spherical Near-Field Measurements,” Electronic Letters, Vol. 13, No. 14, 1977, pp. 393-395. doi:10.1049/el:19770287

[9] F. H. Larsen, “Probe-Corrected Spherical Near-Field An- tenna Measurements,” Ph.D. Dissertation, Technical Uni- versity of Denmark, Copenhagen, 1980.

[10] A. D. Yaghjian and R. C. Wittmann, “The Receiving An- tenna as a Linear Differential Operator: Application to Spherical Near-Field Measurements,” IEEE Transactions on Antennas and Propagation, Vol. 33, No. 11, 1985, pp. 1175-1185. doi:10.1109/TAP.1985.1143520

[11] J. E. Hansen and F. Jensen, “Spherical Near-Field Scan- ning at the Technical University of Denmark,” IEEE Trans- actions on Antennas and Propagation, Vol. 36, No. 6, 1988, pp. 734-739. doi:10.1109/8.1174

[12] J. Hald, J. E. Hansen, F. Jensen and F. H. Larsen, “Sphe- rical Near-Field Antenna Measurements,” In: J. E. Han- sen, Ed., IEEE Electromagnetic Waves Series, Peter Pere- grinus, London, 1998.

[13] O. M. Bucci, F. D’Agostino, C. Gennarelli, G. Riccio and C. Savarese, “Data Reduction in the NF-FF Transforma- tion Technique with Spherical Scanning,” Journal of Elec- tromagnetic Waves and Applications, Vol. 15, No. 6, 2001, pp. 755-775. doi:10.1163/156939301X00995

[14] A. Arena, F. D’Agostino, C. Gennarelli and G. Riccio, “Probe Compensated NF-FF Transformation with Spheri- cal Scanning from a Minimum Number of Data,” Atti della Fondazione Giorgio Ronchi, Vol. 59, No. 3, 2004, pp. 312-326.

[15] F. D’Agostino, F. Ferrara, C. Gennarelli, R. Guerriero and M. Migliozzi, “Effective Antenna Modellings for a NF-FF Transformation with Spherical Scanning Using the Minimum Number of Data,” International Journal of Antennas and Propagation, Vol. 2011, Article ID 936781.
doi:10.1109/8.660964

[16] T. B. Hansen, “Higher-Order Probes in Spherical Near- Field Scanning,” IEEE Transactions on Antennas and Propagation, Vol. 59, No. 11, 2011, pp. 4049-4059.
doi:10.1109/TAP.2011.2164217

[17] O. M. Bucci and G. Franceschetti, “On the Spatial Band- width of Scattered Fields,” IEEE Transactions on Anten- nas and Propagation, Vol. 35, No. 12, 1987, pp. 1445-1455. doi:10.1109/TAP.1987.1144024

[18] O. M. Bucci, C. Gennarelli and C. Savarese, “Representation of Electromagnetic Fields over Arbitrary Surfaces by a Finite and Nonredundant Number of Samples,” IEEE Transactions on Antennas and Propagation, Vol. 46, No. 3, 1998, pp. 351-359. doi:10.1109/8.662654

[19] A. Dutt and V. Rohklin, “Fast Fourier Transforms for Non Equispaced Data,” Proceedings of SIAM Journal Scientific Computation, Vol. 14, No. 6, 1993, pp. 1369- 1393.

[20] R. C. Wittmann, B. K. Alpert and M. H. Francis, “Near- Field Antenna Measurements Using Nonideal Measure- ment Locations,” IEEE Transactions on Antennas and Propagation, Vol. 46, No. 5, 1998, pp. 716-722.
doi:10.1109/8.668916

[21] R. C. Wittmann, B. K. Alpert and M. H. Francis, “Near- Field, Spherical Scanning Antenna Measurements with Nonideal Probe Locations,” IEEE Transactions on An- tennas and Propagation, Vol. 52, No. 8, 2004, pp. 2184- 2186. doi:10.1109/TAP.2004.832316

[22] O. M. Bucci, C. Gennarelli and C. Savarese, “Interpola- tion of Electromagnetic Radiated Fields over a Plane from Nonuniform Samples,” IEEE Transactions on Antennas and Propagation, Vol. 41, No. 11, 1993, pp. 1501-1508.
doi:10.1109/8.267349

[23] O. M. Bucci, C. Gennarelli, G. Riccio and C. Savarese, “Electromagnetic Fields Interpolation from Nonuniform Samples over Spherical and Cylindrical Surfaces,” IEEE Proceedings Microwaves Antennas Propagation, Vol. 141, No. 2, 1994, pp. 77-84.
doi:10.1049/ip-map:19949838

[24] F. Ferrara, C. Gennarelli, G .Riccio and C. Savarese, “Far Field Reconstruction from Nonuniform Plane-Polar Data: A SVD Based Approach,” Electromagnetics, Vol. 23, No. 5, 2003, pp. 417-429. doi:10.1080/02726340390203171

[25] F. Ferrara, C. Gennarelli, G. Riccio and C. Savarese, “NF-FF Transformation with Cylindrical Scanning from Nonuniformly Distributed Data,” Microwave and Optical Te- chnology Letters, Vol. 39, No. 1, 2003, pp. 4-8.
doi:10.1002/mop.11109

[26] G. H. Golub and C. F. Van Loan, “Matrix Computations,” The Johns Hopkins University Press, Baltimore, 1996.

[27] F. D’Agostino, F. Ferrara, C. Gennarelli, R. Guerriero and M. Migliozzi, “On the Compensation of Probe Posi- tioning Errors When Using a Nonredundant Cylindrical NF-FF Transformation,” Progress in Electromagnetics Research B, Vol. 20, 2010, pp. 321-335.
doi:10.2528/PIERB10032402

[28] F. D’Agostino, F. Ferrara, C. Gennarelli, R. Guerriero, and M. Migliozzi, “Two Techniques for Compensating the Probe Positioning Errors in the Spherical NF-FF Transformation for Elongated Antennas,” The Open Electrical & Electronic Engineering Journal, Vol. 5, 2011, pp. 29-36. doi:10.2174/1874129001105010029

[29] S. L. Belousov, “Tables of Normalized Associated Legendre Polynomials,” Pergamon Press, Oxford, 1962.

[30] O. M. Bucci, G. D’Elia and M. D. Migliore, “Advanced Field Interpolation from Plane-Polar Samples: Experi- mental Verification,” IEEE Transactions on Antennas and Propagation, Vol. 46, No. 2, 1998, pp. 204-210.
doi:10.1109/8.660964