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Journal articles on the topic 'Impedance characteristic'

Author: Grafiati

Published: 28 June 2021

Last updated: 1 February 2022

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1

Zhao, Hongshan, Weitao Zhang, and Yan Wang. "Characteristic Impedance Analysis of Medium-Voltage Underground Cables with Grounded Shields and Armors for Power Line Communication." Electronics 8, no. 5 (May 23, 2019): 571. http://dx.doi.org/10.3390/electronics8050571.

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The characteristic impedance of a power line is an important parameter in power line communication (PLC) technologies. This parameter is helpful for understanding power line impedance characteristics and achieving impedance matching. In this study, we focused on the characteristic impedance matrices (CIMs) of the medium-voltage (MV) cables. The calculation and characteristics of the CIMs were investigated with special consideration of the grounded shields and armors, which are often neglected in current research. The calculation results were validated through the experimental measurements. The results show that the MV underground cables with multiple grounding points have forward and backward CIMs, which are generally not equal unless the whole cable structure is longitudinally symmetrical. Then, the resonance phenomenon in the CIMs was analyzed. We found that the grounding of the shields and armors not only affected their own characteristic impedances but also those of the cores, and the resonance present in the CIMs should be of concern in the impedance matching of the PLC systems. Finally, the effects of the grounding resistances, cable lengths, grounding point numbers, and cable branch numbers on the CIMs of the MV underground cables were discussed through control experiments.

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2

Nauwelaers, B., and A. van de Capelle. "Characteristic impedance of stripline." Electronics Letters 23, no. 18 (1987): 930. http://dx.doi.org/10.1049/el:19870655.

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3

Zhang, Y., and J. L. Liu. "Impedance matching condition analysis of the multi-filar tape-helix Blumlein PFL with discontinuous dielectrics." Laser and Particle Beams 30, no. 4 (October 16, 2012): 639–50. http://dx.doi.org/10.1017/s026303461200050x.

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AbstractIn this paper, the characteristic impedance matching of the inner line and outer line of the multi-filar tape-helix Blumlein pulse forming line (BPFL) is analyzed in detail by dispersion theory of tape helix. Analysis of the spatial harmonics of multi-filar tape-helix BPFL shows that the integer harmonic numbers of the excited spatial harmonics are not continuous. In addition, the basic harmonic component still dominates the dispersion characteristics of the multi-filar tape-helix BPFL at low frequency band. The impedance mismatching phenomenon caused by the discontinuity of filling dielectrics in the inner line of BPFL is studied as an important issue. Effects of dielectric discontinuity on the coupled electromagnetic fields and the parameters of the outer line are also analyzed. The impedance matching conditions are both obtained under the situations of continuous filling dielectric and discontinuous dielectrics, respectively. Impedance characteristics of these two situations are analyzed by comparison, and effects of the thickness of support dielectric on the impedance are also presented. When the 6 mm-thickness nylon support of the multi-filar tape helix is used in the filling dielectric of de-ionized water, the characteristic impedances of the inner line and outer line of BPFL are 53 Ω and 14.7 Ω, respectively. After the improvement about substituting de-ionized water by castor oil, the relative permittivities of the support dielectric and filling dielectric are almost the same, and the impedances of the inner and outer line of BPFL become 80 Ω and 79 Ω, respectively. That is to say, the impedance mismatching problem caused by dielectric discontinuity is solved. Circuit simulation and experimental results basically correspond to the theoretical results, and the fact demonstrates that impedance analysis of the multi-filar tape-helix BPFL based on dispersion theory is correct.

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4

Torrungrueng, D., P. Y. Chou, and M. Krairiksh. "An extendedZY T-chart for conjugately characteristic-impedance transmission lines with active characteristic impedances." Microwave and Optical Technology Letters 49, no. 8 (2007): 1961–64. http://dx.doi.org/10.1002/mop.22626.

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5

Wong, George S. K. "Characteristic impedance of humid air." Journal of the Acoustical Society of America 80, no. 4 (October 1986): 1203–4. http://dx.doi.org/10.1121/1.394468.

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6

Bhattacharya, D. "Characteristic impedance of coplanar waveguide." Electronics Letters 21, no. 13 (1985): 557. http://dx.doi.org/10.1049/el:19850393.

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7

Brews, J. R. "Characteristic Impedance of Microstrip Lines." IEEE Transactions on Microwave Theory and Techniques 35, no. 1 (January 1987): 30–34. http://dx.doi.org/10.1109/tmtt.1987.1133591.

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8

Krukonis, Audrius, and Šarūnas Mikučionis. "THE FREQUENCY CHARACTERISTICS OF COUPLED MICROSTRIP LINES / SUSIETŲJŲ MIKROJUOSTELINIŲ LINIJŲ DAŽNINĖS CHARAKTERISTIKOS." Mokslas - Lietuvos ateitis 5, no. 2 (May 24, 2013): 173–80. http://dx.doi.org/10.3846/mla.2013.33.

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The article deals with the use of the finite difference time domain method and uniaxial perfectly matching layer for analysis of frequency characteristics of coupled microstrip transmission lines. It describes calculation techniques for voltage, current, characteristic impedance and effective dielectric constant of each signal conductor. Besides, it analyses the frequency dependencies of characteristic impedance and the effective dielectric constant. Article in Lithuanian. Santrauka Straipsnyje aptariamas baigtinių skirtumų laiko srities metodo taikymas ir absorbuojančio sluoksnio taikymas susietųjų mikrojuostelinių linijų analizei. Sudaryti ir išnagrinėti baigtinių skirtumų laiko srities metodu grįsti susietųjų mikrojuostelinių linijų matematiniai modeliai. Pateikiamos kiekvieno iš laidininkų įtampos, srovės, charakteringojo impedanso ir efektyviosios dielektrinės skvarbos skaičiavimo metodikos. Aptariami skaičiavimo metodikų pranašumai, trūkumai, pateikiamos jų tobulinimo kryptys.

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9

Krukonis, Audrius, and Šarūnas Mikučionis. "EFFECT OF NON-UNIFORMITY OF THE MULTICONDUCTOR LINE CONSTRUCTIONAL PARAMETERS ON THE FREQUENCY CHARACTERISTICS OF THE MEANDER MICROSTRIP DELAY LINE / DAUGIALAIDĖS LINIJOS PARAMETRŲ NETOLYGUMŲ ĮTAKA MEANDRINIŲ VĖLINIMO LINIJŲ DAŽNINĖMS CHARAKTERISTIKOMS." Mokslas – Lietuvos ateitis 6, no. 2 (April 24, 2014): 211–17. http://dx.doi.org/10.3846/mla.2014.32.

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Inhomogeneities of the electromagnetic field are observed at the edges of the electrodynamic delay systems which are designed based on the concept of infinite periodic multiconductor line. The influence of non-uniformity of characteristic impedance and effective permittivity of the multiconductor microstrip line on the frequency responses and characteristics of meander microstrip delay lines is studied in this paper. It is shown that aligning characteristic impedance and effective permittivity of the multiconductor line the bandwidth of the delay line can be significantly extended. Elektrodinaminių įtaisų, grįstų periodinių daugialaidžių linijų struktūra, kraštuose ir galuose pastebimi elektromagnetinių laukų netolygumai. Straipsnyje nagrinėjama charakteringojo impedanso ir efektyviosios dielektrinės skvarbos netolygumo įtaka meandrinių mikrojuostelinių vėlinimo linijų dažninėms charakteristikoms. Parodyta, kad suvienodinus daugialaidės linijos laidininkų charakteringuosius impedansus arba efektyviąsias dielektrines skvarbas galima praplėsti vėlinimo linijos pralaidumo juostą.

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10

Wan, Li Bin, Ya Lin Guan, and Xin Kun Tang. "A Bandpass Filter Based on Novel SCRLH Transmission Line Structure." Applied Mechanics and Materials 456 (October 2013): 624–26. http://dx.doi.org/10.4028/www.scientific.net/amm.456.624.

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In this paper, a novel simplified composite right/left handed (SCRLH) transmission line (TL) structure is proposed.The dispersion and impedance characteristics of the novel structure are first analysed based on Bloch-Floquet theory, which shows that the attenuation constant keeps zero with a relatively smooth characteristic impedance distribution within the passband and that the characteristic impedance is purely imaginary with the inhibition of the electromagetic wave propagation outside the passband.

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11

Wang, Yi, Han Tang, Wen Li Chen, Xing Zhe Hou, Hong Liang Sun, and Kai Bo Luo. "Research on the Measurement of Household Appliance Impedance Characteristic." Advanced Materials Research 986-987 (July 2014): 1574–78. http://dx.doi.org/10.4028/www.scientific.net/amr.986-987.1574.

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Impedance of power line channel is the most important factor for power line communication. All kinds of household appliances randomly connect or disconnect from the network, which give rise to impedance variation on power line channel. The mismatch of impedance would reduce the performance of the signal transmission. The power network is mixed with lines and loads. In order to investigate the main factors that affect power network impedance, this paper proposed a method to measure the impedance of active household appliances. Some household appliances are measured with this method, and the result shows that this method can measure the impedance effictively, which helps the study on the impedance charicteristics.

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12

Bhattacharya, D. "Erratum: Characteristic impedance of coplanar waveguide." Electronics Letters 21, no. 18 (1985): 824. http://dx.doi.org/10.1049/el:19850582.

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13

Vandenberghe, S., D. M. M. P. Schreurs, G. Carchon, B. K. J. C. Nauwelaers, and W. De Raedt. "Characteristic impedance extraction using calibration comparison." IEEE Transactions on Microwave Theory and Techniques 49, no. 12 (2001): 2573–79. http://dx.doi.org/10.1109/22.971652.

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14

Coetzee, Jacob C., and Johannes A. G. Malherbe. "Characteristic impedance for double-sided slotlines." Microwave and Optical Technology Letters 3, no. 3 (March 1990): 85–88. http://dx.doi.org/10.1002/mop.4650030304.

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15

Ball, J. A. R. "Characteristic impedance of unbalanced TDR probes." IEEE Transactions on Instrumentation and Measurement 51, no. 3 (June 2002): 532–36. http://dx.doi.org/10.1109/tim.2002.1017724.

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16

Choo, Jaeyul, Hyo J. Eom, and Dohoon Kim. "Characteristic Impedance of Pyramidal Transmission Line." IEEE Antennas and Wireless Propagation Letters 12 (2013): 445–47. http://dx.doi.org/10.1109/lawp.2013.2254461.

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17

Yla-Oijala, Pasi, Joni Lappalainen, and Seppo Jarvenpaa. "Characteristic Mode Equations for Impedance Surfaces." IEEE Transactions on Antennas and Propagation 66, no. 1 (January 2018): 487–92. http://dx.doi.org/10.1109/tap.2017.2772873.

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18

Wang, Bing-Zhong. "Characteristic impedance of meshed-strip line." International Journal of Infrared and Millimeter Waves 16, no. 6 (June 1995): 1109–14. http://dx.doi.org/10.1007/bf02068280.

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19

Vudhivorn, K., and D. Torrungrueng. "A modified extended ZY T-chart for conjugately characteristic-impedance transmission lines with active characteristic impedances." Microwave and Optical Technology Letters 51, no. 3 (March 2009): 621–25. http://dx.doi.org/10.1002/mop.24124.

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20

Hyeong Tae Jeong, Ji Eun Kim, Ik Soo Chang, and Chul Dong Kim. "Tunable impedance transformer using a transmission line with variable characteristic impedance." IEEE Transactions on Microwave Theory and Techniques 53, no. 8 (August 2005): 2587–93. http://dx.doi.org/10.1109/tmtt.2005.852758.

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21

Huang, Shichun, Liang Yu, and Weikang Jiang. "Measurement of loudspeaker mechanical impedance by changing the sound load at the throat of loudspeaker." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 1 (August 1, 2021): 5457–66. http://dx.doi.org/10.3397/in-2021-3112.

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A loudspeaker is a device that converts electrical energy into acoustic energy by coupling between electrical impedance, mechanical impedance, and radiation impedance. The loudspeaker electro-mechanical-acoustic coupling model provides the experimental feasibility to measure the characteristic parameters. In this paper, an economical and practical measurement method of loudspeaker mechanical impedance is proposed. First, the mathematical relationship between loudspeaker electrical impedance and mechanical impedance is obtained based on the loudspeaker electro-mechanical-acoustic coupling model. Second, two electrical impedances with different known radiation impedance are measured by using a developed measurement system. Finally, the real and imaginary parts of the mechanical impedance are obtained according to the mathematical relationship. This method neither assumes that the loudspeaker mechanical impedance is constant in a frequency band nor does it build FEM models based on structural parameters. A loudspeaker is measured by using a developed measurement system. The result shows that the mechanical impedance and the force factor are functions of frequency. Moreover, a radiation impedance measurement is performed to verify the feasibility and accuracy of the proposed method.

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22

HE, WEI, HANGUANG XIAO, and XINGHUA LIU. "NUMERICAL SIMULATION OF HUMAN SYSTEMIC ARTERIAL HEMODYNAMICS BASED ON A TRANSMISSION LINE MODEL AND RECURSIVE ALGORITHM." Journal of Mechanics in Medicine and Biology 12, no. 01 (March 2012): 1250020. http://dx.doi.org/10.1142/s0219519411004587.

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A novel recursive algorithm was proposed to calculate the input impedance of human systemic arterial tree, and to simulate the human systemic arterial hemodynamics with an 55 segment transmission line model. In calculation of input impedance, the structure of the arterial tree was expressed as a single linked list. An infinitesimal constant was used to replace 0 Hz frequency to calculate the DC and AC part of input impedance simultaneously. The input impedance at any point of the arterial tree can obtain easily by the proposed recursive algorithm. The results of input impedance are in accord with experimental data and other models' results. In addition, some comparisons were conducted about the effects of arterial compliance, length, internal radius and wall thickness on the input impedance of ascending aorta. The results showed input impedances of ascending aorta displayed significantly different characteristics for different kinds of parameters. Finally, the blood pressure and flow waveforms of all arterial segments were calculated and displayed in 3D. The arterial elasticity and viscosity were discussed by changing the Young's modulus and the phase difference, respectively. The simulation results showed that the blood pressure and flow waveforms of the arterial tree reflected accurately the main characteristic features of physiopathological changes, which demonstrated the effectiveness of the proposed model.

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23

Wang, Chuan Bin, Qiang Shen, Guoqiang Luo, and Lian Meng Zhang. "Characteristic Wave Impedance of Ti-Mo System Composites and FGM." Materials Science Forum 475-479 (January 2005): 1537–40. http://dx.doi.org/10.4028/www.scientific.net/msf.475-479.1537.

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In the present paper, the relationship between characteristic wave impedance and compositions was mainly investigated in order to find a suitable theoretical model for predicting the impedance value of Ti-Mo system composites and FGM. At first, dense Ti-Mo composites with different weight fractions of Mo were prepared. Then the transverse and longitudinal wave velocities of the samples were measured and the characteristic wave impedance values were obtained. A mixture model was adopted to estimate the characteristic wave impedance value of Ti-Mo composites. Comparisons between the estimated and experimental results demonstrated that the suggested model was sufficiently accurate to predict the characteristic wave impedance value of Ti-Mo system composites and FGM.

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24

Zhu, Zhibo, Yang Zhao, Wei Yan, Xingfa Liu, and Ming Ju. "Modeling of line impedance stabilization network impedance characteristic based on genetic algorithm." Microelectronics Journal 113 (July 2021): 105095. http://dx.doi.org/10.1016/j.mejo.2021.105095.

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25

Ren, Qunyan, Yaxiao Mo, Li Ma, Shengming Guo, and Tianjun Liao. "Characteristic Acoustic Impedance for Reliable Environmental Characterization." Journal of Theoretical and Computational Acoustics 27, no. 02 (June 2019): 1850054. http://dx.doi.org/10.1142/s2591728518500548.

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The characteristic acoustic impedance is a favorable observation variable for geoacoustic inversion (GI) owing to its higher sensitivity than that of pressure or particle velocity. However, no theoretical explanations have been provided for it. As an attempt to understand the underlying physical mechanism, interpretations based on the normal mode theory are conducted in this study. Moreover, synthetic Bayesian geoacoustic inversion with two recording scenarios of a vertical line array and single receiver are also performed, both of which proved that the impedance can provide improved estimation.

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26

Ward, Leigh C., and Bruce H. Cornish. "Bioelectrical impedance analysis at the characteristic frequency." Nutrition 23, no. 1 (January 2007): 96. http://dx.doi.org/10.1016/j.nut.2006.09.003.

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27

Bogatin, A. S., E. V. Andreev, S. A. Kovrigina, and V. N. Bogatina. "Impedance as a characteristic of relaxation polarization." Bulletin of the Russian Academy of Sciences: Physics 78, no. 4 (April 2014): 317–19. http://dx.doi.org/10.3103/s1062873814040066.

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28

Williams, D. F., U. Arz, and H. Grabinski. "Characteristic-impedance measurement error on lossy substrates." IEEE Microwave and Wireless Components Letters 11, no. 7 (July 2001): 299–301. http://dx.doi.org/10.1109/7260.933777.

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29

Williams, D. F., B. K. Alpert, U. Arz, D. K. Walker, and H. Grabinski. "Causal characteristic impedance of planar transmission lines." IEEE Transactions on Advanced Packaging 26, no. 2 (May 2003): 165–71. http://dx.doi.org/10.1109/tadvp.2003.817339.

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30

Garb, Khona, and Raphael Kastner. "Characteristic impedance of quadruple-ridged square waveguides." Microwave and Optical Technology Letters 8, no. 5 (April 5, 1995): 236–38. http://dx.doi.org/10.1002/mop.4650080505.

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31

Torres-Torres, R. "Extracting characteristic impedance in low-loss substrates." Electronics Letters 47, no. 3 (2011): 191. http://dx.doi.org/10.1049/el.2010.2532.

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32

Qureshi, M. Umar, Mitchel J. Colebank, David A. Schreier, Diana M. Tabima, Mansoor A. Haider, Naomi C. Chesler, and Mette S. Olufsen. "Characteristic impedance: frequency or time domain approach?" Physiological Measurement 39, no. 1 (January 31, 2018): 014004. http://dx.doi.org/10.1088/1361-6579/aa9d60.

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33

Brouaye, F., M. Hélier, and J. Ch Bolomey. "Multisection transmission line with random characteristic impedance." Electronics Letters 35, no. 16 (1999): 1318. http://dx.doi.org/10.1049/el:19990893.

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34

Komarov, V. V. "Characteristic impedance of inhomogeneous T-septum waveguide." Electronics Letters 36, no. 12 (2000): 1032. http://dx.doi.org/10.1049/el:20000739.

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35

Marks, R. B., and D. F. Williams. "Characteristic impedance determination using propagation constant measurement." IEEE Microwave and Guided Wave Letters 1, no. 6 (June 1991): 141–43. http://dx.doi.org/10.1109/75.91092.

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36

Morita, Shigeki, Izumi Kuboyama, Toshihide Asou, Jiro Tanaka, Kouichi Tokunaga, Kenji Sunagawa, and Yasuhiko Harasawa. "-154-THE RELATIONSHIP BETWEEN AORTIC INPUT IMPEDANCE (CHARACTERISTIC IMPEDANCE) AND SYSTOLIC AORTIC PRESSURE." Japanese Circulation Journal 50, no. 6 (June 20, 1986): 504. http://dx.doi.org/10.1253/jcj.50.504_2.

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37

Nørgaard, Kren Rahbek, Efren Fernandez-Grande, and Søren Laugesen. "Compensating for evanescent modes and estimating characteristic impedance in waveguide acoustic impedance measurements." Journal of the Acoustical Society of America 142, no. 6 (December 2017): 3497–509. http://dx.doi.org/10.1121/1.5016808.

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38

Kim, Min Soo, Jin Sang Lee, Pan Kyeom Kim, and Geun Bae Lim. "Electrical Characteristics of Biological Active Point from Three Electrode Method." Key Engineering Materials 326-328 (December 2006): 889–94. http://dx.doi.org/10.4028/www.scientific.net/kem.326-328.889.

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We anticipate the development of new real time biological active point (BAP) systems based on skin impedance, since this measurement method has the superior characteristics of noninvasiveness and easy operation. In this paper, we report on the three electrode measure method that has the advantage of measuring the impedance of the BAPs under the skin. This system easily measured the potential difference between the measurement electrodes and reference electrodes. The BAPs have lower impedance at all frequencies and their reactance is much smaller than that of the surrounding skin. The characteristic frequencies of BAPs are about 20-30HZ higher than that of the surrounding skin. This technology analyzed accurately and objectively the reactance and characteristic frequency of BAPs.

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39

Rose, W. C., and A. A. Shoukas. "Two-port analysis of systemic venous and arterial impedances." American Journal of Physiology-Heart and Circulatory Physiology 265, no. 5 (November 1, 1993): H1577—H1587. http://dx.doi.org/10.1152/ajpheart.1993.265.5.h1577.

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Hemodynamic properties of the systemic vasculature were measured in eight anesthetized dogs using two-port impedance analysis. Blood pressures and flows were measured at the aortic root and the caval-atrial junction. Impedances were computed from 0.05 to 20 Hz to characterize the systemic vasculature. Pseudorandom variations in flow were produced with an extracorporeal perfusion system. Impedance measurements were made at carotid baroreceptor pressures of 50, 125, and 200 mmHg. A six-parameter lumped-element model best fitted the measured impedance spectra. At 125 mmHg, the mean parameter values were venous inertance, 13.5 g.kg.cm-4; venous and arterial compliances, 0.769 and 0.0214 ml.mmHg-1.kg-1; venous and arterial characteristic impedances, 0.028 and 0.084 mmHg.kg.min.ml-1; and arterial-to-venous small-vessel resistance, 0.706 mmHg.kg.min.ml-1. Regression analysis showed significant dependence of small-vessel resistance on baroreceptor pressure. The other parameters were not dependent on carotid sinus pressure, which is consistent with baroreflex control of venous unstressed volume but not compliance. We conclude that two-port impedance analysis is a useful tool for studying venous hemodynamics and the dynamic coupling between the veins and the right heart.

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40

BAO, Zhen, Ya-Bo ZHU, Wen-Xiang HU, and Yu-Jie YANG. "Research on the Impedance Characteristic of Carbon Coils." Journal of Inorganic Materials 24, no. 6 (November 24, 2009): 1137–40. http://dx.doi.org/10.3724/sp.j.1077.2009.01137.

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41

Roullard, J., S. Capraro, T. Lacrevaz, M. Gallitre, C. Bermond, A. Farcy, and B. Fléchet. "Characteristic impedance extraction of embedded and integrated interconnects." European Physical Journal Applied Physics 53, no. 3 (February 22, 2011): 33605. http://dx.doi.org/10.1051/epjap/2010100066.

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42

Huang, K. "Characteristic impedance of rectangular coaxial cone transmission line." IEE Proceedings - Microwaves, Antennas and Propagation 141, no. 4 (1994): 326. http://dx.doi.org/10.1049/ip-map:19941118.

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43

Ly-Gagnon, D. S., S. E. Kocabas, and D. Miller. "Characteristic Impedance Model for Plasmonic Metal Slot Waveguides." IEEE Journal of Selected Topics in Quantum Electronics 14, no. 6 (2008): 1473–78. http://dx.doi.org/10.1109/jstqe.2008.917534.

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44

Wu, Qiuyi, Yimin Yang, Ying Wang, Xiaowei Shi, and Ming Yu. "Characteristic Impedance Control for Branch-Line Coupler Design." IEEE Microwave and Wireless Components Letters 28, no. 2 (February 2018): 123–25. http://dx.doi.org/10.1109/lmwc.2017.2779881.

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45

Safin, Eugen, and Dirk Manteuffel. "Manipulation of Characteristic Wave Modes by Impedance Loading." IEEE Transactions on Antennas and Propagation 63, no. 4 (April 2015): 1756–64. http://dx.doi.org/10.1109/tap.2015.2401586.

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46

Yu, Yantao, Shiyong Chen, Meng Li, and Mingchun Tang. "Modified Wilkinson power divider with uniform characteristic impedance." Microwave and Optical Technology Letters 61, no. 1 (November 26, 2018): 280–83. http://dx.doi.org/10.1002/mop.31419.

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47

Roy, J. S., D. R. Poddar, A. Mukherjee, and S. K. Chowdhury. "Characteristic impedance of a curved microstrip transmission line." Microwave and Optical Technology Letters 1, no. 7 (September 1988): 257–59. http://dx.doi.org/10.1002/mop.4650010710.

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48

Roy, J. S., D. R. Poddar, A. Mukherjee, and S. K. Chowdhury. "Characteristic impedance of a curved microstrip transmission line." Microwave and Optical Technology Letters 2, no. 1 (January 1989): 37. http://dx.doi.org/10.1002/mop.4650020114.

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49

Carin, L., and K. J. Webb. "Characteristic impedance of multilevel, multiconductor hybrid mode microstrip." IEEE Transactions on Magnetics 25, no. 4 (July 1989): 2947–49. http://dx.doi.org/10.1109/20.34333.

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50

Williams, D. F., and B. K. Alpert. "Characteristic impedance, power, and causality [waveguide circuit theory]." IEEE Microwave and Guided Wave Letters 9, no. 5 (May 1999): 181–82. http://dx.doi.org/10.1109/75.766757.

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