Printer Friendly

VERY SIMPLE AND ACCURATE COMPUTER-AIDED-DESIGN (CAD) MODELS DEVELOPED BY GENETIC PROGRAMMING FOR THE QUASISTATIC ANALYSIS OF UNSHIELDED SUSPENDED AND INVERTED MICROSTRIP LINES.

Abstract: Very simple computer-aided-design models are introduced to determine the characteristic parameters such as effective permittivities and characteristic impedances of unshielded suspended and inverted microstrip lines. Computer-aided-design models are determined with the use of the genetic programming. The results of computer-aided-design models are compared with the results of quasi-static analysis, experimental works available in the literature and a commercial electromagnetic simulator. The comparison results clearly show that computer-aided-design models proposed in this work are in very good agreement with the simulation, theoretical and experimental results for the suspended and inverted microstrip lines. The design parameter ranges in this work are 2 [less than or equal to] [[epsilon].sub.r2] [less than or equal to] 20, 0.5 [less than or equal to] w/b [less than or equal to] 10, 0.1 [less than or equal to] a/b [less than or equal to] 1.5, and the respective characteristic impedances of unshielded suspended and inverted microstrip lines are 28[OMEGA] [less than or equal to] [Z.sub.0] [less than or equal to] 185[OMEGA], and 24 [OMEGA] [less than or equal to] [Z.sub.0] [less than or equal to] 159 [OMEGA], respectively. It is observed that the accuracies of computer-aided-design models proposed in this paper are good enough for the most practical cases.

Keywords: Suspended and inverted microstrip, Computer-aided-design models, Genetic programming, Characteristic impedance, Effective permittivity

1. Introduction

Suspended and inverted microstrip (S&IM) lines are very useful transmission lines and they have an air gap between dielectric substrate and ground plane. They have many advantages such as lower dispersion, lower propagation loss and easy connections to conventional microstrip lines. S&IM lines are used to manufacture most of the microstrip components, such as amplifiers, mixers, power dividers, frequency multipliers, and directional couplers. Due to the symmetrical shielding and the wide range of characteristic impedance values achievable make these transmission lines particular suitable for filters [1, 2].

Many researches dealing with S&IM lines have been realized in the literature and they can be classified in three groups [3]. The first group consists of analytical works related with rigorous electromagnetic analysis of S&IM lines and their discontinuities. The works about the applications of S&IM lines such as filters, couplers, phase shifters, power combiners, mixers and antennas can be added in the second group. The third group contains many research papers about computer-aided-design (CAD) models for analyzing of different S&IM lines.

Four CAD models have been proposed for the quasistatic analysis of unshielded S&IM lines in the literature [4-9]. The first CAD model was reported in 1985 [4] and the accuracy of this model is better than [+ or -]1 % according to the exact theoretical data reproduced by Tomar etal [3]. This model contains an empirical expression depended on the geometrical dimensions of unshielded S&IM lines for the effective permittivity and it is valid for [[epsilon].sub.r2] [less than or equal to] 6. The most important disadvantage of this work is the restriction of the dielectric constant [[epsilon].sub.r2] [less than or equal to] 6 for substrate material, because substrate materials with [[epsilon].sub.r2] [greater than or equal to] 6 are often used in practice for example alumina ([[epsilon].sub.r2] = 9.6) and GaAs ([[epsilon].sub.r2] = 12.9). The second quasi-static CAD model is a generalized of the first CAD model [5]. This model is valid for a wider range of design parameters and the accuracy of this model according to the exact theoretical data reproduced in [3] is better than [+ or -]0.6 % for both unshielded suspended and inverted microstrip lines. This model contains a polynomial expression depending on geometrical dimensions of the lines for the effective permittivity. The third CAD model was first reported by Svacania in 1992 [6, 7] and later Schellenberg has modified the Svacania's formulas, uses a conformal mapping approach, coupled with curve-fitting to obtained theoretical data, and proposed two closed-form equations for the effective permittivities of unshielded S&IM lines [8]. These models are valid for [[epsilon].sub.r2] [less than or equal to] 12.9. The claimed accuracies of these models are better than [+ or -]0.65 % and [+ or -]1 % for unshielded S&IM lines, respectively [8]. The last CAD model was proposed by Yildiz and Saracoglu for the effective permittivities of unshielded S&IM lines [9]. This model is based on artificial neural network and does not contain closed-form equations.

The analysis CAD models proposed in the literature except last model contain long mathematical expressions and require extensive calculations to compute the effective permittivities of unshielded S&IM lines. Beside, these models do not have good accuracy except the second model [5]. More significantly, these CAD models do not contain closed-form equations to directly compute the characteristic impedances of unshielded S&IM lines and they are valid for only the effective permittivities of these lines. In the literature, the characteristic impedances of unshielded S&IM lines are calculated by using a formula depending on the effective permittivities of unshielded S&IM lines and characteristic impedance of a conventional microstrip line. For this reason, this formula becomes very complex, contains very long mathematical expressions and requires extensive calculations to compute the characteristic impedances of unshielded S&IM lines. Consequently, CAD models proposed in the literature are not very suitable to compute the propagation characteristics of S&IM lines. The aim of this paper is to present accurate and very simple CAD models developed by genetic programming (GP) for both effective permittivities and characteristic impedances of unshielded S&IM lines.

GP is an automated method for creating a working computer program from a high-level problem statement of the problem and it was applied to many engineering problems [10-15]. According to our researches, GP was also successfully applied to the design problems of microwave planar transmission lines for the first time by Kisioglu and Yildiz [16]. In this application, new and accurate synthesis models developed by GP were proposed to calculate the geometrical dimensions of coplanar waveguide with a finite width ground plane. New synthesis models consist of two closed-form design equations. One of them calculates the strip width of the coplanar waveguide and the other calculates the sloth width of the coplanar waveguide having a desired characteristic impedance for a given dielectric substrate material. In order to show the validities of proposed synthesis models for the coplanar waveguide with a finite width ground plane, obtained results are compared with the results of quasi-static analysis and very good agreements between them were observed [16].

In this paper, CAD models were developed by using GP to directly calculate both the effective permittivities and characteristic impedances of unshielded S&IM lines. CAD models can be used to easily and accurately calculate the propagation characteristics of unshielded S&IM lines. The ranges of validties of these CAD models valid very wide region and they are 2 [less than or equal to] [[epsilon].sub.r2] [less than or equal to] 20, 0.5 [less than or equal to] w/b [less than or equal to] 10, 0.1 [less than or equal to] a/b [less than or equal to] 1.5. In order to show the accuracies and validities of CAD models produced by GP, their results are compared with the results of theoretical [2, 5, 8], experimental works [17-19] available in the literature, and a commercial electromagnetic simulator HFSS [3].

2. Genetic Programming

Soft computing can be defined to be a collection of some computational techniques that try to imitate human intelligence for creating solution of complex problems, which attempt to overcome the impreciseness, uncertainty in the problem by some human-like capabilities such as reasoning, learning, decision making,. Components of soft computing include neural networks, fuzzy systems, evolutionary algorithms such as genetic algorithms, GP and swarm intelligence based algorithms.

GP was developed by Koza and adopted from the process of natural evolution and genetics [20]. GP belongs to the class of evolutionary algorithms which is based on the "principle of survival of the fittest". GP is however a relatively new addition to the group of other evolutionary algorithm techniques such as genetic algorithms, evolutionary programming and evolution strategies [21]. GP is similar to genetic algorithm [22]. The main difference between GP and genetic algorithm is that GP represents a solution as a tree instead of a binary string used in genetic algorithm.

GP differs from other data-driven models such as fuzzy rule-based systems and artificial neural networks [23]. It has found application mostly in the area of symbolic regression. The aim is to find a functional relationship between input and output variables in the symbolic regression problems. GP is a computer program which is often given as a tree model. There are terminals in the tree model where the internal nodes correspond to a set of functions used in the program and the external nodes indicate variables and constants used as the input to functions [24]. GP has been used as an optimization technique on the variety of problems and applications [25, 26].

In applying genetic programming to a problem, there are five major preparatory steps. These five steps involve determining terminal set, function set, fitness function, control parameter, and termination criteria. The first step is the set of terminals which may consist of the program's external inputs, functions with no arguments and constants. The second step is the set of primitive functions that are to be used to generate the mathematical expression that attempts to fit the given finite sample of data. The third step is the design of a fitness measure function. The fourth step includes determining the values of control parameters and in the last step a termination criterion for the algorithm is defined [27, 28].

3. CAD Models Developed by Genetic Programming for Unshielded S&IM Lines

The configurations of unshielded S&IM lines are shown in Figure 1. It is assumed that all conductors used in transmission lines are infinitely thin and perfectly conducting. GP finds a functional relationship between input and output variables for analyzing unshielded S&IM lines. In the analysis models, the inputs are relative permittivity ([[epsilon].sub.r2]), geometrical dimensions of the transmission lines (a/b, w/b) and output is effective permittivity ([[epsilon].sub.eff]) or characteristic impedance ([Z.sub.0]) of unshielded S&IM lines.

CAD models to be produced by GP for the quasistatic analysis of unshielded S&IM lines are essentially derived from the data set. The data set used in this paper has been obtained from the quasi-static analysis results [5]. The data set includes 3600 samples for each unshielded S&IM lines, separately. The ranges of the parameters in the data set are 2 [less than or equal to] [[epsilon].sub.r2] [less than or equal to] 20, 0.5 [less than or equal to] w/b [less than or equal to] 10, 0.1 [less than or equal to] a/b [less than or equal to] 1.5, and the respective characteristic impedances of unshielded S&IM lines are 28[OMEGA] [less than or equal to] [Z.sub.0] [less than or equal to] 185[OMEGA], and 24 [OMEGA] [less than or equal to] [Z.sub.0] [less than or equal to] 159 [OMEGA], respectively.

In order to find the suitable CAD models produced by GP for the quasi-static analysis of unshielded S&IM lines, many experiments were carried out. In these experiments, the most suitable values of population size, mutation rate, reproduction rate and crossover rate are chosen as 50, 0.1, 0.05 and 0.85, respectively. After many trials, accurate and very simple analysis CAD models were determined to compute the characteristic parameters of unshielded S&IM lines for a given relative dielectric constant [[epsilon].sub.r2] and physical dimensions (w/b and a/b) of substrate material. The analysis CAD models determined by GP for calculating the characteristic impedance and effective permittivity of unshielded SM line, which produce very good results, are given below;

[mathematical expression not reproducible] (1)

[mathematical expression not reproducible] (2)

The analysis CAD models produced by GP for computing the characteristic impedance and effective permittivity of unshielded IM line are given below;

[mathematical expression not reproducible] (3)

[mathematical expression not reproducible] (4)

with

u = [w/b] and x =[a/b] (5)

where [[eta].sub.0]=120[pi] [OMEGA] is the intrinsic impedance of free space and ([[alpha].sub.1], [[alpha].sub.2],... ., [[alpha].sub.11]) are unknown coefficients.

The values of unknown coefficients in the analysis CAD models are optimally found by GP and the results are listed in Table 1. The analysis CAD models are obtained by substituting the values of the coefficients in Equations 1, 2, 3 and 4 for the calculation of characteristic parameters of unshielded S&IM lines.

4. Numerical Results and Discussion

In this paper, analysis CAD models developed by GP for unshielded S&IM lines are presented. Many extensive comparisons have been made to confirm the accuracies and validities of CAD models proposed in this work for both unshielded S&IM lines. The results of CAD models are compared with the results of quasistatic analysis, experimental works available in the literature and a commercial electromagnetic simulator HFSS.

The first comparison is made for the effective permittivities and characteristic impedances of unshielded S&IM lines according to the ratio of normalized strip width (w/b) for different a/b ratios ([[epsilon].sub.r2] = 3.78). The obtained results are given in Figures 2 and 3. In these figures, the results of CAD models are compared with the results of Tomar and Bhartia's work [5] known as the best accurate model in the literature. As it can be clearly seen from these figures, there are very good agreement between our CAD model results and Tomar and Bhartia's results.

The results of second comparison are shown in Tables 2 and 3 for characteristic impedances and effective permittivities of unshielded S&IM lines with different geometrical dimensions and relative permittivities, respectively. In these tables, calculated results obtained from CAD models generated by GP are compared with the results of variational method in Fourier transform domain [2] and CAD models [5, 8] available in the literature, and a commercial electromagnetic simulator HFSS [3].

Finally, to consolidate the validities of CAD models proposed in this paper, their effective permittivity results are also compared with the results of experimental works [17-19] for both unshielded S&IM lines with different geometrical dimensions and relative permittivities. The calculated results of CAD models generated by GP in this work are given in Table 4. The results of variational method [2] and analysis CAD models [5, 8] available in the literature and HFSS results are also added in Table 4. The calculated values for effective permittivity obviously show that there are very good agreement again among CAD models developed by GP, theoretical [2, 5, 8], experimental results [17-19] available in the literature and HFSS [3].

Similar good results are also observed for all unshielded S&IM lines to be analyzed. The average percentage errors of CAD models for the characteristic impedance and effective permittivity are calculated to be 0.79% and 0.74%, respectively, for 3600 unshielded SM line samples. The average percentage errors of the CAD models for the characteristic impedance and effective permittivity are calculated to be 0.33% and 0.68%, respectively, for 3600 unshielded IM line samples, as compared with the results of quasi-static analysis [5].

Consequently, the agreement among the results of CAD models developed by GP, analysis CAD models, the results of variational method in Fourier transform domain, experimental works available in the literature, and HFSS obviously confirm the validity of CAD models proposed in this work for analyzing unshielded S&IM lines. The results also illustrate the performance of GP in obtaining high quality solutions.

5. Conclusions

In this work, accurate and very simple analysis CAD models for unshielded S&IM lines were developed by using GP. The proposed CAD models allow the designers to directly and easily calculate the characteristic parameters such as characteristic impedances and effective permittivities of unshielded S&IM lines. The results of CAD models proposed in this work are in good agreement with the result of theoretical, experimental works available in the literature and HFSS. It was observed that the accuracies of CAD models for unshielded S&IM lines were good enough for the most practical cases. The proposed CAD models are also very simple and useful for many microwave engineering applications. Finally, the procedure used in this paper could be also useful for developing simple and accurate analysis and design equations for other microwave transmission lines having different geometrical structure.

6. References

[1] S. M. Musa, M. N. O. Sadiku, "Quasi-TEM modeling of open suspended and inverted substrate microstrip lines", International Journal of Research and Reviews in Computer Science, vol. 3, pp. 1421-1424, 2012.

[2] P. Bhartia, I.J. Bahl, "Millimeter-wave engineering and applications". Wiley, New York, 1984.

[3] R. Tomar, Y. M. Antar, P. Bhartia, "Computer-aided design (CAD) of suspended--substrate microstrips: an overview", International Journal of RF and Microwave Computer-Aided Engineering, vol. 15, pp. 44-55, 2005.

[4] P. Pramanick, P. Bhartia, "Computer-aided design for millimeter wave finlines and suspended substrate microstrip lines", IEEE Trans Microwave Theory Tech, vol. 33, pp. 1429-1434, 1985.

[5] R.S. Tomar, P. Bhartia, "New quasi-static models for computer aided design of suspended and inverted microstrip lines", IEEE Trans Microwave Theory Tech, vol. 35, pp. 453-457, 1987.

[6] J. Svanica, "Analysis of multilayer microstrip lines by a conformal mapping method", IEEE Trans Microwave Theory Tech, vol. 40, pp. 769-772, 1992.

[7] J. Svanica, "A simple quasi-static determination of basic parameters of multilayer microstrip and coplanar waveguide", IEEE Microwave Guided Wave Lett, vol. 2, pp. 385-387, 1992.

[8] J. M. Schellenberg, "CAD models for suspended and inverted microstrip", IEEE Trans Microwave Theory Tech, vol. 43, pp. 1247-1252, 1995.

[9] C. Yildiz, O. Saracoglu, "Simples models based on neural networks for suspended and inverted microstrip lines", Microwave Optical Tech Lett, vol. 39, pp. 383-389, 2003.

[10] A. Baykasoglu, H. Gullu, H. Canakci, L. Ozbakir, "Prediction of compressive and tensile strength of limestone via genetic programming", Expert Systems with Applications, vol. 35, pp. 111-123, 2008.

[11] J. R. Koza, F. H. Bennett III, D. Andre, M. A. Keane, F. Dunlap, "Automated synthesis of analog electrical circuits by means of genetic programming", IEEE Transactions on Evolutionary Computation, vol. 1, pp. 109-128, 1997.

[12] L. S. Belisario, H. Pierreval, "Using genetic programming and simulation to learn how to dynamically adapt the number of cards in reactive pull systems", Expert Systems with Applications, vol. 42, pp. 3129-3141, 2015.

[13] A. K. Patnaik, P. K. Bhuyan, "Application of genetic programming clustering in defining LOS criteria of urban street in Indian context", Travel Behaviour and Society, vol. 3, pp. 38-50, 2016.

[14] K. Ishikawa, W. Kitagawa, T. Takeshita, "Design for electromagnetic device by multiobjective optimization using genetic programming", Electronics and Communications in Japan, vol. 100, pp. 56-65, 2017.

[15] M. V. Lizancos, J. L. P. Ordonez, I. M. Lage, "Analytical and genetic programming model of compressive stregth of eco concretes by NDT according to curing tempareture", Construction and Building Materials,vol. 144, pp.195-206, 2017.

[16] H. Kisioglu, C. Yildiz, "Sonlu genislikte toprak duzlemine sahip es duzlemli dalga kilavuzu icin yeni sentez modelleri", Elektrik, Elektronik ve Biomedikal Muhendisligi Konferansi, ELECO 2016-Bursa, 558-561.

[17] B. E. Spielmen, "Dissipation loss effects in isolated and coupled transmission lines", IEEE Trans Microwave Theory Tech, vol. 25, pp. 648-656, 1977.

[18] E. Yamashita, "Variational method for the analysis of microstrip like transmission lines", IEEE trans Microwave Theory Tech, vol. 16, pp. 529-535, 1968.

[19] M. V. Schneider, "Microstrip lines for microwave integrated circuits", Bell System Tech J, vol. 48, pp. 1421-1444, 1969.

[20] J. R. Koza, "Genetic programming: on the programming of computers by means of natural selection" vol. 229, Cambridge, Massachusetts, London, England: The MIT Press, 1992.

[21] V. Babovic, M. Keijzer, "Genetic programming as a model induction engine", Journal of Hydroinformatics, vol. 2, pp. 35-60, 2000.

[22] J. R. Koza, "Genetic Programming II: Automatic discovery of reusable programs", MIT Press, 1994.

[23] V. Babovic, R. Rao, Evolutionary computing in hydrology, in advances in data-based approaches for hydrologic modeling and forecasting, World Scientific, 2010, pp. 347-369.

[24] M. D. Kramer, D. Zhang, "GAPS: A genetic programming system", Computer Software and Applications Conference, 2000, pp. 614-619.

[25] K. Sickel, J. Hornegger, "Genetic programming for expert systems", IEEE World Congress on Computational Intelligence, Barcelona, Spain, 2010, pp. 2695-2702.

[26] M. Willis, H. G. Hiden, P. Marenbach, B. McKay, G. A. Montague, "Genetic programming: an introduction and survey of applications", In Second International Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications, 1997, pp. 314-319.

[27] R. Poli, W. B. Langdom, N. F. McPhee, J. R. Koza, "Genetic Programming an introductory tutorial and a survey of techniques and applications", Technical Report CES-475, ISSN: 1744-8050, 2007, pp. 927-1028.

[28] J.R. Koza, "Survey of genetic algorithms and genetic programming", Microelectronics Communications Technology Producing Quality Products Mobile and Portable Power Emerging Technologies (WESCON/'95), San Francisco, California, 1995, pp. 589-594.

Celal Yildiz was born in Kayseri, Turkey, 1958. He received the BS degree from Erciyes University, Kayseri, in 1983, the MS degree from Istanbul Technical University, in 1988, and the PhD degree from Erciyes University, in 1992, all in electronic engineering. He is now a professor at the Department of Electrical and Electronics Engineering, Erciyes University. He is working in the areas of neural networks, fuzzy inference systems, optimization techniques and their applications to electromagnetics and microwave engineering problems, the optical fibers, and the diffraction of electromagnetic waves.

Hakan Kisioglu was born in Kahramanmaras, Turkey, 1983. He received BS degree and M.S degree from Erciyes University in the Electrical and Electronics Engineering, Kayseri, Turkey in 2009 and 2011, respectively. He is now a PhD degree student in Erciyes University and he is working as a lecturer at the Department of Electrical and Electronics Engineering, Bozok University. His current research activities include optimization techniquies and their applications to electromagnetic and microwave engineering problems.

Celal YILDIZ (1) and Hakan KISIOGLU (2)

(1) Faculty of Engineering, Department of Electrical and Electronics Engineering, Erciyes University, Kayseri, Turkey.

(2) Faculty of Engineering and Architecture, Department of Electrical and Electronics Engineering, Bozok University, Yozgat, Turkey. yildizc@erciyes.edu.tr, hakan.kisioglu@bozok.edu.tr

Received on: 01.03.2017

Accepted on: 10.05.2017
Table 1. The values of the coefficients used in CAD models for the
unshielded S&IM lines

                                   [[alpha].sub.1]  [[alpha].sub.2]

Suspended   ([Z.sub.0])                3.6450           0.9952
microstrip  ([[epsilon].sub.eff])      1.0501           0.7993
Inverted    ([Z.sub.0])                2.0540           1.0569
microstrip  ([[epsilon].sub.eff])      1.0068           0.0249

            [[alpha].sub.3]  [[alpha].sub.4]  [[alpha].sub.5]

Suspended       0.0533           1.2319           0.9952
microstrip      1.7814           1.0508           0.4085
Inverted        0.7599           3.4134           0.7029
microstrip      0.4235           0.0063           0.0249

            [[alpha].sub.6]  [[alpha].sub.7]  [[alpha].sub.8]

Suspended       5.7193           5.6497           0.9952
microstrip      0.5734           0.0331           1.5063
Inverted        3.7305           3.7305           1.4177
microstrip      0.5449           0.0152           0.0030

            [[alpha].sub.9]  [[alpha].sub.10]  [[alpha].sub.11]

Suspended       1.2505            3.3701            0.2066
microstrip      1.0508
Inverted        0.3105
microstrip

Table 2. Results of CAD model developed by GP, analysis models
available in the literature and HFSS for the characteristic impedance
and effective permittivity of unshielded SM line

                                           Analysis Model
[[epsilon].sub.r2]  a/b   w/b                   [2]
                               [square root of       [Z.sub.0]
                               [[epsilon].sub.eff]]  ([OMEGA])

                          0.5    1.1018               161.84
                          1      1.0830               127.11
                          2      1.0681                92.83
                          3      1.0613                74.22
                          4      1.0574                62.18
2.22                0.2   5      1.0548                53.65
                          6      1.0530                47.65
                          7      1.0517                42.26
                          8      1.0508                38.24
                          9      1.0500                34.94
                         10      1.0494                32.17
                          0.5    1.9184               108.80
                          1      1.8220                92.07
                          2      1.7096                74.58
                          3      1.6417                63.98
                          4      1.5957                56.40
12.9                1     5      1.5622                50.60
                          6      1.5367                45.97
                          7      1.5164                42.17
                          8      1.4999                38.99
                          9      1.4862                36.27
                         10      1.4746                33.93

                              Analysis Model
[[epsilon].sub.r2]                 [5]
                    [square root of       [Z.sub.0]
                    [[epsilon].sub.eff]]  ([OMEGA])

                      1.0955              162.14
                      1.0816              126.61
                      1.0664               92.35
                      1.0587               73.85
                      1.0547               61.86
2.22                  1.0526               53.36
                      1.0516               46.98
                      1.0512               42.00
                      1.0508               38.01
                      1.0502               34.75
                      1.0489               32.04
                      1.9121              108.81
                      1.8296               91.18
                      1.7149               73.77
                      1.6401               63.46
                      1.5883               56.09
12.9                  1.5510               50.41
                      1.5232               45.84
                      1.5019               42.07
                      1.4849               38.90
                      1.4707               36.20
                      1.4582               33.88

                            Analysis Model
[[epsilon].sub.r2]               [8]
                    [square root of       [Z.sub.0]
                    [[epsilon].sub.eff]]  ([OMEGA])

                     1.1146               159.35
                     1.0987               124.64
                     1.0825                90.98
                     1.0740                72.80
                     1.0688                61.04
2.22                 1.0653                52.72
                     1.0628                46.48
                     1.0608                41.62
                     1.0593                37.70
                     1.0581                34.48
                     1.0572                31.79
                     1.9202               108.4
                     1.8257                91.37
                     1.7072                74.10
                     1.6373                63.57
                     1.5912                55.99
12.9                 1.5583                50.17
                     1.5336                45.53
                     1.5142                41.73
                     1.4986                38.54
                     1.4856                35.84
                     1.4747                33.50

                               HFSS (1 GHz)
[[epsilon].sub.r2]                 [3]
                    [square root of       [Z.sub.0]
                    [[epsilon].sub.eff]]  ([OMEGA])

                      1.1027               162.95
                      1.0826               129.38
                      1.0668                96.16
                      1.0611                75.43
                      1.0574                62.80
2.22                  1.0550                53.37
                      1.0540                48.50
                      1.0531                42.51
                      1.0515                38.71
                      1.0512                34.33
                      1.0502                31.46
                      1.9162               109.66
                      1.8237                92.14
                      1.7026                75.05
                      1.6377                64.60
                      1.5903                56.59
12.9                  1.5560                50.57
                      1.5310                46.57
                      1.5076                42.12
                      1.4926                38.15
                      1.4826                35.43
                      1.4741                33.52

                               CAD model
[[epsilon].sub.r2]            (This work)
                    [square root of       [Z.sub.0]
                    [[epsilon].sub.eff]]  ([OMEGA])

                      1.1345              167.35
                      1.1038              128.69
                      1.0809               92.93
                      1.0716               74.31
                      1.0665               62.35
2.22                  1.0633               53.87
                      1.0611               47.49
                      1.0595               42.50
                      1.0583               38.48
                      1.0573               35.16
                      1.0566               32.38
                      1.9109              108.54
                      1.8228               92.67
                      1.7075               75.08
                      1.6351               64.33
                      1.5853               56.64
12.9                  1.5489               50.75
                      1.5211               46.03
                      1.4991               42.16
                      1.4814               38.90
                      1.4667               36.13
                      1.4544               33.73

Table 3. Results of CAD model developed by GP, analysis models
available in the literature and HFSS for the characteristic impedance
and effective permittivity of unshielded IM line

                                     Analysis Model
[[epsilon].sub.r2]  a/b  w/b              [2]
                               [square root of       [Z.sub.0]
                               [[epsilon].sub.eff]]  ([OMEGA])

                          0.5    1.1608              144.59
                          1      1.1348              112.44
                          2      1.1015               81.80
                          3      1.0810               65.43
                          4      1.0673               54.87
2.22                1     5      1.0575               47.39
                          6      1.0502               41.77
                          7      1.0444               37.39
                          8      1.0398               33.86
                          9      1.0360               30.96
                         10      1.0328               28.52
                          0.5    1.5434              108.75
                          1      1.4349               88.92
                          2      1.3174               68.39
                          3      1.2521               56.49
                          4      1.2097               48.41
9.8                 0.6   5      1.1795               42.48
                          6      1.1568               37.92
                          7      1.1390               34.28
                          8      1.1246               31.31
                          9      1.1128               28.82
                         10      1.1028               26.71

                          Analysis Model
[[epsilon].sub.r2]             [5]
                    [square root of       [Z.sub.0]
                    [[epsilon].sub.eff]]  ([OMEGA])

                      1.1636              143.36
                      1.1359              111.37
                      1.1006               80.95
                      1.0792               64.70
                      1.0651               54.23
2.22                  1.0552               46.82
                      1.0479               41.26
                      1.0425               36.91
                      1.0383               33.42
                      1.0350               30.54
                      1.0325               28.13
                      1.5485              107.73
                      1.4430               87.67
                      1.3177               67.61
                      1.2462               56.03
                      1.2004               48.12
9.8                   1.1689               42.27
                      1.1459               37.73
                      1.1287               34.10
                      1.1154               31.11
                      1.1048               28.61
                      1.0964               26.49

                              Analysis Model
[[epsilon].sub.r2]                 [8]
                      [square root of       [Z.sub.0]
                      [[epsilon].sub.eff]]  ([OMEGA])

                      1.1618                143.59
                      1.1711                108.03
                      1.0885                 81.85
                      1.0701                 65.25
                      1.0583                 54.58
2.22                  1.0501                 47.05
                      1.0440                 41.41
                      1.0393                 37.03
                      1.0355                 33.51
                      1.0325                 30.62
                      1.0299                 28.20
                      1.4966                111.47
                      1.5396                 82.17
                      1.3286                 67.06
                      1.2613                 55.36
                      1.2177                 47.44
9.8                   1.1869                 41.62
                      1.1640                 37.14
                      1.1463                 33.57
                      1.1321                 30.65
                      1.1205                 28.21
                      1.1108                 26.15

                              HFSS (1 GHz)
[[epsilon].sub.r2]                 [3]
                      [square root of       [Z.sub.0]
                      [[epsilon].sub.eff]]  ([OMEGA])

                        1.1601         148.64
                        1.1345         113.41
                        1.1036          80.72
                        1.0826          65.73
                        1.0686          56.34
2.22                    1.0578          47.79
                        1.0502          41.43
                        1.0474          37.27
                        1.0416          33.86
                        1.0392          30.83
                        1.0300          29.48
                        1.5440         110.28
                        1.4279          89.76
                        1.3161          69.44
                        1.2329          57.15
                        1.1996          48.01
9.8                     1.1790          42.21
                        1.1615          37.04
                        1.1446          32.69
                        1.1269          29.99
                        1.1050          27.62
                        1.1050          25.76

                            CAD model
[[epsilon].sub.r2]         (This work)
                    [square root of       [Z.sub.0]
                    [[epsilon].sub.eff]]  ([OMEGA])

                      1.1956         142.02
                      1.1586         109.90
                      1.1142          79.79
                      1.0886          64.06
                      1.0719          53.89
2.22                  1.0601          46.64
                      1.0514          41.16
                      1.0447          36.85
                      1.0393          33.38
                      1.0350          30.50
                      1.0313          28.09
                      1.5423         107.92
                      1.4336          88.34
                      1.3102          67.79
                      1.2416          56.09
                      1.1977          48.14
9.8                   1.1627          42.27
                      1.1447          37.72
                      1.1274          34.07
                      1.1137          31.08
                      1.1026          28.57
                      1.0934          26.45

Table 4. Results of CAD models developed by GP, experimental works,
analysis models published in the literature and HFSS for the effective
permittivities of unshielded S&IM lines

                                                 Effective Permittivity
                                                     ([epsilon]eff)
            [[epsilon].sub.r2]   a/b     w/b      Experimental Data

                                                 [18]    [17]    [19]

                                1.6069  0.6541  1.7566
                                0.8034  0.4727  1.5986
            2.55                0.4017  0.3041  1.4775    --      --
Suspended                       0.2008  0.1775  1.3841
Microstrip                              1               1.5269
                                        2               1.3763
                                1.333   3        --     1.2735    --
                                        4               1.2137
                                        5               1.1709
            3.78                        0.5                     1.3689
Inverted                                1.0                     1.2544
Microstrip                              2.0                     1.1664
                                0.333   3.0      --       --    1.1342
                                        4.0                     1.1025
                                        5.0                     1.0712

                          Effective Permittivity
                              ([epsilon]eff)
            Analysis  Analysis  Analysis   HFSS        CAD
             Model     Model     Model    (1 GHz)     model
              [2]       [5]       [8]       [3]    (This work)

            1.5976    1.6002    1.5847    1.6703     1.5996
            1.4879    1.4879    1.4751    1.5587     1.5609
            1.3959    1.3806    1.3853    1.4568     1.5098
Suspended   1.3273    1.2760    1.3149    1.3884     1.4554
Microstrip  1.6276    1.6340    1.6215    1.6240     1.6340
            1.4701    1.4689    1.4577    1.4660     1.4600
            1.3740    1.3675    1.3684    1.3590     1.3574
            1.3098    1.3000    1.3092    1.2929     1.2898
            1.2642    1.2524    1.2670    1.2450     1.2418
            1.4551    1.4682    1.3964    1.4299     1.4297
Inverted    1.3375    1.3391    1.3581    1.3165     1.3163
Microstrip  1.2285    1.2181    1.2301    1.2078     1.2077
            1.1737    1.1608    1.1744    1.1552     1.1552
            1.1340    1.1278    1.1408    1.1242     1.1241
            1.1168    1.1063    1.1185    1.1038     1.1037
COPYRIGHT 2017 AVES
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2017 Gale, Cengage Learning. All rights reserved.

Article Details
Printer friendly Cite/link Email Feedback
Author:Yildiz, Celal; Kisioglu, Hakan
Publication:Istanbul University - Journal of Electrical & Electronics Engineering
Article Type:Report
Date:Jul 1, 2017
Words:5382
Previous Article:Short Range Indoor Distance Estimation by Using RSSI Metric.
Next Article:DIAGNOSIS OF THE PARKINSON DISEASE BY USING DEEP NEURAL NETWORK CLASSIFIER.
Topics:

Terms of use | Privacy policy | Copyright © 2019 Farlex, Inc. | Feedback | For webmasters