ISSN: 2277 – 9043             International Journal of Advanced Research in Computer Science and Electronics Engineering (...
ISSN: 2277 – 9043                 International Journal of Advanced Research in Computer Science and Electronics Engineeri...
ISSN: 2277 – 9043                         International Journal of Advanced Research in Computer Science and Electronics E...
ISSN: 2277 – 9043             International Journal of Advanced Research in Computer Science and Electronics Engineering (...
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  1. 1. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering (IJARCSEE) Volume 1, Issue 6, August 2012 THEORITICAL ANALYSIS OF MICROSTRIP LINE USING QUASI-STATIC APPROACH Akanksha lal, Mukesh Kumar, Rohini SaxenaAbstract- In this paper we propose the estimation of the II. STRUCTURE AND FORMULATIONcharacteristic impedance and the effective dielectric constantof microstrip line using quasi static analysis and performances Microstrip line comprising a conducting strip separated fromare predicted using theoretical analysis. Numerically efficient a ground plane by a dielectric layer known as the substrate,and accurate formulae based on the quasi static method for theanalysis of microstrip line structures are presented. The which is shown in figure 1.analysis formulas for microstrip line are derived and verifiedwith Matlab. Characteristic Impedance of microstrip line for Microstrip linedifferent normalized strip width as well as for differenteffective permittivity is under consideration in this work. Index Terms- Microstrip line, Quasi –static, EffectivePermittivity. W t I. INTRODUCTION In today’s modern communication industry and with thetrend towards operation at X-band, Microstrip transmission h ∈𝑟lines are one of the most popular types of planartransmission lines. Microstrip line has been used extensivelyin microwave as well as transmission line for wide range Ground Planeapplication. Transmission system usually requires a portableand a probable system suited to less or lossless energy Figure 1: Microstrip linetransmission, primarily because of its relative ease offabrication and its simple integration with other passive and In microstrip, the stripline and ground plane are located onactive microwave devices. Microstrip transmission line opposite sides of the substrate. Because of the coupling ofplaying a major role to transport the total amount of energy electromagnetic fields, a pair of coupled lines can supportfed at one point to another. It possess many advantages like two different modes of propagation known as odd and evenmounting active device on top of Microstrip line, high modes. These modes have different characteristicsfrequency response, high-speed digital PCB designs where impedances. The velocity of propagation of these two modessignals need to be routed from one part of the assembly to is equal, when the lines are imbedded within an infiniteanother with minimal distortion, and avoiding high cross- homogeneous dielectric medium. But for coupled microstriptalk and radiation. Motivated by these inherent advantages, lines involving in homogeneous medium, a part of the fieldmain concern is led towards the analysis of Microstrip line extends into the air above the substrate. This fraction isespecially the variation of characteristic impedance of different for the two modes of coupled lines. Consequently,Microstrip line with various transmission line parameter, the effective dielectric constants are not equal for the twoeffective permittivity. Throughout the years, Microstrip modes. When the two conductors of a coupled line pair aretransmission lines structures are the most common option identical we have a symmetrical configuration. Thisused to realize microwave, radar and othercommunication symmetry is very useful for simplifying the analysis anddevices. Due to its numerous advantages over the other design of such coupled lines. If the two lines do not have thetransmission lines, the microstrip transmission lines have same dimension, the configuration is called asymmetric.achieved importance and generated interest to microwave This paper aims to provide the reader with a comprehensiveintegrated circuit designers for many years. analysis of all fundamental concepts related to the open symmetrical coupled microstrip transmission lines. Manuscript received July 15, 2012.Akanksha lal, ECE Deptt., SHIATS-DU, Allahabad,India-211007,Phone/MobileNo.-+91-9616501289 III. ANALYSIS BY QUASI STATICMukesh kumar, ECE Deptt., SHIATS-DU, Allahabad, India- 211007,Phone/MobileNo.-+91_9935966111 A Microstrip line can be quasi-statically analyzed by the useRohini Saxena , ECE Deptt., SHIATS-DU, Allahabad,India-211007, of elliptical integral formulae. It consists in transforming thePhone/MobileNo.-+91-9208548881 geometry of the PCB into another conformation. 130 All Rights Reserved © 2012 IJARCSEE
  2. 2. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering (IJARCSEE) Volume 1, Issue 6, August 2012 1 (∈ 𝑟 +) ≤∈ 𝑒𝑓𝑓 ≤∈ 𝑟 (4) Strip 2 conduct or Several different equations have been developed for use in calculating characteristic impedance for microstrip design. x z Probably the most useful are the following which are w reported to be accurate to within about 1%. t 60  h W  (5) Zo  ln  8   y  eff  W 4h  h Dielectric substrate 0 r Where Ground   1 2 plane  r  1  r  1  h  W W  0.041    for  1 2 Figure 2: Symmetric diagram of microstrip line  eff   1  12  2 2  W  h  h  Where ℎ is the hight of substrate, 𝑡 is thickness of microstrip (6)line, 𝑊 is slot width of microstrip line. One of the mostchallenging problems associated with this configurationarises from the fact that the small strip is not immersed in a 120 Zo single dielectric. On one side there is the board dielectric, W W   eff  h  1.393  0.667 ln  h  1.444 and on the top is usually air. The technique that has been   developed to handle this challenge uses, the concept of (7)effective relative dielectric constant , ∈ 𝑒𝑓𝑓 . This value Whererepresents some intermediate value between the relative   1   r 1   1  h  2 W  for  1dielectric constant of the board material,∈ 𝑟 , and that of air  eff   r 1  12  2 2  W  h(assumed equal to 1) that can be used to compute microstrip  parameters as though the strip were completely surrounded (8)by material of that effective relative dielectric constant. One These are relatively equations for the calculation ofobvious advantage of the microstrip structure is the "open" characteristic impedance, given 𝑊, ℎ, and ∈ 𝑒𝑓𝑓 . However,line which makes it very easy to connect components. Aside the more useful calculation involves determination of thefrom the difficulty of calculating the value of ∈ 𝑒𝑓𝑓 , there is 𝑊 ratio, given a required characteristic impedance. Here,another important effect. It is clear that ∈ 𝑒𝑓𝑓 will depend on ℎ then, is the design challenge since the equations areboth 𝑊and ℎ. Hence, the phase velocity along the microstrip transcendental for the 𝑊 ℎ parameter. Now, modify to thewill depend on these parameters. Assuming the relativepermeability of all materials in the line design is well above equations which is a consequence of considering theapproximated by 𝜇 𝑟 = 1, the phase velocity will be given by finite thickness (t) of the microstrip. This modification is in the form of an "effective" Microstrip width (𝑊𝑒 ), which is cvp  (1) used to replace W in those equations:  eff t   2h   W 1 Since the characteristic impedance 𝑍 𝑜 of the line will also We  W  1  ln   for     t  h 2depend on these parameters, every time we need to design amicrostrip with a new characteristic impedance, we will be (9)faced with the additional complication of having to dealwith a change in phase velocity (or delay time) and t   4W  W 1consequently of the wavelength of waves on that microstrip. We  W  1  ln   for To get an idea of the range of εeff, consider the cases of a   t  h 2very wide width W and then a very narrow width W. (10) 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 ∈ 𝑒𝑓𝑓 =∈ 𝑟 (2) IV. RESULT AND DISCUSSIONEqn. (3.56) is in the form of an "effective" microstrip width(𝑊𝑒 ), which is used to replace 𝑊. a.) CHARACTERISTIC IMPEDANCE V/S For a wide microstrip, nearly all of the electric field lines NORMALISED STRIP WIDTHwill be concentrated between the metal planes, similar to thecase of a parallel plate capacitor, and for narrow width W Normalized strip width is known as ratio of width ofthe electric field lines will be about equally divided between Microstrip line and height of the substrate. The graphthe air and the board dielectric so that: represents the variation of characteristic impedance with normalized strip width for substrate is chosen to be of glass 1 fiber. 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 ∈ 𝑒𝑓𝑓 = ∈ 𝑟+ 1 (3) 2This gives a range: 131
  3. 3. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering (IJARCSEE) Volume 1, Issue 6, August 20121.1 Normalized strip width when 𝒘 𝒉 ≤ 𝟏 when the value of normalized strip width is greater than equal to 1.Graph 1.1 shows the variation of characteristic impedance Microstrip characteristic impedancewith normalized strip width. 70 65 microstrip characteristic impedance, W/h<=1 900 60 55 800 Zo(ohms) 50 700 45 600 40 Zo(ohms) 500 35 30 400 25 300 20 3.5 3.6 3.7 3.8 4.1 4.2 3.4 3.9 4 200 𝜖 𝑓𝑓 (𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑝𝑒𝑟𝑚𝑖𝑡𝑡𝑖𝑣𝑖𝑡𝑦) 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 W/h ratio Graph2.1: variation of characteristic impedance v/s Graph1.1. variation of characteristic impedance effective permittivity v/snormalized strip width 2.2 Effective permittivity for 𝒘 𝒉 ≤ 𝟏1.2 Normalized strip width when 𝒘 𝒉 ≥ 𝟏Grap1.2 shows the variation of characteristic impedance Figure 4.4 shows the variation of characteristic impedancewith normalized strip width. with different value of effective permittivity. In the graph it . is clear that, as we increase the effective relative microstrip characteristic impedance, W/h=>1 permittivity, the value of characteristic impedance decreases 70 when the value of normalized strip width is less than equal 65 to 1. 60 microstrip characteristic impedance 55 180 50 Zo(ohms) 160 45 40 140 35 Zo(ohms) 120 30 25 100 20 1 1.5 2 2.5 3 3.5 4 4.5 5 W/h ratio 80 60 3.3 3.35 3.4 3.45 3.5Graph1.2. variation of characteristic impedance v/s 3.1 3.15 3.2 3.25 normalized strip width Graph2.2: variation of characteristic impedance v/s As seen in both the above graph, that when effective permittivitynormalized strip width is kept between 1 to 5, then thecharacteristic impedance decreases with increases in The characteristic impedance of any type ofnormalized strip width. But when the same normalized strip transmission line decreases with increase in relativewidth is kept between 0 to 1 then there is a sudden and rapid permittivity and can be expressed by using formula fromdecrease in characteristic impedance transmission line is given by R  jL Z0 b.)CHARACTERISTIC IMPEDANCE V/S G  jC (11) EFFECTIVE PERMITIVITY Where, R= Resistance per unit length,2.1 Effective permittivity for 𝒘 𝒉 ≥ 𝟏 L  Inductance per unit lengthGraph 2.1 shows the variation of characteristic impedance G  Conductance per unit lengthwith different value of effective permittivity. In this graph itis clear that, as we increase the effective relative C  Capacitance per unit lengthpermittivity, the value of characteristic impedance decreases 132 All Rights Reserved © 2012 IJARCSEE
  4. 4. ISSN: 2277 – 9043 International Journal of Advanced Research in Computer Science and Electronics Engineering (IJARCSEE) Volume 1, Issue 6, August 2012Form the above mention formula, the condition arises [11] M. E. Goldforb and R. A. Pucel, “Modding Via Hole Grounds in Microstrip,” IEEE Microwave and Guided Ware Letters,R  C  L  G for distortion less transmission line. Since Vol.1, No. 6, PP. 135-137, June 1991.there is no wires or long conducting element L and G [12] M. Kahrizi, K. Sarkar and Zoran A. Maricevic, “Dynamic Analysis of a Microstrip Line Over a Perforated Ground Plane”,cannot be changed so it is very evident from the above IEEE Transaction on Microwave Theory and Techniques, Vol.condition that only R and C can be inversely proportional 42, No. 5, May 1994. [13] N. Jain and B. Brown, “Dispersion Characteristics ofto each other as C is dependent on relative permittivity and Microstrip Transmission line on Glass Microwave IC’S”, IEEE R can be treated as characteristic impedance it can be Microwave and Guided Wave Letter, Vol. 7, No. 10, Oct. 1997. [14] R.J. Akello, B. Easter, and I.M. Stephenson, “Equivalentknuckled with the fact that whenever C Increases R circuit of the symmetric crossover junction,decreases. “Electronics Letters, vol.13,no.4,PP.117-118, Feb 1977. V. CONCLUSIONWork has been done to demonstrate the utility of microstripline and its advantages especially energy is to be transferredfrom one point to another, in a very compact and efficient AUTHOR’S PROFILEform. A simple and inexpensive method also known asquasi-static has been applied for calculating the Akanksha lal is working as a Asst. Prof. in the Department of Electronics & Communication Engineering in SHIATS, Allahabad. Shecharacteristic impedance as well as effective permittivity. received her M.Tech. Degree in Advanced Communication SystemsVariation of characteristic impedance for different value of Engineering from SHIATS, Allahabad in 2010. His research is focused onnormalized strip width as well as different value of effective Microwave Engineering,Wireless communication. Mukesh Kumar is working as a Asst. Prof. in the Department ofpermittivity is represented. It has been observed that Electronics & Communication Engineering in SHIATS, Allahabad. Hecharacteristic impedance decreases with advancement of received his M.Tech. Degree in Advanced Communication Systemsnormalized strip width and also decreases for increasing Engineering from SHIATS, Allahabad in 2010. His research is focused on Microwave Engineering, Wireless Sensors Networks and Computereffective permittivity. This property can be applied in Networks as well as Optical fiber communication.microwave transmission theory to design different antenna Rohini Saxena is working as a Asst. Prof. in the Department ofmodels for different purposes along with the advantage of Electronics & Communication Engineering in SHIATS, Allahabad. She received her M.Tech. Degree in Advanced Communication Systemsminimal distortion, and avoiding high cross-talk and Engineering from SHIATS, Allahabad in 2009. His research is focused onradiation. Microwave Engineering, Wireless Sensors Networks and Computer Networks and Mobile communication. VI. REFRENCES . [1] Baklem and A. Dmar, “Invarted Defected Ground Structure for Microstrip line filter reducing Packaging Complicity, Department of Electrical, Czech Technical University, 2008. [2] A. Z. Elsherbeni, C. E. Smith and B. Moumnch, “Minimization of the Coupling between a two Conductor Mirostrip Transmission Line using Finite difference Method”, Journal of Electromagnetic Waves and Application, Vol. 10, No. 4, 509- 513, 1006. [3] B. Easter, “The Equivalent Circuit of some Microstrip Discontinuities”, IEEE Transaction on Microwave Theory and Techniques, Vol. 23, No. 8, PP.655-660 Aug. 1975. [4] C. K. Wu and H. S. Wu, “Electric- Magnetic- Electric Slow- Wave Microstrip Line and Bond pass Filter of Compressed Size”, IEEE Transaction on Microwave Theory and Techniques, Vol. 50, No. 8, Aug, 2002. [5] E. Tunier. Lee B. T., M. Islam and D. P. Nickirk, “Quasi-Static Conductor Loss Calculations in Transmission Theory and Techniques, Vol. 42, PP. 1807-1815, 1994. [6] E. Tunnier, and P. Nickirk, “Highly Accurate Quasi-Static Modding of Microstrip Lines over Lossy Subptrates”, IEEE Microwave and Guided Wave Letter, Vol. 2, No. 10, October 1992. [7] E. Yamshita, “Variational Method for the Analysis of Microstrip Like Transmission Lines”, IEEE Transaction on Microwave Theory and Techniques, Vol. 16 No. 8, Aug, 1968. [8] H. Wang, Y. Ji, and T. H. Hubiay, “Experimental and Numerical study of the Radiation from Microstrip Bends”, University of Missouri-Rolla, 2000. [9] J. C. Rautis, and V. Demir, “Microstrip Conductor loss Models for Electro-Magnetic Analysis”, IEEE Transaction on Microwave Theory and Techniques, Vol. 51, No. 3, March. 2003. [10] J. S. Lim, C.S. Kim and J. S. Park, “Design of 10.1B 900 Branch Line Coupler using Microstrip Line with defected ground Structure”, Electronics Letters, Vol. 56, No. 21, Oct. 2000. 133

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