International Journal of Electromagnetics and Applications 2012, 2(6): 174-181 DOI: 10.5923/j.ijea.20120206.07

Loss Computation of Multilayer Coplanar using Single Layer Reduction Method

A. K. Verma, Paramjeet Singh*

Department of Electronic Science University of Delhi South Campus, New Delhi 110021, India

Abstract In this paper, the quasi-static spectral domain approach (SDA) and single layer reduction (SLR) method applicable for multilayer coplanar waveguide (CPW) on isotropic substrate that incorporates two layer model of conductor thickness is used to compute the impedance, effective dielectric constant, dielectric loss and conductor loss. The transverse (TTL) technique is used to find the Green’s function for the multilayer CPW in Fourier domain. Die lectric loss of multilayer coplanar waveguide is computed by converting multilayer CPW structure into equivalent single layer CPW using SLR method. Perturbation method is used to compute the conductor loss. The effect of finite conductor thickness is analysed on the impedance, effective dielectric constant, dielectric loss and conductor loss. The present formulation also accounts for low frequency dispersion in computation of quasi-static effective dielectric constant and . Ke ywo rds Conductor Loss, Dielectric Loss, Multilayer Coplanar Waveguide, Quasi-Static Spectral Domain Approach, Single Layer Reduction Method, Transverse Transmission Line Technique

the impedance, effective relative permittivity, dielectric loss 1. Introduction and conductor loss of multilayer CPW structures using quasi-static SDA method on isotropic dielectric substrate. There has been a growing interest in different Dispersion characteristics of multilayer CPW is also configurations of coplanar waveguide (CPW) transmission analysed using single layer reduction (SLR) method. line such as conductor backed CPW, CPW with finite ground width, shielded multilayer CPW, elevated or suspended CPW, asymmetric CPW etc. The CPW offers many 2. Coplanar Waveguide Analysis advantages over microstrip line such as easy connection of The conventional CPW consist of centred conductor both series and shunt components without drilling holes between two infinite ground planes with all on the same through the dielectric substrate, less dispersive and provides plane. The height of substrate is also infinite. But in practical ease of controlling the characteristics of line by changing the case, both the width of the ground planes and height of strip and slot width. Therefore, CPW transmission lines are substrate are finite. The cross section structure of shielded widely used in the design of components and interconnect in multilayer coplanar waveguide of finite conductor thickness modern microwave circuit design. The accurate modelling of under investigation using the quasi-static SDA formu lation transmission lines is important in the design and is shown in Figure. 1. development of modern integrated circuits. Most research In this paper an efficient method for calculating the line done in literature on CPW was based under the assumption of shielded multilayer CPW of finite conductor of zero conductor thickness using the conformal mapping thickness is presented. The effect of conductor thickness is and spectral domain approach (SDA) method. But in accounted by accommodating the two layer strip conductor practical cases, the conductor thickness can not be zero and model that is suggested for a microstrip line[4]. The potential affects the impedance, effective dielectric constant and and charge distribution basis function on the strips is losses etc. Several research papers have been presented to required to compute the line capacitance. The potential on characterize planar transmission line structure with finite the strips is expressed in terms of charge distribution on the metallization thickness[1-13]. upper and lower strips. The unknown charge distribution This paper presents the effects of finite strip thickness on function can be expanded in term of linear combination of basis function. The total potential in the range[0, L] is equal * Corresponding author: [email protected] (Paramjeet Singh) to the sum of the potential on strips conductor and potential Published online at http://journal.sapub.org/ijea in two slot region. Then, Galerkin method is applied to find Copyright © 2012 Scientific & Academic Publishing. All Rights Reserved the unknown coefficient of chare density basis function. The

175 International Journal of Electromagnetics and Applications 2012, 2(6): 174-181

total charge on the coplanar waveguide is sum of charge at ~ ~ where Vd is potential on dielectric slot region and Vc is upper and lower strip of centre conductor. Therefore, the potential on conductor strip region. The potential at lower quasi-static SDA obtains the total charge on the central strip. ~ ~ and upper surface of the conductor are 1 β + 1 β By using the total charge on the central strip the per unit Vc ( n ) Vd ( n ) ~ 2 ~ 2 length capacitance is computed. The effective dielectric and Vc (β n )+ Vd (β n ) respectively. constant and characteristic impedance of the CPW ~ ~ ~ ~  V1 (β )+ V1 (β ) transmission line can be determined using capacitance per β + β = c n d n Vc ( n ) Vd ( n ) ~ 2 ~ 2  (3) unit length. Vc (β n )+ Vd (β n ) The Green’s function for multilayer CPW in Fourier domain is obtained by transverse transmission line (TT L) technique. The Green’s function for the multilayer CPW shown in Figure 1 is given by  ~ ~  ~ G11 (βn ) G12 (βn ) G(βn ) = ~ ~  (4) G 21 (βn ) G 22 (βn ) where ~ 1 G11 (β n ) = (5a ) β n (GF1 + GF3 ) ~ 1 G 22 (β n ) = (5b) β n (GF2 + GF4 )

~ ~  ε r3 sinh(βn h 3 )  G12 (βn ) = G 22 (βn )   (5c) ε r3 coth(βn h 3 ) + GF1 

~ ~  ε r3 sinh(βn h 3 )  G 21 (βn ) = G11 (βn )   (5d) ε r3 coth(βn h 3 ) + GF2  ε + ε coth(β h ) coth(β h ) GF = ε r2 r1 n 1 n 2 (5e) Fi gure 1. Mult ilayer Shielded Coplanar Waveguide 1 r2    ε r1 coth(βn h1 ) + ε r2 coth(βn h 2 ) 

The charge density basis functions are confined only on ε r4 + ε r5 coth(βn h 4 ) coth(βn h 5 ) GF = ε   (5f) conductors strip and are zero outside the conductor strips. 2 r4 ε coth(β h ) + ε coth(β h ) The basis function for the charge for centre strip W, left  r4 n 4 r5 n 5  ground G and right ground G strip is ρ (x), ρ ( x), ρ (x) ε + coth(β h )GF  1 2 s1i s2i s3i GF = ε r3 n 3 2 (5g) respectively, where i = 1, 2, 3.... the number of basis terms 3 r3    ε r3 coth(βn h 3 ) + GF2  of the corresponding strips. The Fourier transform of these  ε r3 + coth(βn h 3 )GF1  basis functions of charge density on central conductor of GF = ε   (5h) 4 r3 ε β + width W , left ground G1 and right ground G2 are  r3 coth( n h 3 ) GF1  ~ ~ ~ ρs1i (βn ), ρs2i (βn ), ρs3i (βn ) respectively. In the spectral On substituting Eq.(1), Eq.(3) and Eq.(4) in Eq.(2),  ~ ~  domain, the charge density basis function for lower and G11 (β ) G12 (β )  ~ n ~ n  × upper surface of conductor plane is given by- G β G β  (6)  21 ( n ) 22 ( n ) ρ~ (β )= si n  N N N  1 1 1  N N N   ∑ a1ρ~ (β )+ ∑ b1ρ~ (β )+ ∑ c1ρ~ (β )   1 1~ 1 1~ 1 1~   i s1i n i s2i n i s3i n  ∑ a ρ (β )+ ∑ b ρ (β )+ ∑ c ρ (β )  i = 1 i = 1 i = 1  =  i s1i n i s2i n i s3i n  (1) N N N  i = 1 i = 1 i = 1   1 1 1  N N N  ∑ a2ρ~ β + ∑ b2ρ~ β + ∑ c2ρ~ β   1 1 1  i s1i ( n ) i s2i ( n ) i s3i ( n )  ∑ a2ρ~ β + ∑ b2ρ~ β + ∑ c2ρ~ β  i = 1 i = 1 i = 1  i s1i ( n ) i s2i ( n ) i s3i ( n ) i = 1 i = 1 i = 1  ~ ~ V 1 β )+V 1 β ) 1 1 1 2 2 2  c ( n d ( n  where, a i , bi , ci and a i , bi , ci are unknown constant  ~ ~  V 2 (β )+V 2 (β ) coefficients associated with central conductor, left ground  c n d n  Now take the inner product of Eq. (6) with testing function and right ground respectively for lower and upper surface of ~ ~ ~ ρt1j (βn ), ρt2 j (βn ) , ρt3j (βn ) and applying the Parseval’s the conductor, N1 is number of basis function. The Green’s function and the basis function in Fourier domain are related identity. By Galerkin’s method solve for the unknown to potential on strip and slot region by following expression, constant of the charge basis function The line capacitance ~ ~ ~ per unit length of finite conductor thickness CPW is G(β )~ρ (β ) = V (β ) + V (β ) (2) n si n c n d n computed by substituting the constants in Eq. (7).

A. K. Verma et al.: Loss Computation of Multilayer Coplanar Waveguide using Single Layer Reduction Method 176

N1 where q is filling factor for coplanar waveguide. The C = (a1Q + a 2Q ) dielectric loss[15] of the coplanar waveguide is given by, ε ∑ i i i i (7) o 8.686π ε′req (ε′ −1) i=1 α = reff tan(δ ) (14) d λ ε′ − eq 0 ε′reff ( req 1) G1 +S1 +W The conductor loss of CPW is computed by perturbation Q = ρ (x)dx where i ∫ s1i method (Pertb. M.),[16-18]. G1 +S1 R s α c = × 2 ( ) − 2 The following charge distribution basis function on central 16ZK k (1 k ) and ground conductor strip is used[14]. 1  2a   b − a + ∆   ln −1   + (15) − −      (x S1 G1 ) a  ∆   b + a + ∆   cos (i −1) π   W    ρ = 1  2b   b − a + ∆  s1i (x)  ln −1    2 (8a)   ∆ + − ∆   2 (x −S1 − G1 )− W  b    b a   1−    W  where K(k) is co mplete elliptic integral o f first kind, ∆ is

(G1 + S1 ≤ x ≤ G1 + S1 + W) stopping distance, k = a b , a = W 2 , b = S1 + W 2 . For

  1  (x − G1 ) symmetric configuration of CPW structure S1=S2=S. cos i −  π    2  G1  ρ (x) = , cot(k h )+ csc(k h ) s2i = ωµ c 3 c 3 2 (8b) where R s c h 3 Im   x   k c h 3  1−   G1  1 2   ( ≤ ≤ ) σc 0 x G1 k = ω µ ε 1 − j  c o o ωε   1  (x − L + G )  o  − π 2 cos i   For single ground coplanar waveguide the conductor loss   2  G 2  ρs3i (x) = , is computed from[9], 2 L − x  (8c) ε 1− Rs reff   αc = [Φ1 + Φ2 ] (16) G 2 '   480π K(k2 )K(k2 ) (G1 + S1 + W + S2 ≤ x ≤ L)  '  − The characteristic impedance (Z*) and effective dielectric 1  2ak 2  1  (b a)k 2  where Φ1 = log Φ 2 = log  * 2a  ∆  b − a ∆ constant (ε reff ) of CPW are computed from the line     * capacitance of the structure filled with dielectric (Cd ) and 2a ' b − a air (C ) from the following equations, k 2 = , k 2 = a a + b b + a * 1 Z = (9) c C* (ε* )C (ε = 1) o d r a r 3. Dispersion Analysis of Multilayer * * * Cd (ε r ) CPW ε reff = (10) Ca (ε r =1) A dispersion formu la[19] for effective dielectric constant has been proposed for coplanar waveguide where co is the velocity of light in free space. 2   Die lectric loss of multilayer CPW is calculated by ε r − ε reff (f = 0) converting multilayer CPW structure into equivalent single ε reff (f ) =  ε reff (f = 0) +  (17)  1 + aF−b  layer CPW structure using SLR method. The complex  ( )  effective re lative permittivity is computed by - * * f co ε where F = , f TE = is the cutoff frequency of * Cd ( r ) f εreff = = ε′reff − jε′reff′ (11) TE 4h ε r −1 Ca (εr = 1) the TE mode, b = 1.8 (ε′reff − jε′reff′ −1) 1 ε′ − jε′′ = +1 (12) req req  W  q log(a) = u log  + v (18a)  S  ε′req′ ε′′ reff 2 tan δeq = = (13) u = 0.54 − 0.64 p + 0.015 p (18b) ε′req ε′reff + q −1

177 International Journal of Electromagnetics and Applications 2012, 2(6): 174-181

v = 0.43 − 0.86 p + 0.540 p 2 (18c) * R + jωL Z = (21a )  W  o + ω p = log  (18d) G j C  h  γ* = (R + jωL) (G + jωC) (21b) This dispersion formula was obtained under the assumption of infinitely thin conductors and infinity conductivity. To account the dispersion at low frequency an approximation for computation of increased due to skin effect in strip conductor is used here. At the lower end of RF and microwave, the finite conductivity of a strip permits penetration of magnetic fie ld inside the conductor, causing increase in effective relative permittivity and impedance with decrease in operating frequency. The penetration of the magnetic field in a conducting strip increases the effective permeability of the CPW. The effective permeability, expressed by a factor K, is computed on the air-substrate CPW by the following expression in term of Fi gure 2. Circuit Model of Coplanar Waveguide capacitance. At lower frequency, we have K>>1 and at higher The total loss is αT = Re( γ* ) Np per unit length, the phase frequency K →1 . As the frequency decreases, the field penetration inside the conductor increases and effective relative constant is β = Im( γ* ) radian per unit length. The effective permittivity increases at low frequency. dielectric constant is calculated from the following relation, 2 2  Kε (f = 0) +  ε r eff = (β βo ) , where βo is free-space phase constant.  reff  ε reff (f ) =  ε − Kε (f = 0)  (19)  r reff  −b  (1 + aF )  5. Result and Discussion Zo (f = 0) Zo (f ) = K (20) In this section, first we have validated the static SDA ε reff (f = 0) formulation that include two layer conductor thickness C (δ = 0,ε =1) model against EM simulator- Ansoft High Frequency where K = o s r C(δ ,ε =1) Structure Simu lator (HFSS)[20] and Computer Simulation s r Technology (CST) microwave studio[21]. Co (δs = 0, ε r = 1) is the capacitance without skin effect and

C(δs , ε r =1) is capacitance with skin effect on air substrate Conformal Mapping h3=0.1μm of CPW transmission line. h3=5µm 1.0E-10

8.0E-11 4. Circuit Model of CPW 6.0E-11 The primary line constants of a multilayer coplanar waveguide are resistance (R), conductance (G), capacitance 4.0E-11 (C) and inductance (L). These parameters are computed fro m Capacitance (F/m) p.u.l. 2.0E-11 the conductor loss, dielectric loss, real part of effective 0 10 20 30 40 50 60 70 80 90 relative permittivity and impedance. high dielectric constant W ( µm) disappears at high frequency.

R = 2Zoα c (20a) (a) 2α G = d (20b) HFSS CST [18] PM Zo 0.5 ' ε r eff C = (20c) 0.4 co Zo 0.3

' 0.2 Zo ε r eff = Loss (dB/mm) L (20d) 0.1 co The circuit model can calculate the complex 0 10 20 30 40 50 characteristic impedance, phase constant and total loss of Frequency (GHz) * the structure. The complex characteristic impedance ( Zo ) and complex ( γ* ) is given by, (b)

A. K. Verma et al.: Loss Computation of Multilayer Coplanar Waveguide using Single Layer Reduction Method 178

Dielectric Loss (HFSS) Dielectric Loss (CST) HFSS CST [18] PM Dielectric Loss (PM) Conductor Loss (HFSS) 0.4 Conductor Loss (CST) Conductor Loss (PM) 7.5E-05 0.01 0.3 0.008 7.0E-05 0.006 0.2 6.5E-05 0.004 Loss (dB/mm) 0.1 6.0E-05 0.002 Dielectric Loss (dB/mm) 5.5E-05 0 Conductor Loss (dB/mm) 0 10 20 30 40 50 0 5 10 15 20 25 30 35 Conductor Thickness (μm) Frequency (GHz)

(b) (c) Fi gure 4. Variat ion of (a) Effect ive dielectric constant and impedance ( b) Fi gure 3. (a) Variat ion of Capacit ance p.u.l. of CPW with the width of dielectric and conductor loss with conductor thickness of CPW h1=254µm, central conduct or S1=50μm, S2=50μm, h1=500μm, h2=5μm, h4→∞, ε r1=3.78, (b) h2=254 µm, h4=0 µm , h5=10 H, ε r1 =9.8, εr2=12.9, εr5=1, tanδ1=0.0001, εr2=12.9, εr4=1.0. Loss versus frequency of coplanar waveguide (b) h3=1.5 7 t anδ2=0.0003, W=120µm, S1=90µm, σ = 4.1x10 S/m , H= h1+ h2 µm , ( c ) h3=3.0 µm, h1→∞, h2=600 µm, h4=0, h5→∞, ε r1=1, εr2 =12.9, εr5 =1, 7 t anδ2=0.0003, W=10 µm, S1=20 µm, σ = 3.0x10 S/m The average deviation in impedance of present model and Next we validated the frequency dependent, i.e., dynamic CST with HFSS are 1.35% and 0.96% respectively. Figure line parameters at low frequency obtained from the present (4b) shows the effects of conductor thickness on dielectric model (PM) against the result from HFSS and CST. In loss and conductor loss. The average deviations in conductor Figure 3(a) the capacitance per unit length (p.u.l.) of CPW is loss of present model and CST with HFSS are 3.35% and compared with conformal mapping method. In Figure 17.77% respectively. The average deviations in dielectric 3(b)-(c) the loss of CPW are compared against the HFSS, loss of present model and CST with HFSS are 1.17% and CST present model (PM) and[18] for different conductor 0.67% respectively. Figure 5(a)-(e) shows variation of thickness. Figure 4(a) show the effects of conductor effective dielectric constant, impedance, die lectric loss and conductor loss for multilayer CPW with frequency. thickness on effective dielectric constant and impedance for multilayer CPW. The effective dielectric constant and Ereff (HFSS) Ereff (CST) impedance decreases with increase of conductor thickness. Ereff (SLR) Ereff (CM) In our study HFSS is taken as reference. The simulation is 7.4 carried at 1 Ghz to compute εeff(f=0), Z(f=0) and dielectric 7.2 loss. For these computations, the strip conductor is treated as 7 a perfect conductor. The finite conductivity is considered for 6.8 computation of frequency dependent line parameters. The 6.6 variation in line parameters are shown with respect to 6.4 conductor thickness between 3μm-30μm. The average

Effective Dielectric Constant 6.2 deviation in effective dielectric constant of present model 0 20 40 60 80 100 and CST with HFSS are 2.21% and 0.47% respectively. Frequency (GHz)

Ereff (HFSS) Ereff (CST) (a) Er ef f ( PM) Impedance (HFSS) Impedance (CST) Impedance (PM) Zo (HFSS) Zo (CST) 7.0 60 Zo (SLR) Z o ( CM) 52

6.5 55 50 6.0 50

48 5.5 45 Impedance () Impedance (ohm)

Effective Dielectric Constant 5.0 40 46 0 5 10 15 20 25 30 35 0 20 40 60 80 100 Conductor Thickness (μm) Frequency (GHz)

(a) (b)

179 International Journal of Electromagnetics and Applications 2012, 2(6): 174-181

Diel. Loss (HFSS) Diel. Loss (CST) The shielded multilayer CPW structure shown in Figure 1

8.0E-03 Diel. Loss (SLR) can be converted into other structures such as dielectric covered CPW, suspended CPW, elevated CPW, top shield 6.0E-03 without conductor back etc. The dispersion in effective dielectric constant of CPW at low frequency due to finite 4.0E-03 conductivity of strip conductor is also incorporated. As the frequency decreases, the effective re lative permittivity 2.0E-03 increases due to skin effect in conductor. The impedance of Dielectric Loss (dB/mm) 0.0E+00 CPW line also shows the similar behaviour at low frequency 0 20 40 60 80 100 region. It is clearly seen that good agreement exists between Frequency (GHz) present model and EM simulator.

(c) Diel. Loss (HFSS) Diel. Loss (CST)

Cond. Loss (HFSS) Cond. Loss (CST) 8.0E-03 Diel. Loss (SLR) Cond. Loss (Pertb. M.) 0.4 6.0E-03 0.3 4.0E-03 0.2

0.1 2.0E-03 Dielectric Loss (dB/mm)

Conductor Loss (dB/mm) 0 0.0E+00 0 20 40 60 80 100 0 20 40 60 80 100 Frequency (GHz) Frequency (GHz)

(d) (a) Loss (HFSS) Loss (CST) Cond. Loss (HFSS) Cond. Loss (CST) Loss (CM) Cond. Loss (Pertb. M.) 0.4 0.3 0.3 0.25 0.2 0.2 0.15

Loss (dB/mm) 0.1 0.1 0.05 0 Conductor Loss (dB/mm) 0 20 40 60 80 100 0 0 20 40 60 80 100 Frequency (GHz) Frequency (GHz)

(e) (b) Fi gure 5. Propagat ion characterist ics of coplanar waveguide (a) effect ive Fi gure 6. Losses of coplanar waveguide (a) dielect ric loss (b) conductor dielectric constant (b) impedance (c) dielectric loss (d) conductor loss (e) loss, h1=127 µm , h2=254 µm, h3=5 µm , h4=0, h5=10H, ε r1=9.8, ε r2 =12.9, Total Loss, h1=127 µm , h2=254 µm, h3=3 µm , h4=0, h5=1 0H, ε r1 =9.8, 7 εr5=1, tanδ1=0.0001, tanδ2=0.0003, W=24 µm , S1=18 µm, σ = 4.1x10 S/m εr2=12.9, εr5 =1, t anδ1=0.0001, tanδ2=0.0003, W=24 µm , S1=18 µm, σ = 4.1x10 7 S/m Loss (HFSS) Loss (CST) The results are further improved on using the circuit Loss (CM) model (CM). In Figure 6(a)-(b) the dielectric loss and 0.4 conductor loss of multilayer CPW are compared for 1-100 0.3 GHz. The SLR method has been used to compute the frequency 0.2 dependent effective dielectric constant, impedance,

Loss (dB/mm) 0.1 dielectric loss and conductor loss. Figure 7(a)-(c) show the variation of attenuation constant of multilayer CPW for 0 different conductor thickness by circuit model. Figure 0 20 40 60 80 100 8(a)-(b) show the variation of effective dielectric constant Frequency (GHz) and loss of multilayer micro coplanar strip (MCS) with frequency. (a)

A. K. Verma et al.: Loss Computation of Multilayer Coplanar Waveguide using Single Layer Reduction Method 180

Loss (HFSS) Loss (CST) 6. Conclusions Loss (CM) 0.4 In this paper, computationally efficient quasi-static SDA is used to study the effect of conductor thickness on effective 0.3 dielectric constant, impedance, dielectric loss and conductor 0.2 loss of shielded multilayer CPW on isotropic layered media. The accuracy of the method is investigated through the

Loss (dB/mm) 0.1 comparison between results obtained using quas i-static SDA, 0 Ansoft HFSS, CST software and the agreement is very good. 0 20 40 60 80 100 The SDA formulation incorporates the two layer model of Frequency (GHz) conductor thickness and concept of permeability due to field penetration in the imperfect conductor. This formulation (b) accounts for the effect of conductor thickness and low Loss (HFSS) Loss (CST) frequency dispersion on computation of quasi-static Loss (CM) effective relative permittivity and characteristic impedance. 0.4 The models accuracy is comparable to the accuracy of HFSS and CST, without using complex and time consuming full 0.3 wave methods. The present formulation can be incorporated 0.2 in the CAD of CPW based circuits and other planar transmission line with finite conductor thickness Loss (dB/mm) 0.1 conveniently. 0 0 20 40 60 80 100 Frequency (GHz)

(c) REFERENCES Fi gure 7. Att enuat ion constant of coplanar waveguide with [1] T. Kitazawa and Y. Hayashi, “Quasistatic and Hybrid Mode frequency from circuit model (a) h3=1 µm (b) h3=3 µm (c) h3=5 µm , Analysis of Shielded Coplanar Waveguide with metal h1=127 µm, h2=254 µm, h4=0, h 5=10H, ε r1=3.78, εr2=9.6, εr5 =1, coating,” IEE Proceedings, vol.134, no.3, pp.321-323, June t anδ1=0.0001, t anδ2=0.0003, W=24 µm , S1=18 µm 1987.

Ereff (HFSS) Ereff (CST) [2] T. Kitazawa and T. Itoh, “Propagation Characteristics of Ereff (SLR) Ereff (CM) Coplanar-Type Transmission Lines with Lossy Media,” IEEE 7.4 Transactions on Microwave Theory and Techniques, vol.39, 7.2 no.10, pp.1694-1700, October 1991. 7 6.8 [3] Eikichi Yamashita and Kazuhiko Atsuki, “Analysis of 6.6 Thick-Strip Transmission Lines,” IEEE Transactions on Microwave Theory and Techniques, vol.19, pp.120-122, 6.4 January 1971.

Effective Dielectric Constant 6.2 0 20 40 60 80 100 [4] V. K. Tripathi and R. T. Kollipara, “Quasi-TEM Spectral Frequency (GHz) Domain Analysis of Thick Microstrip for Microwave and

Digital Integrated Circuits,” Electronics Letters, vol.25, no. (a) 18, pp.1253-1254, August 1989. Loss (HFSS) Loss (CST) [5] Jeng-Yi Ke and Chun Hsiung Chun, “Dispersion and Loss (CM) 0.30 Attenuation Characteristics of Coplanar with 0.25 Finite Metallization Thickness and Conductivity,” IEEE 0.20 Transactions on Microwave Theory and Techniques, vol.43, 0.15 no.5, pp.1128-1135, May 1995. 0.10

Loss (dB/mm) [6] Ian McGgregor, Fatemeh Aghamoradi, and Khaled Elgaid, 0.05 “An Approximate Analytical Model for the Quasi-Static 0.00 Parameters of Elevated CPW Lines,” IEEE Transactions on 0 20 40 60 80 100 Microwave Theory and Techniques, vol.58, no.12, Frequency (GHz) pp.3809-3814, December 2010. (b) [7] Frank Schneider, Thorsten Tischler, Wolfang Heinrich, Fi gure 8. Multilayer micro coplanar st rip (MCS) (a) effect ive dielect ric “Modeling Dispersion and Radiation Characteristics of constant (b) loss, h1=127 µm , h2=254 µm, h3=3 µm , h4=0, h5=10H, ε r1 =9.8, Conductor-Backed CPW With Finite Ground Width,” IEEE

εr2=12.9, εr5 =1, t anδ1=0.0001, tanδ2=0.0003, W=24 µm , S1=18 µm, σ = Transactions on Microwave Theory and Techniques, vol.51, 4.1x10 7 S/m no.1, pp.137-143, January 2003.

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