Microwaves Theory and Antennas - 21662 Module 3 Strip Lines Introduction: ‘All microwave equipment used co-axial lines, waveguides for transmitting microwaves from one device to another till the year about 1965. Later on, development of planar transmission fines, by using thin film technology and photolithographic techniques, it is possible to fabricate the complete transmission line circuits. There are four basic types of planar transmission lines which are widely used in microwave integrated circuits (MICs). They are 1. Microstrip lines 2. Parallel strip lines 3. Coplanar strip lines 4, Shielded strip lines. Microstrip lines: ECE /KVGCE‘Microwaves Theory and Antennas - 21EC62 Figure 1 shows a microstrip line consisting of a single ground plane and a thin strip ‘conductor on a low loss dielectric substrate abave the ground plate. Figare 1: Mlustrating micro strip ine ‘The'lectrc field lines remain partially in air and partially in the lower dielectric substrate as shown in figure 1. Since microstrip lines radiate electro-magnetic energy. The radiation lossis proportional to the square of the frequency. By using thin and high dielectric materials, the radiation losses can be reduced. ECE /KVGCE‘Microwaves Theory and Antennas - 216062 ‘Characteristic impedance Z; of Microstrip Lines ‘The characteristic impedance of a microstrip line depends’on the width "w” of the strip line, the thickness "t" of the strip line, the distance "h* between the stripline and ground plane and the effective homogeneous dielectric constant €,, of the dielectric substrate. Different methods have been developed for determining the characteristic impedance of a microstrip line in terms of the above mentioned parameters w,t,h and ¢... These methods are extremely complicated. A fairly easy way of determining Z, is to compare it with the characteristic impedance of wire-over-ground line and suitably modifying Z,. For this let us consider a microstrip line of width "w”, thickness "t" mounted on a dielectric slab of thickness having dielectric constant "e,” as shown in fig. (a) and a wire-over-ground line of diameter ‘6! with its axis at a height ‘h' over ground line. The space between wire and ground is filled with a dielectric material having same dielectric constant as the substrate €, as shown in fig. (b). wy ‘ zt Ground plane Ground © pase Figure : (2) Microstrip line () Wire-over-ground line ‘The characteristic impedance of a wire-over-gtound transmission line is given by oo), 4h Pel veel itial ‘The characteristic impedance Z, of the microstrip line can be calculated using a similar ‘equation as 1 but with modified Values for dielectric constant €, and the diameter d. Effective Dielectric Constant ¢,, eet ‘The effective dielectric constant € , for a microstrip line is related to the relative dielectric ‘constant through an empirical relation ™ given by €,, = 0.475 €, + 0.67 sme where €, = relative dielectric constant €,, = effective relative dielectric constant for a microstrip line ECE /aveceMicrowaves Theory and Antennas - 21EC62 £xpression for Diameter d of the Wire-over-ground ‘The rectangular conductor of the microstrip line has to be transformed into an equivalent circular conductor so that the diameter d of the circular conductor can be expressed in terms of ‘w' and ‘t’, Another researcher obtained one more empirical relationship connecting ‘d’, ‘w’ and ‘t’ given by 4 = 0.67w (08+ ) w ‘The above relation hold god forthe ratio (= ) varying from 0: 10 0.8. Using equations 3 and 2 in 1 , we get the characteristic impedance Z, of microstrip line as 4h osw(os+ = SEATS, { (410.67) n oer" (oaw +1) 60 - In 20" [oaise, +087 e+e ia O8wst. bet The velocity of wave propagation is given by c_ 3x10" "Se. For a wide strip line (i.c., w >> h), the characteristic impedance was calculated tobe ne NES ‘Example 1: Calculate the characteristic impedance Z, of a microstrip line given that the thickness of the dielectric substrate h = 175 microns, thickness of the strip = 70 microns, the width w = 250 microns and the dielectric constant of the substrate material is 4.5. Solution : Since his less than 0.8 w (= 0.8 x 250 = 200 pr). 87 598h = ve mom “|e “| _ tn| —(998)(175 x10) © YAS+TAT "| 08% 250 x 10%+ 70x10 * Z, = 48480Microwaves Theory and Antennas - 21EC62 Example 21 Calculate the characteristic impedance of a wide microstrip line having negligit negligible thickness and having a width of 0.8 mm. The thickness 7 03.55. of the substrate is 0.2 mm and has a Solution : Given w = 0.8 mm, h=0.2 mm,t «0,€,=3.55. Since w >> h, the characteristic impedance given by %* Fe(%)= (68) 4 2, = $00 LOSSES IN MICROSTRIP LINES Let us consider a microstrip line consisting of a conductive copper strip attached to a dielectric sheet with ground plane as shown in fig. This type of transmission line is widely used in microwave integrated circuits and computer technology. In addition to the two characteristics of a microstrip line namely characteristic impedance and velocity of wave there is another characteristic of the line namely attenuation. The attenuation constant of microstrip line depends on frequency of operation, electrical properties of substrate ‘and the conductors (both microstrip and ground plane) and the geometry of mounting of strip on the dielectric. ‘Figure 1 Tustrating microstrip line When the dielectric substrate of dielectric constant € , is purely non-miagrietic, then three types of losses occur in microstrip lies, They are | (@) Dielectric losses in the substrate : (b) Ohinic losses in the strip conductor and the ground plane (©) Radiation losses a ECE /KVGCEMicrowaves Theory and Antennas - 2162 (¢) Dielectric Losses All dielectric materials possess some conductivity ¢ but it will be emall such thats < qe. When this conductivity is not negligible, then the displacement current density leads the conduction current density by 9°, 'thus introducing loss tangent for # lossy dielectric as shown in fig. Figure : Mostrating los tangent for lary dielectric ‘The dielectric attenuation constant is given by aaa where 6 = conductivity of the dielectric substrate in ty/em. From figure, the dielectric loss tangent is given by Oy @e Eliminating o, we get @etand [p a= 2sgne fe . ay = 3 VEE «tan 8 nepersieni aoe i i§=- 1 ECE /KVGCEMicrowaves Theory and Antennas - 215052 ‘The space sbove the microstrip is air where there are no diclectric losses, but below the microstrip, there is noa-magnetic dielectric substrate. Due to this mix up, equation (6.9) has to be modified. This modification was done by researchers Weich, Pratt and lateron by Puce! to obtain an empirical relationship for a, 23 = 164 dBicm a, x10 2 where I neper = 8.686 4B €,, = effective dielectric constant of substrate q = dielectric fling factor = $*=—+ ‘Substituting for © from equation (1) into equation (2 ), we get a, = 1.63410 Eee 3 2ne have = 2nf=2n = “ = a Re where A, = J = mnie wavelngan inte dietetic inom 2g = free space wavelength in cm Using equation( 4 )in (3) and replacing € by €,€. we get 2c é, a, = 1.634 x wxax (2 }(5) =e ‘Substituting for ¢ = 3 x 10° m/sec, € = 8.854 x 10 Fim, we get a, = 14x10 an x31 6154104 (85} “ G, = 273 (b) Ohmic Losses Ina microstripline, the major contribution to losses at microwave frequencies is from the finite conductivity of the microstrip conductor placed on a low-loss dielectric substrate. Due to the current flowing through the strip, there will be ohmic losses and hence attenuation of the microwave signal takes place.Microwaves Theory and Antennas - 216052 vn R= PEED = surface skin resistance in Oem? Substituting for R,, we get _ 8686 [RIB apiemfor ~>1 = owe o : (c) Radiation Losses At microwave frequencies, the microstrip line acts as an antenna radiating a small amount of power, resulting in radiation losses. This lass depends onthe thickness ofthe substrate, the characteristic impedance Z,, the effective dielectric constant and the frequency of operation. Researcher Lewin showed that the ratio of radiated power P._, to the total dissipated power P, for an open microstrip is given by Fa . © where A, = Free-space wavelength F(e,.) = radiation factor given by etl €-1 indent! Fe) =e 26)" ven!Microwaves Theory and Antennas - 21EC62 ‘Example : A microstrip line is composed of negligible thickness copper conductors mounted on a dielectric substrate of thickness 1.4 mm, loss tangent of 4 x 10 and dielectric constant 0f9.6. The width of the microstrip line is 3 mim and operated at 10 GHz frequency. Determine (@ the characteristic impedance Z, (©) the effective dielectric constant (©) attenuation due to dielectric losses (@) attenuation due to conductor losses (©) radiated power P,,,if the total dissipated power if 4 mw (Assume conductivity of copper as o = 5.8 x 10? y/em). Solution : Given h = 1.4 mm = 0.14 cm, tan @=4x 10%, €, f= 10x 10° Hz, P,=4 mw. (a) Since w > h, the microstrip line can be considered to be wide the characteristic impedance is given by 4 Fle) - (3) Z, = 56.782 6, w= 3mm =03.em, (®) the effective dielectric constant €,, is given by €,, = 0475 €, + 0.67 (0.475) (9.6) + 0.67 ” «,, = 5.23 (©) the attenuation due to dielectric losses is given by ‘ae,) tan @ a, = 273 (a ) %, Blom = Sart. 523 we have, a= So" 96-1 ECE /KVGCEMicrowaves Theory and Antennas - 21EC62 Osz x88 4% 10~* 7 a = @73)(2A59 ( 1312 o, ey (@) The attenuation due to conductor losses = S885 [FTE apiem ze = S686 [rftone Zw _ 8686 [(x) (10 x 10°) (4x x 107) (1) * 6678) (03) 1 58x10" (©) the radiation factor is given by Entl_ oma ae fen +1 Fe.) ia ~ 2a) =1 nH 2 Fe.) = eee aay" aA S Fee) = 1.0254 the radiation resistance is given by 2 R= wont (*) Fn) 10 ECE /KVGCEMicrowaves Theory and Antennas - 21E062 Replacing Ay by £, we get _ Wonth FF le, R 107 x 10 x 11 = 20( 3x10" (1.0254) “ R, = 5290 From equation (6.18), the radiated power is given by R, 529 of = _—— Pat = ZR = Seqg Xm “ P, = 0.373 mw PARALLEL STRIP LINES Figure shows a parallel strip lines consisting of two perfectly parallel strips made of ‘sopper. The space between the parallel strips is filled with a dielectric material having uniform thickness. The width of each strip fs "w" and the thickness of the dielectric material is "d" and has a dieléctric constant of €. ~ ‘Figure: Mlustrating parallel strip lines 1 ECE /KVGCEMicrowaves Theory and Antennas - 21£C62 the inductance alofig the two conducting strips is given by Le he henry/m where: H, = permeability of the conductor The capacitance between the two conducting parallel strips is given by c= S™ faradim ‘The seties resistance of both strips is given by aed 2Rs_ 2 fate, R= 2Rs_2 [nthe wowYo co where Rg = surface resistance ©, = conductivity of the strips in u/m. ‘The shunt conductance of the parallel strip line Is given by Saw hs d vim conductivity of the dielectric material between the two strips G where o, = 12 ECE /KVGCEMicrowaves Theory and Antennas - 21EC62 Characteristic Impedance Z, Tacha bps en era 24 fem 37 a {e"eYen ee) ‘The phase velocity ofthe TEM wave propagating through the parle strip Tne given ot 1 ETE nee ee Attenuation Losses “Atmicrowave frequencies, the propagation as y= VEN = {B+ jal) (G+ 00) rece ccol and Gc ob tends sppsied) rot[fEsofh mor ‘Comparing real parts, the attenuation constant is given by 1 IC iL on sf +o arome =§ ‘And comparing imaginary parts, p= ot ‘The anenuation constant for conductor losses is given by the 1* term of equation 5 RC 2 ‘Substituting for R, C and L from respective equations 3,2 and 1 , we get 12 fete, few ee ee eDwyo, Yd md constant of a parallel stripline can be expressed BMicrowaves Theory and Antennas. - 21EC62 ‘And the attenuation constant for dieletric losses is given by the 2% term of equation Sas He %=2YC Again substituting for G, C and L from respective equations 4,2 and 1, we get Example : A gold parallel strip line of width 20 mm contains material between the strip lines having a dielectric constant of 225 and thickness of ss 4mm. Determine the characteristic impedance and the phase velocity of the propagating. microwave. Solution : Given w = 20 mm, d= 4 mm, €,,=2.5. for w >> d, the characteristic impedance Z, is given by 371 (a 377 a £O2-B( * Z, = 50270 the phase velocity is given by 3x10! oe as v, = 2x 10" m/sec ECE /KVGCEMicrowaves Theory and Antennas» 21EC62 Example : A lossless parallel strip line has copper conducting strips each of width w= 18 thm separated by quarts dielectric of dielectric constant 3,8 having thickness of 2.5 nf, The conductivity of copper is 5.8 10° gin and that of quartz is 2x 10 e3/m. The frequency of ‘operation is 12 GHz. Determine (a) Characteristic impedance of parallel strip line (0) Phase velocity of the propagating wave (©) Stripstine inductance (q) Strip-tine capacitance (@) Series resistance for both strips €O Shunt conductance of the dielectric (@) Attenuation constant for conductor losses (h) Attenuation constant for dielectric losses Solution : Given w= 18 mm, €, = 3.8, d = 2.5 mm, f= 12 GHz, 6, = 5.8 x 107 g/m, 82x 104 Gm, . (&) Since w >> 4 : a RE) . 37 (22) 18mm “ Z, = 26360= an Microwaves Theory and Antenni Ch) the phane velocity in given by oxo lene = 1.84% 108 mv/see yo 4m 1077 1 2.5 107% - 186 «107 = 0.175 p/m (d) the atrip tine capacitance Is given by aM 6 Sow ‘ © = 242.25 prim (©) ‘The series resintance for both strips is given by 2 pati Reds 2 [Rtn "Ww o 2 R12 10" x ae 10" oe * igi 3.810" o R = 3.176 O/m (0) The shunt conductance of the dielectric substrate is given by = Sa a d 2.%10°*% 18 x10 25x10 * G = 144% 10° Gm (g) Attenuation constant for conductor losses is given by 1 frte way o, 16 ECE /KVGCEMicrowaves Theory and Antennas - 21EC62 7 1 in x 12 x 10° x 8854 x 10°" x 38 * 325x107 58x 10 a @, = 0.06 nepers/m (h) Attenuation constant for dielectric losses is given by 188 9, a, = 4 a (188) (2 x10~*) ~ 38 0.02 nepers/m