EKT 345 MICROWAVE ENGINEERING CHAPTER : PLANAR TRANSMISSION LINES 1
Tansmission Lines A device used to tansfe enegy fom one point to anothe point efficiently Efficiently minimum loss, eflection and close to a pefect match as possible (VSWR 1:1) Impotant to be efficient at RF and micowave fequencies, since feq used ae highe than DC and low feq applications as feq gets highe, any enegy loss is in tansmission lines ae moe difficult and costly to be etieved
Some Types of Tansmission Lines Some types of tansmission lines ae listed as follow: Coaxial tansmission line tansmission line which a conducto completely suounds the othe Both shaes the same axis, sepaated by a continuous solid dielectic o dielectic spaces Flexible able to be bent without beaking 3
Some Types of Tansmission Lines Waveguides Hollow-pipe stuctue, in which two distinct conducto ae not pesent Open space of the waveguide is whee electomagnetic enegy finds the path of least esistance to popagate Do not need any dielectic medium as it uses ai as medium of enegy tansfe Plana tansmission lines Plana looks like a 3D line that have been un ove and flattened Usually made up of a laye of dielectic, and one o seveal gound (metallic planes) Fou types of plana lines discussed in this chapte; (1) Stipline, () micostip (3) dielectic waveguide (4) Slotline 4
Why Plana? Waveguides High powe handling capability low loss bulky expensive Coaxial lines high bandwidth, convenient fo test applications difficult to fabicate complex micowave components in the medium 5
Cont d Plana Tansmission Lines Compact Low cost Capability fo integation with active devices such as diodes, tansistos, etc 6
STRIPLINE Figue 3.1: Stipline tansmission line (a) Geomety (b) Electic and magnetic field lines. 7
Cont d Also known as sandwich line evolved fom flattened coaxial tansmission line The geomety of a stipline is shown in Figue 3.1. Consist of a; (1) top gound plane, () bottom gound plane and (3) a cente conducto W is the width of thin conducting stip (centeed between two wide conducting gound planes). b is the distance of gound planes sepaation. The egion between the gound planes is filled with a dielectic. Pactically, the centeed conducto is constucted of thickness b/. 8
Cont d Figue 3.: Photogaph of a stipline cicuit assembly. 9
10 Cont d The phase velocity is given by: p c v µ 0 0 1 0 0 0 k v p µ ω ω β Thus, the popagation constant of the stipline is: [3.1] [3.]
Cont d Fom equation [3.1], c 3 x 10 8 m/sec is the speed of light in fee-space. The chaacteistic impedance of a tansmission line is given by: Z L C LC C 0 1 v C [3.3] L and C ae the inductance and capacitance pe unit length of the line. Thee is a solution as explained in [Text book by M. Poza]. The esulting fomula fo the chaacteistic impedance is: p Z 0 30π b We + 0. 441b [3.4] 11
Cont d Whee W e is the effective width of the cente conducto given by: W e b W b 0 fo W b 0.35 ( 0.35 W b ) W fo < 0. 35 These fomulas assume a zeo stip thickness, and ae quoted as being accuate to about 1 % of the exact esults. It is seen fom equation [3.4] and [3.5] that the chaacteistic impedance deceases as the stip width W incease. b > [3.5] 1
Cont d When designing stipline cicuits, one usually needs to find the stip width, W. By given chaacteistic impedance (and height b and pemittivity ), the value of W can be find by the invese of the fomulas in equation [3.4] and [3.5]. The useful fomulas is: W b x fo Z0 0.85 0.6 x fo Z0 < 10 > 10 [3.6] Whee, x 30π Z 0 0.441 [3.7] 13
Cont d The attenuation due to dielectic loss is: k tanδ α d Np / m [3.8] The attenuation due to the conducto loss: α c 3.7 10 Rs Z 30π 0.16Rs B Z0b 0 A ( b t) fo Z0 < 10 Np / m fo Z 0 > 10 [3.9] 14
Cont d With: A 1 + W b t + 1 π b b + t t ln b t t [3.10] B 1+ b W ( 0.5 + 0.7t) 0.5 + 0.441t W + 1 ln π 4πW t [3.11] Whee t is the thickness of the stip 15
STRIPLINE [EXAMPLE.1] Find the width fo a 50 Ω coppe stipline conducto, with b 0.3 cm and.0. If the dielectic loss tangent (tan δ) is 0.001 and the opeating fequency is 10 GHz, calculate the attenuation in db/λ. Assume the conducto thickness of t 0.01 mm and suface esistance, R s of 0.06 Ω 16
SOLUTION: Since x Z 0.(50) 74. < 10 30π Z 0 0.441 0.830 and Eq [3.6] gives the width as W bx (0.3)(0.830) 0.66 cm. At 10 GHz, the wave numbe is k πf 1 310.6m c 17
SOLUTION: The dielectic attenuation is α d k tanδ (310.6)(0.001) Suface esistance of coppe at 10 GHz is R s 0.06 Ω. Then fom eq [3.9] 3.7 10 R s Z0 A αc 0.1Np / m 30π ( b t) The total attenuation constant is α αc + α d 0.77Np / m 0.155Np / m since A 4.74 18
SOLUTION: In db; α α( db / m) 0log e.41db / m At 10 GHz, the wavelength on the stipline is; c λ.0cm f So in tems of the wavelength the attenuation is α( db / λ) (.41)(0.00) 0.049dB / λ 19
SOLUTION: But why do we need to convet Np/m to db/m using this way? α ( Np / m) α( db / m) 0log e.41db / m loss to the tansmission line is eflected by the attenuation constant. The amplitude of the signal decays as e -α. The natual units of the attenuation constant ae Nepes/mete, but we often convet to db/mete in micowave engineeing. To get loss in db/length, multiply Nepes/length by 8.686. 0
STRIPLINE [EXAMPLE.] Find the width fo 50 Ω coppe stipline conducto with b 0.5 cm and 3.0. The loss tangent is 0.00 and the opeating fequency is 8 GHz. Calculate the attenuation in db/λ. Assume a conducto thickness of t 0.003 cm. The suface esistance is 0.03 Ω. 1
SOLUTION: Z0 3 50 86.603 < 10 x W b x 30π Z 0 W 0.441 bx 30π 3 50 The wave numbe at f 8 GHz k 0.441 0.6474 ( 0.5 10 )( 0.6474 ) 0.00337 m ( 9 8 10 ) 3 1 πf π 90.46m 8 c 3 10
SOLUTION: The dielectic attenuation is k tanδ 90.46 0.00 αd ( )( ) The conducto attenuation is A 1 + W b t + 1 b π b + t t b ln t t 0.9 ( 0.00337) 1 0.005 + 0.003 10 ( 0.005) Np/m 0.003 10 A 1+ + ln 0.005 0.003 10 π 0.005 0.003 10 0.003 10 A 4.173 3
SOLUTION: α c α 3.7 10 R s Z 0 A 30π 30π ( b t) ( 0.03)( 3)( 50)( 4.173) 3.7 10 c ( 0.005 0.003 10 ) 0.108 Total loss: α αd + αc 0.9 + 0.108 0.398 In db: α α( db/ m) 0loge 0.398 0loge 3. 459 Np/m db/m 4
SOLUTION: The guided wavelength: 8 c 3 10 λg 9 f 3 8 10 The attenuation in db/λ: 0.0165 α ( db / λ) ( 3.459)( 0.0165) 0. 07488 5
STRIPLINE DISCONTINUITY Figue 3.3: geomety of enclosed stipline 6
7 Cont d By deivation found in Text book (page 141), the suface chage density on the stip at y b/ is: ( ) ( ) ( ) ( ) [ ] + +,,,, 0 b y x E b y x E b y x D b y x D y y y y s ρ odd n n a b n a x n a n A 1 0 cosh cos π π π [3.1] The chage density on the stip line by unifom distibution: ( ) > < 0 1 W x fo W x fo x s ρ [3.13]
Cont d The capacitance pe unit length of the stipline is: C Q V odd a W sin ( nπw a ) sinh ( nπb a ) ( nπ ) cosh ( nπb a ) n 1 0 Fd / m [3.14] The chaacteistic impedance is then found as: Z 0 L C LC C 1 v C p cc [3.15] 8
MICROSTRIP Figue 3.3: Micostip tansmission line. (a) geomety. (b) Electic and magnetic field lines. 9
Cont d Micostip line is one of the most popula types of plana tansmission line. Easy fabication pocesses. Easily integated with othe passive and active micowave devices. The geomety of a micostip line is shown in Figue 3.3 W is the width of pinted thin conducto. d is the thickness of the substate. is the elative pemittivity of the substate. 30
Cont d The micostip stuctue does not have dielectic above the stip (as in stipline). So, micostip has some (usually most) of its field lines in the dielectic egion, concentated between the stip conducto and the gound plane. Some of the faction in the ai egion above the substate. In most pactical applications, the dielectic substate is electically vey thin (d << λ). The fields ae quasi-tem (the fields ae essentially same as those of the static case. 31
Cont d The phase velocity and the popagation constant: v p c e β k0 e 1 < < [3.16] [3.17] Whee e is the effective dielectic constant of the micostip line used to compensate diffeence between the top and bottom of the cicuit line The effective dielectic constant satisfies the elation: e and is dependent on the substate thickness, d and conducto width, W 3
Cont d The effective dielectic constant of a micostip line is given by: + 1 1 e + [3.18] 1 1+ 1d The effective dielectic constant can be intepeted as the dielectic constant of a homogeneous medium that eplaces the ai and dielectic egions of the micostip, as shown in Figue 3.4. W Figue 3.4: equivalent geomety of quasi-tem micostip line. 33
34 Cont d The chaacteistic impedance can be calculated as: ( ) [ ] + + + + 1 1 1.444 0.667 ln 1.393 10 4 8 ln 60 0 d fo W d fo W d W d W d W W d Z e e π [3.19] Fo a given chaacteistic impedance Z 0 and the dielectic constant Є, the W/d atio can be found as: ( ) ( ) 0.61 0.39 1 ln 1 1 ln 1 8 > < + + d W fo d W fo B B B e e d W A A π [3.0]
Cont d Whee: A B Z0 + 1 60 377π Z 0 + 1 0.3 1 + + 0.11 Consideing micostip as quasi-tem line, the attenuation due to dielectic loss can be detemined as ( ) e 1 tan ( 1) k0 δ α d Np / e m Whee tan δ is the loss tangent of the dielectic. [3.1] 35
Cont d This esult is deived fom Equation [.37] by multiplying by a filling facto : e ( ) e 1 ( 1) Which accounts fo the fact that the fields aound the micostip line ae patly in ai (lossless) and patly in the dielectic. The attenuation due to conducto loss is given appoximately by: R s αc Np / Z W 0 m [3.] Whee R s (ωμ 0 /σ) is the suface esistivity of the conducto. 36
MICROSTRIP [EXAMPLE.3] Calculate the width and length of a micostip line fo a 50 Ω chaacteistic impedance and a 90 phase shift at.5 GHz. The substate thickness is d 0.17 cm, with.0. 37
MICROSTRIP [EXAMPLE.4] Design a micostip tansmission line fo 70 Ω chaacteistic impedance. The substate thickness is 1.0 cm, with.50. What is the guide wavelength on this tansmission line if the fequency is 3.0 GHz? 38
MICROSTRIP [EXAMPLE.5] Design a quate wavelength micostip impedance tansfome to match a patch antenna of 80 Ω with a 50 Ω line. The system is fabicated on a 1.6 mm substate thickness with.3, that opeates at GHz. 39
40 MICROSTRIP DISCONTINUITY By deivation found in text book (page 147), the suface chage density on the stip at y d is: ( ) ( ) ( ) ( ) + + d y x E d y x E d y x D d y x D y y y y s,,,, 0 0 ρ + odd n n a d n a d n a x n a n A 1 0 cosh sinh cos π π π π [3.3] The chage density on the micostip line by unifom distibution: > < 0 1 W x fo W x fo s ρ [3.4]
MICROSTRIP DISCONTINUITY The capacitance pe unit length of the stipline is: C Q V odd 4a sin( nπw a) sinh( nπd a) ( nπ ) W [ sinh( nπd a) cosh( nπd a) ] n 1 0 + 1 Fd / m [3.5] The chaacteistic impedance is then found as: Z 0 1 v C p e cc [3.6] 41
DIELECTRIC WAVEGUIDE Figue 3.6: Dielectic waveguide geomety. 4
Cont d The dielectic waveguide is shown in Figue 3.6. is the dielectic constant of the idge. 1 is the dielectic constant of the substate. Usually 1 < The fields ae thus mostly confined to the aea aound the dielectic idge. Convenient fo integation with active devices. Vey lossy at bends o junctions in the idge line. Many vaiations in basic geomety ae possible. 43
SLOTLINE Figue 3.7: Geomety of a pinted slotline. 44
Cont d The geomety of a slotline is shown in Figue 3.7. Consists of a thin slot in the gound plane on one side of a dielectic substate. The chaacteistic impedance of the line can be change by changing the width of the slot. 45