EELE 3332 – Electromagnetic II Microstrip Transmission Lines Islamic University of Gaza Electrical Engineering Department Dr. Talal Skaik 2013 1 Transmission lines 2 Microstrip Microstrip line is one of the most popular types of planar transmission lines because of ease of fabrication and integration with other passive and active microwave devices. The geometry is shown, it consists of a conductor of width W printed on a grounded dielectric substrate of thickness h and relative permittivity εr. Microstrip transmission line. (a) Geometry. (b) Electric and magnetic field lines. 3 Microstrip 4 Microstrip 5 Microstrip Since some of the field lines are in the dielectric region and some are in air, (the dielectric region does not fill the air region above the strip (y>h)), an effective dielectric constant εe is considered in the analysis. The effective dielectric constant satisfies the relation 1 er and it is dependent on the substrate thickness h, and conductor width W. 111 rr e 221 12hW / εe can be interpreted as the dielectric constant of a homogeneous medium that replaces the air and dielectric regions of the microstrip, as shown. Dr. Talal Skaik 2012 IUG 6 Microstrip 111 rr e 221 12hW / Given the dimensions of the microstrip line, the characteristic impedance can be calculated as 60 8hW lnfor W/ h 1 Wh4 e Z=0 120 for W/ h 1 Wh/ 1.393 0.667lnWh / 1.444 e c The velocity is calculated as u e The propagation constant is = uce 7 Microstrip For a given characterestic impedance Z0r and dielectric constant , the Wh/ ratio can be found as: 8eA 2 A for W/ h 2 W e 2 h 2 1 0.61 B1 ln(2 B 1) r ln( B 1) 0.39 for W/ h 2 2 rr Z 110.11 where A=0 rr 0.23 60 2rr 1 377 B 2Z0 r 8 Microstrip - Losses Attenuation can be caused by dielectric loss and conductor loss. If αd is attenuation constant due to dielectric loss, and αc is the attenuation due to conductor loss, the total attenuation constant is: α= αd + αc Considering the microstrip as a quasi-TEM line, the attenuation due to dielectric loss can be determined as: k0re( 1) tan 2 f d Np/m , k0 2er ( 1) c where tan is the loss tangent of the dielectric. The attenuation due to conductor loss is given approximately by: R s Np/m c ZW 0 where R / 2 is the surface resistivity of the conductor. s 0 9 Microstrip - Example Example: Calculate the width and length of a microstrip line for a 50 characterestic impadance and a 90o phase shift at 2.5 GHz. The substrate thickness is h=0.127 cm, with r =2.20. Solution: We first find W/ h for Z0 50 , and initially guess that W/ h 2. 377 B 7.985 2Z0 r 2 1 0.61 W/ h B 1 ln(2 B 1) r ln( B 1) 0.39 3.081 2 rr So W/ h 2; otherwise we would use the expression for Wh/ 2. So, W 3.081 h 0.391 cm 111 The effective dielectric constant is rr 1.87 e 221 12hW / The length l for a 90o phase shift is found as o 8 o (90 )( /180)(3 10 ) 90 l e l l l 2.19 cm c (2f ) e 10 Stripline The geometry is shown, it consists of a thin conducting strip of width W centered between two wide conducting ground planes of separation h, and the entire region between the ground planes is filled with a dielectric. In practice, stripline is usually constructed by etching the centre conductor on a grounded substrate of thickness h/2, and then covering with another grounded substrate of the same thickness. Notice that all fields exist within the dielectric substrate. Dr. Talal Skaik 2012 IUG 11 Stripline 1 c The velocity is : u 00 rr The propagation constant is = ucr 30 h The characterestic impedance is: Z0 r Whe 0.441 where We is the effective width of the centre conductor given by W 0for 0.35 W W h e hh 2 W 0.35W / h for 0.35 h These formulas assume a zero strip thickness, and are quoted as being accurate to about 1% of the exact results. * Notice that Z0 decreases as theDr. Talalstr Skaikip width 2012 IUG W increases. 12 Stripline Given the characterestic impedance Z0 , and height h and permittivity r , the strip width can be found by: W x for r Z0 120 h 0.85 0.6 x for r Z0 120 30 where x 0.441 r Z0 Dr. Talal Skaik 2012 IUG 13 Stripline - Losses The attenuation due to dielectric loss is given by: k tan = Np/m (general for TEM waves) , k r d 2 uc The attenuation due to conductor loss is approximately: 3 2.7 10 RZsr 0 AZ for r 0 120 30 (ht ) c Np/m 0.16R s BZfor 120 r 0 Zh0 2W 1 h t 2 h t with A 1+ ln h t h t t h0.414 t 1 4 W B 1 0.5 ln 0.5W 0.7 t W 2 t where t is the thickness of the strip. Dr. Talal Skaik 2012 IUG 14 Microstrip applications 15 Low Pass Filters 16 Bandpass Filters 17 Microstrip Antennas 18 Design tools - txline software Example: Calculate the width and length of a microstrip line for a 50 Ω characteristic impedance and a 90o phase shift at 2.5 GHz. The substrate thickness is h=0.127cm, with εr=2.20. Use txline software to design. Dr. Talal Skaik 2012 IUG 19 .