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 lnfor 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  B1  ln(2 B  1) r  ln( B  1)  0.39  for W / h  2  2    rr Z 110.11 where A=0 rr 0.23 60 2rr 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:

k0re(  1) tan  2 f d  Np/m , k0 2er ( 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 (2f ) 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 0.35W / 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 h0.414 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