Embed Size (px)
Citation preview
EELE 3332 – Electromagnetic II
Microstrip Transmission Lines
Islamic University of Gaza
Electrical Engineering Department
Dr. Talal Skaik
2013 1
2
Transmission lines
3
Microstrip
Microstrip transmission line. (a) Geometry. (b) Electric and magnetic field lines.
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.
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 and
it is dependent on the substrate thickness h, and conductor width W.
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
1 e r
1 1 1
2 2 1 12 /
r re
h W
7
0
1 1 1
2 2 1 12 /
Given the dimensions of the microstrip line, the characteristic impedance
can be calculated as
60 8ln / 1
4Z =
120
/ 1.393 0
r re
e
e
h W
h Wfor W h
W h
W h
/ 1
.667 ln / 1.444
The velocity is calculated as
The propagation constant is =
e
e
for W hW h
cu
u c
Microstrip
8
0 r
2
For a given characterestic impedance Z and dielectric constant ,
the / ratio can be found as:
8 / 2
2
12 0.611 ln(2 1) ln( 1) 0.39 / 2
2
A
A
r
r r
W h
efor W h
eW
hB B B for W h
where
0
0
1 1 0.11A= 0.23
60 2 1
377
2
r r
r r
r
Z
BZ
Microstrip
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:
9
Microstrip - Losses
00
( 1) tan 2 Np/m ,
2 ( 1)
where tan is the loss tangent of the dielectric.
The attenuation due to conductor loss is given approximately by:
r ed
e r
k fk
c
0
0
Np/m
where / 2 is the surface resistivity of the conductor.
sc
s
R
Z W
R
10
r
Example: Calculate the width and length of a microstrip line for a 50
characterestic impadance and a 90 phase shift at 2.5 GHz. The substrate
thickness is h=0.127 cm, with =2.2
o
0.
Microstrip - Example
0
0
We first find / for 50 , and initially guess that / 2.
3777.985
2
12 0.61/ 1 ln(2 1) ln( 1) 0.39 3.081
2
/ 2; otherwise we would use the e
Solution:
r
r
r r
W h Z W h
BZ
W h B B B
So W h
o
8
xpression for / 2.
, 3.081 0.391
1 1 1The effective dielectric constant is 1.87
2 2 1 12 /
The length for a 90 phase shift is found as
(90 )( /180)(3 10 )90
(2 )
r re
oo
e
e
W h
So W h cm
h W
l
l l lc f
2.19 cml
Dr. Talal Skaik 2012 IUG 11
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 12
Stripline
0 0
0
1The velocity is :
The propagation constant is =
30The characterestic impedance is: Z
0.441
where is the effective width of the centre conductor given by
r r
r
er
e
cu
u c
h
W h
W
W
2
0
0 0.35
0.35 / 0.35
These formulas assume a zero strip thickness, and are quoted as being
accurate to about 1% of the exact results.
* Notice that Z decreases as the str
e
Wfor
W h
Wh hW h for
h
ip width increases.W
Dr. Talal Skaik 2012 IUG 13
Stripline
0
0
0
0
Given the characterestic impedance Z , and height and permittivity ,
the strip width can be found by:
120
0.85 0.6 120
30 0.441
Z
r
r
r
r
h
x for ZW
h x for Z
where x
Dr. Talal Skaik 2012 IUG 14
Stripline - Losses
d
3
0
The attenuation due to dielectric loss is given by:
tan = Np/m (general for TEM waves) ,
2
The attenuation due to conductor loss is approximately:
2.7 10
30 ( )
r
s r
c
kk
u c
R Z
h t
0
0
0
for 120
Np/m 0.16
for 120
2 1 2with 1+ ln
0.414 1 4 1 0.5 ln
0.5 0.7 2
is the thickness of the strip
r
sr
A Z
RB Z
Z h
W h t h tA
h t h t t
h t WB
W t W t
where t
.
15
Microstrip applications
16
Low Pass Filters
17
Bandpass Filters
18
Microstrip Antennas
Dr. Talal Skaik 2012 IUG 19
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.
