prof. david r. jackson dept. of ece notes 10 ece 5317-6351 microwave engineering fall 2011...
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Prof. David R. JacksonDept. of ECE
Notes 10
ECE 5317-6351 Microwave Engineering
Fall 2011
Waveguides Part 7:Planar Transmission Lines
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Stripline
Common on circuit boards
Fabricated with two circuit boards
Homogenous dielectric (perfect TEM mode)
Field structure for TEM mode:
(also TE & TM Modes)
bW
0, ,
Electric FieldMagnetic Field
TEM mode
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Analysis of stripline is not simple TEM mode fields can be obtained from static analysis Closed stripline structure is analyzed in the Pozar book
0, , W b/2
b
a >> ba
Stripline (cont.)
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For lossless TEM mode:
0
1
1 1
p
p
p
L LCZ
C C
Lv
LC
C
v
v C
We can find Z0 if C is known
Inductance / unit length
Capacitance / unit length
Stripline (cont.)
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From static, conformal mapping solution (S. Cohn)
0
30 ( )
( ')
K kZ
K k
sech2
' tanh2
Wk
b
Wk
b
K elliptical integral
Exact solution:
Stripline (cont.)
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Curve fitting this exact solution:
00 ln(4)4 r
e
bZ
W b
Effective width
2
0 ; 0.35
0.35 ; 0.1 0.35
e
W
bW W
b b W W
b b
for
for
Z0 as W
Stripline (cont.)
00
1 / 2
2 4 4PPW
r
bb bZ
W W W
Note: The factor of 1/2 in front is from the parallel combination of two PPWs.
ln 40.441
Note :
Fringing term
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Inverting this solution to find W for given Z0:
0
0
0
; 120
0.85 0.6 ; 120
30 ln(4)
r
r
r
X ZW
bX Z
XZ
for
for
Stripline (cont.)
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Attenuation
Dielectric Loss:
0 0tan tan2 2 2
r r cd
c
k kkk
t b
W0, ,
Rs
Stripline (cont.)
c c cj j
(TEM formula)
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3 00
00
(2.7 10 ) ; 12030 ( )
0.16 ; 120
1 21 2 ln
( )
1 11 0.414 ln 4
2 20.7
2
s rr
c
sr
R ZA Z
b t
RB Z
Z b
W b t b tA
b t b t t
b t WB
W W tt
wher
for
for
e 2sR
Stripline (cont.)Conductor Loss:
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Inhomogeneous dielectric
No TEM mode
Cannot phase match across dielectric interface
Requires advanced analysis techniques Exact fields are hybrid modes (Ez and Hz)
For d /0 << 1 dominate mode is quasi-TEM
, , W d
Microstrip
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Microstrip (cont.)
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For the equivalent TEM problem:
0
p effr
effr
cv
k
r0
effr
Equivalent TEM problem
Actual problem
Microstrip (cont.)
d
d
W
W
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1 1 1
2 21 12
eff r rr
dW
Microstrip (cont.)
1/ 0 :
2eff rrW d
/ : effr rW d
Effective permittivity:
Limiting cases:
(narrow strip)
(wide strip)
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0
60 8ln ; 1
4
120; 1
1.393 0.667 ln 1.444
effr
effr
d W W
W d d
Z W
dW W
d d
for
for
Microstrip (cont.)
Characteristic Impedance:
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Inverting this solution to find W gives Z0:
2
8; 2
2
12 0.611 ln(2 1) ln 1 0.39 ; 2
2
A
A
r
r r
e W
e dW
WdB B B
d
for
for
0
0
1 1 0.110.33
60 2 1
377
2
r r
r r
r
ZA
BZ
where
Microstrip (cont.)
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Attenuation
Dielectric loss:
01
tan2 1
effrr r
d effr r
k
0
sc
R
Z W
“filling” factor
very crude (“parallel-plate”) approximation
Conductor loss:
Microstrip (cont.)
(More accurate formulas are given later.)
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More accurate formulas for characteristic impedance that account for dispersion and conductor thickness:
0 0
1 00
0 1
eff effr reff effr r
fZ f Z
f
0
1200
0 / 1.393 0.667 ln / 1.444effr
ZW d W d
( / 1)W d
21 ln
t dW W
t
d
W
er
t
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Microstrip (cont.)
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d
W
er
t
2
1.5
(0)(0)
1 4
effr reff eff
r rfF
1 1 11 /0
2 2 4.6 /1 12 /
eff r r rr
t d
W dd W
2
0
4 1 0.5 1 0.868ln 1r
d WF
d
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Microstrip (cont.)
where
( / 1)W d
Note:
:
effr r
f
f
As
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Microstrip (cont.)
2
0
effr k
"A frequency-dependent solution for microstrip transmission lines," E. J. Denlinger, IEEE Trans. Microwave Theory and Techniques, Vol. 19, pp. 30-39, Jan. 1971.
Frequency variation
r
r
W
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d
W
er
t
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Microstrip (cont.)More accurate formulas for conductor attenuation:
2
0
1 21 1 ln
2 4s
c
R W d d d t
hZ d W W t d
12
2
W
d
2
0
/2 2ln 2 0.94 1 ln
2 0.942
sc
W dR W W W d d d te
WhZ d d h W W t dd
2W
d
21 ln
t dW W
t
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Microstrip (cont.)Note:
It is necessary to assume a nonzero conductor thickness in order to accurately calculate the conductor attenuation.
The perturbational method predicts an infinite attenuation if a zero thickness is assumed.
10 : 0szt J s
s as
d
W
er
t
sszJ Practical note: A standard thickness
for PCBs is 0.7 [mils] (17.5 [m]), called “half-ounce copper”.
1 mil = 0.001 inch
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TXLINE
This is a public-domain software for calculating the properties of some common planar transmission lines.
http://web.awrcorp.com/Usa/Products/Optional-Products/TX-Line/
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TXLINE (cont.)
TX-Line™ Transmission Line Calculator
TX-Line is a FREE, easy-to-use, Windows-based interactive transmission line calculator for the analysis and synthesis of transmission line structures. TX-Line enables users enter either physical characteristics or electrical characteristic for common transmission medium such as:
MicrostripStriplineCoplanar waveguideGrounded coplanar WGSlotline
TX-Line runs on Microsoft® Windows® 2000-SP4, XP-SP2, Vista-SP1, Windows® 7
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Microstrip (cont.)
REFERENCES
L. G. Maloratsky, Passive RF and Microwave Integrated Circuits, Elsevier, 2004.
I. Bahl and P. Bhartia, Microwave Solid State Circuit Design, Wiley, 2003.
R. A. Pucel, D. J. Masse, and C. P. Hartwig, “Losses in Microstrip,” IEEE Trans. Microwave Theory and Techniques, pp. 342-350, June 1968.
R. A. Pucel, D. J. Masse, and C. P. Hartwig, “Corrections to ‘Losses in Microstrip’,” IEEE Trans. Microwave Theory and Techniques, Dec. 1968, p. 1064.