ece 563 & tcom 590 microwave engineering planar transmission lines: striplines and microstrips...
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ECE 563 & TCOM 590Microwave Engineering
Planar Transmission Lines:
Striplines and Microstrips
October 14, 2004
Planar Transmission Lines
Parallel Plate Waveguide
lengthunit per inductance w
dL
lengthunit per ecapacitanc d
wC
find also TEMFor
fieldsstray unconfined :geDisadvanta
modes TE TM,support also plates Parallel
plates ofwidth wand platesbetween distance d
wherec1
v;w
dZ
find mode, TEMfor Equation sLaplace' Solve
rr
p0
Surface Waves on a Grounded Dielectric Slab
dependence z w/o)TE(Hor )TM(Eeither is F where
xd ;0)y,x(F)kx
(
dx0 ;0)y,x(F)kx
(
find toz
use,k,Hfor similarly EkE
zzz
z22
02
2
z22
0r2
2
22
222
zz2
z2
0r
0 x
z//////////////////////////////////////
dat x cont. H (4) dat x cont. H (4)
dat x cont. E (3) dat x cont. E (3)
x as;0H (2) x as;0E )2(
0x;0x
H0E (1) 0x;0E (1)
TE TM
Cond. Bound.insert xd ,DeCeF
dx0 ,xkcosBxksinAF
kh and kk
:rs wavenumbecutoff
zy
yz
zz
zyz
hxhxz
ccz
20
22220r
2c
Surface Waves on a Grounded Dielectric Slab
hd2
02
c
cc
z2
c
y
hdc
zyx
hDeh
j
k
j)dk(cosAk)4(
x
E
k
jH
DedksinA)3(
0C(2) 0B)1(
0HEH
Surface Waves on a Grounded Dielectric Slab – TM Mode
..0,1,2,3,..n ;1d2
nc
2
ckf
n)dk(1
of sfrequencie cutoffat modesHigher
)dk)(1()hd()dk( & )hd()dk(tan)dk(
as (6) and (5) rewite (6) k)1(hk
rs wavenumbecutoff from geliminatin
(5) k
h)dk( tan e
h
D)dk( cos
k
A
and De)dk( sinA Since
r
0c
0r
20r
22crcc
20r
22c
2
c
rc
hdc
c
r
hdc
Surface Waves on a Grounded Dielectric Slab – TM Mode
TM mode cutoff frequencies
Surface Waves on a Grounded Dielectric Slab – TE Modes
1,2,3,....n ;14
)12(
2
2/)12()(1
at sfrequencie cutoff ;))(1()()(
)()(cotan )(-
tolead B.C.
0
0
20
22
r
c
r
rc
cc
d
cnckf
ndk
dkhddk
hddkdk
TE mode cutoff frequencies
Stripline
Triplate transmission line
Stripline
Advantage (compared to parallel plates)– transverse fields remain in the vicinity of the
center conductor between 2 grounded planes– 2 conductor line, no lower frequency cutoff:
down to f=0 , up to cutoff of first TE mode.– Miniaturization
Stripline
• Compared to coax or waveguide– Advantage if Gunn diodes or mixer diodes to
be apart of circuit design.– Advantage, large bandwidth, mini-size– Disadvantage- lack of isolation, lower power
handling
• Dominant mode - TEM
Stripline
Stripline
C
120
CCCZ
fringing with ecapacitancC
fringing without ecapacitancC ;C42CC
C ecapacitanc needCv
1
C
LCC
LZ
/1/c vTEM
r0
0
r
0
f
pfp
p0
rp
Stripline
)0b
t( ,
44.
30
fringing with ecapacitancC
0 )(thickness when t 44.02ln2)/1(/
width
effective wwhere ,
/1/
30
2C ;
]42C[
120
0
f
0
p
p
0
bw
bZ
C
C
btbw
Z
tb
w
CZ
er
f
e
fer
e
fr
Stripline
441.030
x
120for ,x-0.6- 0.85 w/b
120for x, w/b
0
0
0
Zwhere
Z
Z
r
r
r
0.35 for w/b
,w/b)- (0.35 w/b /bw
0.35 for w/b w/b /bw2
e
e
Losses
k tan )2/1( sok and 0k TEM,For
k and
,2
tan
2
tan
tan)tan1(
and j wheree fields Recall,
then is loss totalThe
. loss,conductor or , loss, dielectriceither
by caused becan lineion transmissain n Attenuatio
dc
002222
2
22
222
22200
22
z-tj
cd
cd
rc
c
c
crc
jkk
wherejk
kk
jkkk
jkkkjk
Attenuation due to conductor losses(approximate result)
t
4ππln
2
1
w
0.414t5.0
)7.05.0(1B
2ln
)(t-b
2w1A where
120for 16.0
120for )(30
107.2
0r0
0r0
3
tw
b
t
tb
tb
tb
ZBbZ
R
ZAtb
ZR
sc
rsc
Planar Transmission Lines
rh
////////// tw
//////////////////////
Microstrip Lines
Popular fabricated by photolithographic processes easily integrated with other passive and active microwave devices convenient, economical; therefore, widespread use
Problem radiation and undesired modes by lines at discontinuities
Microstrip
effoverall
dielectricroverall0
p
rr
p
Let
onsider C
matched bet can' cair v
in butc
vdielectricat velocity hase- p
TEMsupport tounable
wt
heverywhere eff
Microstrip Design
50-1246 p. '88, Aug,36 MTT, IEEE see (example, postulated
been have ipsrelationshMany critical. is of Value
. effective with ipsrelationsh TEM use - TEM Quasi
negligible cknessribbon thi 1, t/h 5)
by w controlled Z4)
hloosely wor 10(w/h)0.1 3)
millimeter offraction h 2)
lossradiation reduce High 1)
:objectives Design
eff
0
r
r
r
r
r
r
r
rr
rr
hwhw
hwhw
hw
hwhw
0TEM
2/1
0297.0TEM
2/1
1255.0TEM
2/1eff
22/1eff
*
where,
6.0/,)/)(1(60.01
6.0/,)/)(1(63.01
16 & 20w/h0.05 when 1%error relative
1for w/h ,)/
121(
2
1
2
1
1for w/h],)/1(04.0)/
121[(
2
1
2
1
(1977) Triveli & Bahl* 0.005for t/h
Microstrip Design Relationships
Normalized Wavelength vs w/h
Z0 and W/d approximation
Effects to Dampen Signal Propagation along a Microstrip
• Signal heats conductor through Ohmic Losses
• Signal heats substrate which is not lossless
• Signal leaks away as radiation
cd
z-z20
)e ~ (V eP P
long)not length (
band narrowin ion concentratcurrent
depth 1
;1
R
(m).in w1,for w/h dB/m, wZ
R 68.8
depthsskin 4 to3 plate ground & t Assume
WGms
s
0
s
skinf
f
c
Ohmic Losses
eff
ggg
d
d
dd
d
dBq
cc
0
eff
r
r
eff
),/(,tan
3.27
1
1 q factor, filling dielectricinsert loss) no air, is
region(upper system dielectric mixed a have wemicrostripIn
Np/m tan 2/
tangentloss dielectrictan
board substrate dielectri ofy onductivit 2
Dielectric Losses
.microstripopen theofextremity at the radiated is
power theof 1%at which )]mm(h/[ 2.14f(GHz)
oflimit frequency upper givesdesign for this
1
1ln
2
11)(F
)(Fh
240resistance radiationR ,Z
R
P
P
ends). at theleast (at itiesdiscontinuat excited bemay hich w
modesorder higher unguided of existence toRelated
4/1r
eff
eff
effeff
eff
r
eff
2
0
2r
0
r
t
rad
Radiation Losses
lines.between talk -crossby line along losses
onlynot :Radiation lines. theenclose - thisBeyond
10 when GHz 4 and 2.5 when GHz 3
toup used becan substrate thick mm 1open An
:Example
rr
Radiation Losses
Quality factor
frequency) ofnt (independe tan
1
tan
27.3
nattenuatio dielectric torelatedfactor quality Q
950 Q
GHz @10 Alumina mil 25for fh 4780Q
mhos/m 105.8Copper for
f20R ,f
R
h5.39
3.27Q
eff
0
d
d
c
GHzc
7
GHzsGHz
scc
Microstrip-line Realization
e)(inductanc )tan(ZjThen Z
circuitshort i.e. ,0Let Z
ce)(capacitan )cotan(ZjThen Z
circuitopen i.e. ,let Z
)tan(ZjZ
)tan(ZjZZ ZRecall
0in
0in
0
00in
Microstrip-line
Realization
Microstrip Filter Design
MicrostripLine
CircuitElements
Microwave Transmission
Microwave TransmissionNotes on striplines and microstrips· less bulky than waveguides· no need for welding and brazing· planar circuits - 2 dimensional universe· but high field concentration
· limits power· breakdown· heating center condition
· Open structure - radiates
Microwave Advances
• Considerable Interaction– distribution of analog microwave signals via high speed
fiber - optic links
– optically controlled microwave devices & circuits
• Photonics
• Lightwave Techniques– fiber optics
– image processing
– high speed
•High Speed Circiuts•MMIC’s - Monolithic Integrated Circuits
•High speed & high frequency
Microwave Advances• Fiber-optic cables to route microwave
signals– reduce size and weight– large bandwidth– immunity to interference– crosstalk isolation– potentially smaller transmission losses– applications
• feeds for phased array antennas
• delay lines, cable TV signal signal distribution
Millimeter Wave Monolithic Integrated Circuits (MIMIC)
• Affordable, reliable, reproducible wave and millimeter wave components
• frequency– tests up to 40 GHz– pulse power goal S-band (3 GHz) to 75 GHz
• Materials Research– GaAs– High electron mobility transistors (HEMT’s)– CAD– MHDL-Microwave Hardware Descriptive
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