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

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– image processing

– high speed

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•High speed & high frequency

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• 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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