Waveguides

1

General Solutions for TEM,Ge e a So ut o s o ,TE and TM Waves

Figure 3.1 (p. 92)(a) General two-conductor transmission line and (b) closed waveguide.

2

General Solutions for TEM,Ge e a So ut o s o ,TE and TM Waves

ikhFi dB CA l2

0,equation sLaplace' from , Solve 1.

:line0),(TEMaanalyzingfor Procedure 2

yxyx

HE

t

zz

,,ˆ1, ,,, .3

,in constantsunknown theFind B.C.Apply .2

TEM

HEZyxez

Zyxhyxyxe

yx

xt

,,, ,,,, 2

TEM

eyxhzyxHeyxezyxE

HZzjzj

y

, , .5

, .4

0

121

CLIVZcv

ldHIldEV

rp

C

caseTE:0,equationHelmholtzfrom,Solve1

:s waveguide0)( TMor 0)( TE analyzingfor Procedure

222

yxhkyxh

HE zz

caseTM :0,equation Helmholtz from ,Solve

caseTE :0,

equation Helmholtz from ,Solve 1.

22

2

2

2

22

yxekyxe

yxhkyx

yxh

zcz

zcz

3

,

q, 22

yyx

y zcz

General Solutions for TEM,Ge e a So ut o s o ,TE and TM Waves

, , ,

,,,:case TE .2

HjEHjEHjHHjH

eyxhzyxH

zzzz

zjzz

,,,:case TM

, , ,

2222

eyxezyxE

xkE

ykE

ykH

xkH

zjzz

cy

cx

cy

cx

constantunknowntheFindB CApply3

,

,

, 2222

ky

EkjE

xE

kjE

xE

kjH

yE

kjH z

cy

z

cx

z

cy

z

cx

, , .4

constant unknown theFind B.C.Apply .3

TMTE22

kHEZk

HEZkk

k

y

x

y

xc

c

waves)TMor(TENp/mtanLoss Dielectric toDuen Attenuatio

2

kj

yy

waves)(TEM Np/m tan

waves)TMor (TE Np/m2

k

j

d

dd

4

)(p2d

Parallel Plate Waveguidea a e ate Wavegu de

Figure 3.2 (p. 98) Geometry ofFigure 3.2 (p. 98) Geometry of a parallel plate waveguide.

Figure 3.3 (p. 102) Bouncing plane wave interpretation of the TM1 parallel plate

id d

Figure 3.5 (p. 106) Field lines for the (a) TEM, (b) TM1, and (c) TE1 modes of a parallel plate waveguide. There is no variation across the width

5

waveguide mode. of the waveguide.

Rectangular Waveguideecta gu a Wavegu de

Figure 3.7 (p. 107)Geometry of a rectangular waveguide

Figure 3.6 (p. 107) Photograph of Ka-band (WR-28) rectangular waveguide components. Clockwise from top: a variable attenuator, and E-H (magic) tee junction, a directional coupler, an adaptor to ridge waveguide, an E-plane swept bend an adjustable short and a sliding matched load Courtesy of Agilent

Geometry of a rectangular waveguide.

6

bend, an adjustable short, and a sliding matched load. Courtesy of Agilent Technologies, Santa Rosa, CA

Rectangular Waveguideecta gu a Wavegu de

Figure 3.9 (p. 114) Field lines for some of the lower order modes of a rectangular waveguide. Reprinted from ld d l l © il )

7

Fields and Waves in Communication Electronics, Ramo et al, © Wiley, 1965)

Circular WaveguideC cu a Wavegu de

Figure 3.11 (p. 117)f i l idGeometry of a circular waveguide.

Figure 3.14 (p. 125) Field lines for some of the lower order modes of a circular waveguide.i d f ld d l l © il )

8

Reprinted from Fields and Waves in Communication Electronics, Ramo et al, © Wiley, 1965)

Coaxial LineCoa a e

0,1,1

ModesTEM2

bVa 0, ,,

0,,

0

22

ab

bVlnln, 0

e

abVzE jkz ˆ

ln,, 0

e

abVzH jkz

ˆ

ln,, 0

Figure 3.15 (p. 126)Coaxial line geometry.

k

ababZ

r

,ln602ln 0

9

Coaxial LineCoa a e

bkff cc

2 1

ModesOrder Hihger

max

baba

ff ccmax

Figure 3.17 (p. 129) Field lines for the

Figure 3.16 (p. 129) Normalized cutoff frequency of

Figure 3.17 (p. 129) Field lines for the (a) TEM and (b) TE11 modes of a coaxial line.

10

g (p ) q ythe dominant TE11 waveguide mode for a coaxial line.

Coaxial Line (optional)Coa a e (opt o a )

11

Coaxial LineCoa a e

12

Coaxial LineCoa a eFigure coaxial connectors

13

StriplineSt p e

Figure 3.22 (p. 137)Stripline transmission line. (a) Geometry. (b) Electric and magnetic field lines.

14

Stripline transmission line. (a) Geometry. (b) Electric and magnetic field lines.

Stripline (Analysis Formula)St p e ( a ys s o u a)

441.030

0

bWbZ

er

0 35for0

of width effective the:

WWWe

0.35for 3.0

0.35for 02

bW

bW

bb

Wb

We

0 isconductor of thickness

t

bb

0forFormula t

2768841ln30 2tbtbtbZ0for Formula t

27.61ln0 wwwZ

r

15

Stripline (Synthesis Formula)St p e (Sy t es s o u a)

120for 6.085.0120for

0

0

ZεxZεx

bW

r

r

tan3.27tan

:nAttenuatio Loss Dielectric

k r

441.030 where0

0

Zεx

r

r

2 0d

107.2

:nAttenuatioConductor

03

0

ZR

r

mode)order high lewest theis (TE modeorder higher for Cutoff

120for16.0

120for 30

107.20

0

ZεBR

ZεAtb

ZR

s

rrs

c

GHz)(in 4//

115bwb

fr

c

120for 00

ZεBbZ r

tb

btb

bWA ,2ln121with

cmin and bw

tW

Wt

tWbB

ttbtb

4ln

21414.05.0

70501

16

tWtW 27.05.0

Stripline (Graphic Analysis)St p e (G ap c a ys s)

17

Microtrip Linec ot p e

If:supported mode TEM No

d mode TEM-quasi

cv

eff0

eff

p

k

v

01

pCvC

LZ

Figure 3.25 (p. 143) Microstrip transmission line. (a) Geometry. (b) Electric and magnetic field lines.

eff

0g

p

2

eff

eff

vc

CC

18

air

pvC

Microtrip Linec ot p e

• Advantages1. Low cost, small size2. Absence of critical matching & cutoff freq.3. Easy integrated with active device4 Good repeatability and reproducibility mass production4. Good repeatability and reproducibility, mass production5. Compatibility with monolithic circuits

• Disadvantages ( cf waveguide, coaxial circuits)1. Higher loss2 Lower power handling capability2. Lower power handling capability3. Greater temperature instability

• The synthesis & analysis formula are well documented• Many discontinuities have been characterized• Commercial programs are available for optimization & prediction

19

Commercial programs are available for optimization & prediction

Microtrip Linec ot p e

r rr r

r eff 121

eff r2

rr eff121

ff 2

: factor filling q

eff

r

11111eff

q

qqq rr

121

r12

q

dW /

2

20

Microtrip Linec ot p e

21

Microtrip Line (Analysis Formula)c ot p e ( a ys s o u a)

:1For

2

dW

104.01211

21

21

2

eff dW

Wdrr

48ln60

eff0 d

WWdZ

111

:1For dW

1201211

21

21 eff Wd

rr

444.1ln667.0393.1

120

eff

0

dW

dW

Z

22

dd

Microtrip Line (Synthesis Formula)c ot p e (Sy t es s o u a)

A

A

dW

ee

W2 2for

28

r WBBB

de

dW

2for61.03901ln112ln12

2

rr

rr

ZA

dBBB

0 11.023011where

2for 39.01ln2

12ln1

rr

rr

B

A

0

377

23.01260

where

rZB

02

:nAttenuatio LossDielectric :factorFilling :nAttenuatioConductor

Np/m 12

tan1

eff

eff0

r

rd

k

1

1g

eff

eff

r

r

Np/m

0WZRs

c

23

eff r e 0

Microtrip Line p(Further Considerations)

• Finite Conductor Thickness Effect of Dispersion

2

0

Wt

Wfd

Ff r

2

eff5.1eff

eff

14

041

0

rW d

f

dW

cfd

F r 1ln215.014

dW

tW

dt

dW

W 21 4ln1

25.1

f

fZfZeff

eff

eff

eff00

01010

dW

td

dt

dWd

212ln1

25.1

dWdtr /

6.41

effeff

24

Other types of LinesOt e types o es

Figure 3.33 (p. 156)Geometry of a printed slotline.

Figure 3.35 (p. 157)Covered microstrip line.

1 Easy fabrication1. Easy fabrication2. quasi-TEM operation3. radiation problem gap width ~/2

Figure 3.34 (p. 156)Coplanar waveguide geometry.

3. radiation problem gap width /24. monolithic application5. surface wave mode coupling

25

p g