1

Prof. David R. JacksonDept. of ECE

Notes 10

ECE 5317-6351 Microwave Engineering

Fall 2011

Waveguides Part 7:Planar Transmission Lines

2

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

3

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.)

4

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.)

5

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.)

6

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

7

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.)

8

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)

9

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:

10

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

11

Microstrip (cont.)

12

For the equivalent TEM problem:

0

p effr

effr

cv

k

r0

effr

Equivalent TEM problem

Actual problem

Microstrip (cont.)

d

d

W

W

13

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)

14

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:

15

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.)

16

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.)

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

17

Microstrip (cont.)

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

18

Microstrip (cont.)

where

( / 1)W d

Note:

:

effr r

f

f

As

19

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

d

W

er

t

20

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

21

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

22

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/

23

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

24

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.