ece 497 js lecture -07 planar transmission linesjsa.ece.illinois.edu/ece497js/lect_09.pdf · title:...

1Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004

ECE 497 JS Lecture -07Planar Transmission Lines

Spring 2004

Jose E. Schutt-AineElectrical & Computer Engineering

University of [email protected]


ε

Microstrip

2119.9 ln 4 16 22( 1)o

r

h hZw wε

= + + +

2

2

119.9 ln(4) ln( /16) 12 22

1 + ln ln 0.942 2 2

ro

rr

r

r

w eZh

e wh

π π επ π εε

ε ππε

−= + +

+ + +

w/h < 3.3

w/h > 3.3


1 2 3

31 1 211 12 13

VI V VC C Cz t t t

∂∂ ∂ ∂∂ ∂ ∂ ∂

− = + +

32 1 221 22 23

VI V VC C Cz t t t

∂∂ ∂ ∂∂ ∂ ∂ ∂

− = + +

3 31 231 32 33

I VV VC C Cz t t t

∂ ∂∂ ∂∂ ∂ ∂ ∂

− = + +

31 1 211 12 13

IV I IL L Lz t t t

∂∂ ∂ ∂∂ ∂ ∂ ∂

− = + +

32 1 221 22 23

IV I IL L Lz t t t

∂∂ ∂ ∂∂ ∂ ∂ ∂

− = + +

3 31 231 32 33

V II IL L Lz t t t

∂ ∂∂ ∂∂ ∂ ∂ ∂

− = + +

Three-Line Microstrip


11 13( )V IL Lz tα α∂ ∂

∂ ∂− = −

11 13( )I VC Cz tα α∂ ∂

∂ ∂− = −

Subtract (1c) from (1a) and (2c) from (2a), we get

This defines the Alpha mode with:

1 3V V Vα = − 1 3I I Iα = −and

The wave impedance of that mode is:

11 13

11 13

L LZC Cα

−=

−

and the velocity is( )( )11 13 11 13

1uL L C C

α =− −

Three-Line – Alpha Mode


In order to determine the next mode, assume that

1 2 3V V V Vβ β= + +

1 2 3I I I Iβ β= + +

( ) ( ) ( ) 31 211 21 31 12 22 32 13 23 33

V II IL L L L L L L L Lz t t tβ∂ ∂∂ ∂β β β

∂ ∂ ∂ ∂− = + + + + + + + +

( ) ( ) ( ) 31 211 21 31 12 22 32 13 23 33

I VV VC C C C C C C C Cz t t tβ∂ ∂∂ ∂β β β

∂ ∂ ∂ ∂− = + + + + + + + +

By reciprocity L32 = L23, L21 = L12, L13 = L31

By symmetry, L12 = L23

Also by approximation, L22 ≈ L11, L11+L13 ≈ L11

Three-Line – Modal Decomposition


( ) ( )31 211 12 13 12 112

V II IL L L L Lz t t tβ∂ ∂∂ ∂β β

∂ ∂ ∂ ∂ − = + + + + +

In order to balance the right-hand side into Iβ, we need to have

( ) ( ) ( )12 11 2 11 12 13 2 11 12 22L L I L L L I L L Iβ β β β β+ = + + ≈ +

212 122L Lβ=

or 2β = ±

Therefore the other two modes are defined as

The Beta mode with

Three-Line – Modal Decomposition


The Beta mode with

1 2 32V V V Vβ = + +

1 2 32I I I Iβ = + +

The characteristic impedance of the Beta mode is:

11 12 13

11 12 13

22

L L LZC C Cβ

+ +=

+ +

and propagation velocity of the Beta mode is

( )( )11 12 13 11 12 13

1

2 2u

L L L C C Cβ =

+ + + +

Three-Line – Beta Mode


The Delta mode is defined such that

1 2 32V V V Vδ = − +

1 2 32I I I Iδ = − +

The characteristic impedance of the Delta mode is

11 12 13

11 12 13

22

L L LZC C Cδ

− +=

− +

The propagation velocity of the Delta mode is:

( )( )11 12 13 11 12 13

1

2 2u

L L L C C Cδ =

− + − +

Three-Line – Delta Mode


1 0 1

1 2 1

1 2 1

E

−

= −

1 2 3

Alpha modeBeta mode*

Delta mode*

Symmetric 3-Line Microstrip

In summary: we have 3 modes for the 3-line system

*neglecting coupling between nonadjacent lines


1 2 3

εr = 4.3

113 17 5( / ) 16 53 16

5 17 113C pF m

=

346 162 67( / ) 152 683 152

67 162 346L nH m

=

0.45 0.12 0.450.5 0 0.50.45 0.87 0.45

E = − − −

0.44 0.49 0.440.5 0 0.50.10 0.88 0.10

H = − − −

Coplanar Waveguide


73 0 0( ) 0 48 0

0 0 94mZ

Ω =

56 23 8( ) 22 119 22

8 23 56cZ

Ω =

0.15 0 0( / ) 0 0.17 0

0 0 0.18pv m ns

=

1 2 3

εr = 4.3

Coplanar Waveguide


WS' S'WS

εrh

2Sk

S W=

+

( ) : Complete Elliptic Integral of the first kindK k

'( ) ( ')K k K k=

2 1/ 2' (1 )k k= −

30 '( ) (ohm)( )1

2

ocpr

K kZK k

πε

=+

1/ 22

1cpr

v cε

= +

Coplanar Waveguide


S WW

εrh

120 '( ) (ohm)( )1

2

ocsr

K kZK k

πε

=+

Coplanar Strips


Characteristic Microstrip Coplanar Wguide Coplanar strips

eeff* ~6.5 ~5 ~5

Power handling High Medium Medium

Radiation loss Low Medium Medium

Unloaded Q High Medium Low or High

Dispersion Small Medium Medium

Mounting (shunt) Hard Easy Easy

Mounting (series) Easy Easy Easy

* Assuming εr=10 and h=0.025 inch

Qualitative Comparison


3-Line Matching Network

• Extend matching network synthesis to multiconductor transmission line (MTL) systems, specifically coupled microstrip

• Characterize MTL systems by their “normal mode parameters”– Mode configurations– Propagation constants– Characteristic impedance matrices


Longitudinal Immittance Matrix Functions (LIMFs)

• Given terminations, the immittance matrices are expressed as “input”longitudinal functions looking toward the load

m,c m,cin,out

m,c m,cin,out in,out

, ,

,

ΓS

Y Z


Calibration Methods1st order calibration: 6 distinct TRL calibrations were required

to deembed the fan-in and fan-out sections 2nd order calibration: 1 multimode TRL calibration required to

deembed all fan-ins and fan-outs

Multiconductor transmission line matching network device under test


Bias Networks and Multiline/Multimode TRL

• Self-biasing for DC power done using air bridges

• Regulator circuit may be built on board with surface mount/chip components

• Calibration must include all modes and allow for the 6-port discontinuity S-parameter measurement

Proposed calibration fixture for transistor amplifier device discontinuity with self-biasing network


3-line Transistor Amplifier

The general amplifier structure with generic matching networks

Note that a transistor seating hole may be present for convenience, but is not necessary

Photograph of a three-line transistor amplifier autobiased w/o matching networks


Transistor Amplifier Matching

S-parameter comparison between unmatched and matched three-line amplifier. Dotted line - unmatched; dashed line -matched. Design frequency: 3.1 GHz.

Matching• 2 - 0.8 pF chip cap.• 2 - 0.4 pF chip cap.

Gains• 3.38 dB @ 3.1 GHz

m=5.14 / um= 1.76• 6.22 dB @ 3.22 GHz

m=6.54 / um= 0.32


2p

h

w

α

dielectric

ground

signal strip

V Transmission Line


0

50

100

150

200

250

0 0.1 0.2 0.3 0.4 0.5 0.6w/h

CHARACTERISTIC IMPEDANCE

30º37.5º45º52.5º

60ºMicrostrip

0.7 0.8 0.9 1

Zo (o

hms)

Calculated values of the characteristic impedance for a single-line v-strip structure as a function of width-to-height ratio w/h. The relative dielectric constant is εr = 2.55.

V-Line Characteristic Impedance


1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

0 0.1 0.2 0.3 0.4 0.5 0.6

w/h

EFFECTIVE PERMITTIVITY

30º

37.5º

45º

52.5º

60º

Microstrip

0.7 0.8 0.9 1

Effe

ctiv

e R

elat

ive

Die

lect

ric C

onst

ant

Calculated values of the effective relative dielectric constant for a single-line v-strip structure as a function of width-to-height ratio w/h. The relative dielectric constant is εr = 2.55

V-Line – Effective Permittivity


h

y

x

Region 2

Region 3

Region 4

Region 6

Region 1

Region 5

2pw

dielectricground surface

signal strip

s

Three-Line – V Transmission Line


74.00 -0.97 -0.23C (pF/m) = -0.97 74.07 -0.97

-0.23 -0.97 74.00

425.84 20.35 7.00L (nH/m) = 20.36 422.85 20.36

7.00 20.35 425.84

52.49 -5.90 -0.57C (pF/m) = -5.90 53.27 -5.90

-0.57 -5.90 52.49

609.74 113.46 41.79L (nH/m) = 113.54 607.67 113.54

41.79 113.46 609.74

Microstrip V-line

Comparison of the inductance and capacitance matricesbetween a three-line v-line and microstrip structures. The parameters are p/h = 0.8 mils, w/h = 0.6 and εr = 4.0.

h

y

x

Region 2

Region 3

Region 4

Region 6

Region 1

Region 5

2pw

dielectricground surface

signal strip

s1 2 3

V-Line and Microstrip


0

50

100

150

200

250

300

350

0 0.2 0.4 0.6 0.8 1 1.2s/h

Mutual Inductance

V-linemicrostrip

Lm

(nH

/m)

0

5

10

15

20

25

30

35

40

0 0.2 0.4 0.6 0.8 1 1.2s/h

Mutual Capacitance

V-linemicrostrip

Cm

(pF/

m)

Plot of mutual inductance (top) and mutual capacitance (bottom) versus spacing-to-height ratiofor v-line and microstrip configurations. The parameters are w/h = 0.24, εr = 4.0.

V-Line: Coupling Coefficients


0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1 1.2s/h

Coupling Coefficient

V-linemicrostrip

Kv

Plot of the coupling coefficient versus spacing-to-height ratio for v-line and microstrip configurations. The parameters are w/h = 0.24, εr = 4.0.

V-Line vs Microstrip: Coupling Coefficients


0.5

0.6

0.7

0.8

0.9

1

1 3 5 7 9 11 13 15 17

microstrip

V-60

V-30

Frequency (GHz)

Linea

r Atte

nua ti

on

Propagation Function

2p

h

w

α

dielectric

ground

signal strip

Advantages of V Line* Higher bandwidth

* Lower crosstalk

* Better transition

ground reference

ground reference

dielectric

substrate

signal strip

Advantages of V-Line


-8

-7

-6

-5

-4

-3

-2

-1

0

0 5 10 15 20 25

Insertion Loss

VlineMicrostrip20

*log

10*|

S21|

Frequency (GHz)

V-Line vs Microstrip: Insertion Loss

ece 497 js lecture -07 planar transmission linesjsa.ece.illinois.edu/ece497js/lect_09.pdf · title:...

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