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Crosstalk minimization using multiple dielectric substrates

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Authors Valentine, Wendy Leesa, 1964-

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Crosstalk minimization using multiple dielectric substrates

Valentine, Wendy Leesa, M.S.

The University of Arizona, 1993

U M I 300 N. Zeeb Rd. Ann Arbor, MI 48106

CROSSTALK MINIMIZATION

USING MULTIPLE DIELECTRIC SUBSTRATES

by

Wendy Leesa Valentine

A Thesis Submitted to the Faculty of the

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

In Partial Fulfillment of the Requirements For the Degree of

MASTER OF SCIENCE WITH A MAJOR IN ELECTRICAL ENGINEERING

In the Graduate College

THE UNIVERSITY OF ARIZONA

19 9 3

2

STATEMENT BY AUTHOR

This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department of the Dean of the Graduate College when in his or her judgement the proposed use of the matrial is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED:

APPROVAL BY THESIS DIRECTOR

This thesis has been approved on the date shown below:

. ^~-v V'? hz Andre^^^Xangellaris Date

Associate Professor of Electrical and Computer Engineering

3

ACKNOWLEDGEMENTS

First and foremost, I would like to thank my advisor, Dr. Andreas

Cangellaris, for his longstanding patience and cooperation in getting

me through this. I would also like to thank Dr. Palusinski and Dr.

Rosenblit for agreeing to be on my committee. For the lessons they

taught me in class and the useful conversations outside of class, I'd

like to thank Dr. Dudley, Dr. J. R. Wait, Dr. Dvorak, and Dr. Gaskill.

I, like every other ECE graduate student, am indebted to Sandi Sledge

for diligently guiding me through the occasionally bewildering maze

of paperwork. I am likewise grateful to the National Consortium for

Graduate Degrees for Minorities in Engineering (GEM) and the

Semiconductor Research Corporation (SRC) for their financial support.

I would like to thank Dean Vern Johnson, Dean Morris Farr, Dean

Glenn Smith, and Dean Adela Allen for their concern and attention.

I'd like to offer a special thanks to David Jarrett who accepted and

encouraged me, even when he thought my brain had gone on

vacation arid to Joseph Wozniak, whose loving concern comforted me

during some of my discouraging moments. To Rob Lee and Diana

Wright who badgered me, counseled me, encouraged me, and skied

with me, thanks. Your efforts and concerns were noticed and

appreciated. I'd also like to thank the unofficial ECE Parchesi Club-

Monica C de Baca, Mike Chan, Mike Pasik, and Chris Spring—for

occasionally letting me sit in on their games. Gene Climer, Sam

Howells, Karen Kolczak, Mary Sepich, Don Wallace, Joy Watanabe, the

Williams Family—you all did much (probably more than you realize)

to enrich my U of A experience.

Finally, I owe an incredible debt to my family. They've tolerated my

moods and quirks since the beginning. Without their love and

support, I would not be who or where I am today. Thankyou.

4

TABLE OF CONTENTS

Page

LIST OF ILLUSTRATIONS 5

ABSTRACT 8

1. INTRODUCTION 9

2. MICROSTRIP LINES AND CROSSTALK 1 0

2.1 Fields 10

2.2 Crosstalk 17

3. RESULTS AND DISCUSSION 2 7

3.1 Software 2 7

3.2 Geometries 3 1

3.3 Family of curves and SPICE simulations 3 3

4. CONCLUSIONS .....6 2

5. REFERENCES 6 5

5

LIST OF ILLUSTRATIONS

Figure Page 2 -1 F ie ld l i nes fo r a s ing le conduc to r i n a homogeneous

medium located over a ground plane 1 0

2 -2 F ie ld l i nes fo r a s ing le mic ros t r ip t r ansmiss ion l i ne 1 1

2 -3 F ie ld l i nes fo r t he even and odd modes fo r a pa i r o f

microstrip transmission lines 1 6

2 -4 In i t i a l impressed vo l t ages on the ac t ive and qu ie t l i nes 19

2 -5 Ef fec t o f even and odd modes hav ing d i f f e ren t ve loc i t i e s 2 0

2 -6 Mic ros t r ip s t ruc tu re 25 2 -7 50MHz s igna l and i t s de r iva t ive , fo=50MHz, t r= t f=1 .0ns , 2 6

3 -1 SPICE mode l fo r t r ansmiss ion l i ne s imula t ions 2 8

3 -2 SPICE mode l fo r n coup led t r ansmiss ion l i nes , [3 ] . . . . . 2 9

3 -3 De ta i l ed mode l fo r t he i t h l i ne [3 ] 3 1

3 -4 S ing le d i e l ec t r i c subs t r a t e geomet ry 3 2

3 -5 Doub le d i e l ec t r i c subs t r a t e geomet ry 3 2

3 -6 Tr ip l e d i e l ec t r i c subs t r a t e geomet ry wi th bu r i ed

conductors 3 3

3 -7 Cra t v s . £ r fo r a s ing le d i e l ec t r i c subs t r a t e w i th conduc to r s

located h=26.0 mils above the ground plane 3 7

3 -8 SPICE p lo t fo r 2 mic ros t r ip l i nes wi th a s ing le d i e l ec t r i c

substrate, £r=3 3 8

3 -9 SPICE p lo t fo r 2 mic ros t r ip l i nes wi th a s ing le d i e l ec t r i c

substrate. Er=10 3 9 3 - 1 0 C r a t v s . E n f o r a d o u b l e d i e l e c t r i c s u b s t r a t e . £ ^ = 1 0 ,

conductors are located h=26.0 mils above the ground

plane 40 3 -11 Crat vs. £rj for a double dielectric substrate. Er2=9 t


plane 4 1

6

LIST OF ILLUSTRATIONS - Continued

3-12 Crat vs. £ri for a double dielectric substrate. £r2=8,


plane 42 3 -13 SPICE p lo t fo r 2 mic ros t r ip l i nes wi th a doub le d i e l ec t r i c

substrate. £r i=3 , er2=10» hl=10.4 mils 43

3-14 SPICE p lo t fo r 2 mic ros t r ip l i nes wi th a doub le d i e l ec t r i c substrate. £ri=3, £r2=10, hl=13.0 mils 44

3 -15 SPICE p lo t fo r 2 mic ros t r ip l i nes wi th a doub le d i e l ec t r i c substrate. £r i=3 , £r2=8, hl=15.6 mils 45

3 -16 SPICE p lo t fo r 2 microstrip lines with a double dielectric substrate. £ri=4, £r2=8, hl=23.4 mils 4 6

3 -17 SPICE p lo t fo r 2 mic ros t r ip l i nes w i th a doub le d i e l ec t r i c substrate. £r i=4, Er2=10, hl=20.8 mils 4 7

3 -18 SPICE p lo t fo r 2 mic ros t r ip l i nes wi th a doub le d i e l ec t r i c substrate. £r i=3, Er2=9> hl=15.6 mils 4 8

3 -19 SPICE p lo t fo r 2 mic ros t r ip l i nes wi th a doub le d i e l ec t r i c substrate. £ri=3, £r2=10» hl=15.6 mils 4 9

3 -20 SPICE p lo t fo r 2 mic ros t r ip l i nes wi th a doub le d i e l ec t r i c substrate. £ri=3, £r2=10» hl=18.2 mils 5 0

3 -21 SPICE p lo t fo r 2 mic ros t r ip l i nes wi th a doub le d i e l ec t r i c substrate. £ri=3, £r2=10, hl=13.0 mils. Active line is

terminated into approximately 2.5Zo. (Figure 3-14 shows

that this case had backward crosstalk when the

terminations were approximately matched.) 5 1

3 -22 SPICE p lo t fo r 2 mic ros t r ip l i nes w i th a doub le d i e l ec t r i c substrate. £ri=3, £r2=10, hl=13.0 mils. Quiet line is

terminated into approximately 2.5Zo on both ends.

(Figure 3-14 shows that this case had backward crosstalk

when the terminations were approximately matched.) 5 2

7

LIST OF ILLUSTRATIONS - Continued

3-23 SPICE p lo t fo r 2 mic ros t r ip l i nes wi th a doub le d i e l ec t r i c substrate. £ri=4, er2=10, hl=20.8 mils. Active line is

terminated into approximately 4Zo. (Figure 3-17 shows

that this case had no backward crosstalk when the

terminations were approximately matched.) 5 3

3 -24 SPICE p lo t fo r 2 mic ros t r ip l i nes wi th a doub le d i e l ec t r i c substrate. £ri=4, er2=10, hl=20.8 mils. Quiet line is

terminated into approximately 4Zo on both ends. (Figure

3-17 shows that this case had no backward crosstalk

when the terminations were approximately matched.) 5 4

3 -25 Tr ip ly coup led t r ansmiss ion l i nes . S igna l i s i npu t t o the

center line 5 5 3 -26 Tr ip ly coup led t r ansmiss ion l i nes . S igna l i s i npu t t o the

end line 6 0

3 -27 SPICE p lo t fo r 3 mic ros t r ip l i nes w i th doub le d i e l ec t r i c substrate. Input and output signals on center line. En—3, er2=10, hl=13.0mils 5 6

3 -28 SPICE p lo t fo r 3 mic ros t r ip l i nes w i th doub le d i e l ec t r i c substrate. Input and output signals on center line. £ri=4,

£12=10, hl=20.8 mils 5 7

3 -29 SPICE p lo t fo r 3 mic ros t r ip l i nes wi th doub le d i e l ec t r i c substrate. Input and output signals on outside line. £r i = 3 ,

£i2=10, hl=13.0 mils 5 8

3 -30 SPICE p lo t fo r 3 mic ros t r ip l i nes wi th doub le d i e l ec t r i c substrate. Input and output signals on outside line. £ri=4,

£,2=10, hl=20.8 mils 5 9

3 -31 Cra t v s . £ r fo r a t r ip l e d i e l ec t r i c subs t r a t e w i th conduc to r s

located h=26.0 mils above the ground plane 6 1

8

ABSTRACT

A method to predict appropriate dielectric constants and thicknesses

for double dielectric substrate microstrip structures to minimize

forward crosstalk is presented. Ratios of the elements in the

capacitance matrix are compared to those in the inductance matrix to

determine if forward crosstalk will be minimized. Curves showing

Crat, where Crat is the ratio of the Cn element to the C12 element, as a function of the relative permitivity, er, and SPICE simulations are

presented for particular geometries. The method accurately predicts

combinations of dielectrics that will produce a structure exhibiting

greatly reduced crosstalk.

CHAPTER 1

9

INTRODUCTION

As the push for ever faster speeds and smaller devices continues, the

challenge of maintaining signal integrity becomes increasingly

difficult. The issue of crosstalk becomes more important as the circuit densities increase and the noise margins tighten.

Gilb and Balanis [1] showed that forward crosstalk could be

eliminated by using multiple layers of dielectric in the substrate for

a pair of microstrip lines. Forward crosstalk results when the even

and odd modes travel down the microstrip lines at different

velocities. The presence of additional layers in the substrate changes

the velocities of the even and odd modes relative to one another. By

comparing the ratio of the C matrix elements to those of the L matrix

for a given conductor geometry, we can determine which dielectric

geometries will equalize the even and odd mode velocities.

The fields of microstrip lines are briefly discussed in Chapter 2, and a

description of crosstalk in terms of even and odd modes is presented.

Results are presented for various dielectric geometries in Chapter 3.

After a discussion of the software used to produce the data, SPICE

curves depicting the forward and backward crosstalk are presented

for single, double and triple dielectric substrate geometries. Finally,

a brief discussion of the manufacturability of these structures,

conclusions, and recommendations for future work are given in

Chapter 4.

1 0

CHAPTER 2

MICROSTRIP LINES AND CROSSTALK

2.1 Fields

The electric and magnetic fields surrounding a single conductor

located above an infinite ground plane in a homogeneous medium

are shown in Figure 2-1. Assuming the current to be heading out of

the paper, the electric field lines travel from the conductor to the

ground plane. The fringing fields at the edges of the conductor

extend outward beyond the boundaries of the conductor. These

fringing fields will interact and couple with other conductors if they

are nearby. The magnetic field lines for the structure surround the

single conductor. These, too, extend beyond the boundaries of the

conductor and will interact with other nearby conductors.

Figure 2-1 Field lines for a single conductor in a homogeneous

medium located over a ground plane.

When we add a substrate layer between the conductor and the

ground plane to form a microstrip configuration, Figure 2-2, we see a

change in the electric field lines. Along the dielectric-air interface,

1 1

we see an additional bowing out of the fringing fields. This effect is a

result of the electric fields reconfiguring themselves to obey

Maxwell's equations inside each of the regions while maintaining

continuity conditions at the interface. The greater the dielectric

mismatch at the interface, the more exaggerated the effect.

When we add a second microstrip line to the structure, the fields of

the two conductors will interact, as stated above. We can analyze the

fields for any pair of microstrip lines using coupled-mode theory to

determine propagating modes. Consider an arbitrary pair of

microstrip lines. We assume that the waves traveling on the lines

are transverse electromagnetic (TEM) waves. The generalized

telegraphist equations [4] describe the voltages and currents on the

lines,

The quantities v and i are vectors denoting the voltages and

currents, respectively, on the microstrip lines; L and C are matrices

denoting the per-unit-length (PUL) inductances and capacitances,

respectively, for the pair of lines,

Figure 2-2 Field lines for a single microstrip transmission line.

arvCM)! ro Li a_rv(z , t ) i 3zLi(z , t )J " L C 0 J at L i (z , t ) J

( i )

1 2

i _ l " L l l L l 2 l r -_rCllCl2l Ll2I L22J LC2I C22J

Assuming v(z,t) = V(z)ejwt and i(z,t) = I(z)ejwt, expanding (1)

yields the following set of equations,

dVi ~^~ = - jcoL 11I1 - JC0L12I2 (2)

dV2 dz = - jcoL2iIi - JC0L22I2 (3)

d l i • ^ -= - j a )CnVi+ jcoCi 2V2 (4)

^=-j(0C2lVl+j0)C22V2 (5)

These equations explicitly show the coupling effects between the two

conductors. The voltage on a single line is a function of the currents

on both lines. Likewise, the current on a single line is a function of

the voltages on both. It is the off diagonal elements of the L and C matrices, Ljj, Qj (i * j), that effect the coupling between the

conductors. These elements describe the mutual inductance and the

capacitance between the two conductors. For the L matrix, the off

diagonal elements are positive and equal to one another, Ly = Lji (i*j). For the C matrix, they are negative and equal, Qj < 0 and Qj =

Cji (i*j). Noting this, let

Zi = jcoLn (6)

Z2=jcoL22 (7)

Zm=jCoLi2=jcoL2i (8)

Yi . j f f lCn (9 )

Y2 =jcoC22 (10)

1 3

Ym =-jcoCi2 =-jcoC2i (11)

The Zj (i=l,2) denote the series impedance of each line, while the Yj

(i=l,2) denote the admittance of each line. Zm and Ym represent the

mutual impedance and admittance, respectively, between the two

lines. Rewriting equations (2) - (5) using using equations (6) - (10)

y i e lds

dVi = - Z i l i - Zml2 (12 )

dV2 " ^ -Zml i -Z 2 I 2 (13 )

^ = - YiV, - Y m V 2 (14 )

^ •= -Y m V! -Y 2 V 2 (15 )

By eliminating Ii and I2, we can reduce the four coupled equations,

(12) - (15) to a pair of coupled equations that relate the voltages on

the two microstrip lines. First, take the derivative with respect to z

of (12) and (13),

A')\T 1 AT t AJ^ (16)

(17 )

and then substitute (14) and (15) into (16) and (17). to obtain the

desired pair of coupled equations,

d2Vi - ^ •=a iVi+b iV 2 (18 )

d2V 1 dz2 ~

7 dli *dz

7 dl2

" d z

d2V2

dz2 ~~ v dl2

" Z 2 dz ^"dz

d2V2 d z 2 = a2V2 + b2Vi

14

(19)

where

a i = (Z iY i + Z m Y m ) (20 )

a2 = (Z2Y2 + ZmYm) (21)

b i = (Z iY m + Z m Y 2 ) (22 )

b2 = (Z2Ym + ZmY i) (23)

If we combine (18) and (19) (e.g., substitute Vi from (19) into (18)),

we arrive at the eigenvalue equation for the propagating modes,

(d4 d2 (dz? " ^ a 2 + a i ^dz2 + a l & 2 - b ib2 j V(z ) = 0 (24)

Assuming the voltage V(z) has the form Voe_Yz and substituting this

into (24), we arrive at the characteristic equation

Y 4 - ( a i + a 2 )Y 2 + a ia? , - b ib2 = 0 (25 )

The four roots of this equation are

\2,3,4 = ±yc'yn = ±y ai \ a2 1 2 V (al'a2)2 + 4bib2 (26)

where

Yc2 - ai 2 ^ +2 V(ai_a2)2 + 4blb2 (27)

Yji2 = ai 2 a2 " 2 V(ai"a2)2 + 4bib2 (28)

1 5

Yc and Yn are the propagation constants for the two propagating

modes, the c and k modes, of an arbitrary pair of coupled lines. The

positive and negative roots of each propagation constant correspond

to positive and negative traveling waves in each mode. If the

microstrip lines are identical, the structure symmetric and the generalized coupled modes, c and tc, will simplify to an even and an

odd mode.

The identical lines of a symmetric structure will have the same

impedances and admittances, Ln=L22 and Cn=C22- Hence, from (6) -

(11) and (20) - (23) above, ai = a2 and bi = b2. Applying this simplification to Yc and yn yields the propagation constants for the

even and odd modes,

Yc=Y e =±V0 + b ) =W( Y + Y m ) (Z + Z m ) (29 )

% = Yo = ±V( a " b ) =W( Y " Y m)( z " Z m ) (30 )

Figure 2-3 shows the field lines for the even and odd modes. For the

even mode, the current on each conductor is flowing out of the page

and the field lines for each conductor considered separately are the

same. The electric field lines begin on the conductors and end on the

ground plane, and the magnetic field lines surround the conductors

in a counterclockwise direction. Because the electric field lines for

each conductor are emanating from the conductor, they cancel each

other at the center of the structure, along the line of symmetry. This

mode exhibits no electrical coupling between the lines. Since the

magnetic fields for each conductor are in a counterclockwise

direction, they destructively interfere between the conductors, but

constructively interfere above and below them. Thus, each magnetic

field line encircles both conductors and the two microstrip lines are

magnetically coupled. Essentially, the even mode behaves as though

a magnetic wall lay along the line of symmetry.

1 6

For the odd mode, the current on one conductor (left) is coming out

of the page while the current on the other (right) is going into the

page. The field lines are opposite for the two conductors. The

"\ /

I " "•

T

EVEN MODE

H

4% J"" WW WW*

ODD MODE

Figure 2-3 Field lines for the even and odd modes for a pair of

microstrip transmission lines.

1 7

conductor on the left has the same field properties as those described

above—electric field lines emanating outward from the conductor

and magnetic field lines encircling the conductor in a

counterclockwise direction. The fields for the conductor on the right

have the opposite properties. The electric field lines are directed

into the conductor and the magnetic field lines encircle it in a

clockwise direction. As a result, the magnetic fields repel each other

above and below the conductors, forcing the field lines away from

each other between the conductors. There is no magnetic coupling

present here. The electric fields, on the other hand, attract each

other. Fringing field lines emanating from the left conductor

combine with those directed toward the right conductor. The two

microstrip lines are electrically coupled. The odd mode behaves as

though an electric wall lay along the line of symmetry.

2.2 Crosstalk

The even/odd mode fields described above illustrate the coupling

that can occur between two microstrip lines. Because of this effect, a

signal present on one of the lines may induce a signal on the other

line. This is crosstalk. In other words, crosstalk is the noise voltage

or current that appears on a transmission line due to a voltage or

current present on a neighboring transmission line.

We will define an active line as one on which a signal has been

launched. A quiet line is defined as one that has not had a signal

launched on it. Crosstalk noise from an active transmission line will

appear at all points along a neighboring quiet line. However, we are

only interested in the noise that appears at the ends of the line,

either the near end or far end, because these are the signals that are

transmitted to other parts of the system. The near end of a line is

the end from which signals are launched. The opposite end is the far

1 8

end. This means that the active line determines which end is

considered near and which is considered far, see Figure 2-4. We will

call the signals appearing at the near end of the quiet line backward crosstalk and those appearing at the far end of the quiet line

forward crosstalk.

Forward crosstalk is important because it occurs at the end of the

line that is connected to the next stage of the circuit. For instance,

consider the case where two adjacent microstrip lines are the digital

outputs of one circuit stage to the inputs of the next. Further,

assume that one of the lines is active while the other is quiet. If the

forward crosstalk is large enough, it is possible for the quiet line to

deliver a false high or low to the following input stage. Reducing the

forward crosstalk will lessen the chances of delivering a false signal.

Consider the modal fields shown in Figure 2-3. The field structures

for the two modes are very different. Because of this, we would

expect the modes to have different characteristics. This is indeed the

case. For this inhomogeneous structure, we find that the proportion

of E and H fields located in the air compared to the proportion

located in the substrate is different for the two modes. As a result,

the apparent inductance and capacitance of each mode are different,

and hence their characteristic impedances and velocities are

different. Expressed in terms of the modal inductances and

capacitances, the characteristic impedances and velocities are written

as follows,

(31)

(32)

1 9

1 Ve Vl^CT

(33)

1 Vo = Vl^

(34)

where Zo is characteristic impedance, v is velocity, L is inductance, C

is capacitance, and the subscripts e and o refer to the even and odd modes, respectively.

The even and odd modes are really just mathematical constructs to

describe the behavior of a signal traveling down a pair of coupled

transmission lines. Suppose we choose an even and an odd mode to

describe a signal as it appears at the beginning of a pair of lines. If

these modes behave differently as they travel down the lines, it

follows that at some distance down the lines the signal they describe

will be a distorted version of the original. Figures 2-4 and 2-5

illustrate the case of differing velocities, where the even mode is

traveling faster than the odd mode.

1V

active

near end far end t = 0

quiet

Figure 2-4 Initial impressed voltages on the active and quiet lines.

Figure 2-4 shows the initial voltages on a pair of coupled microstrip

lines. A pulse of magnitude one has been launched on the active line.

No signal has been impressed on the quiet line. Figure 2-5a shows

2 0

actjve iwwwwfflaawwwww

Even mode

Odd mode

Resultant pulse

quiet

active

quiet

active

quiet

active

quiet

(a) t-0

I rzi 2

(b) t = t1

MWMMMjl

(c) t = t2

(d) t = t3

inn

JUL

Figure 2-5 Effect of even and odd modes having different velocities.

2 1

how we can describe this scenario in terms of even and odd modes.

The even mode has a positive pulse on each line that is equal to half

the magnitude of the "real" pulse in Figure 2-4. The odd mode has a

positive pulse on the active line and a negative pulse on the quiet

line. Again, the magnitude of the pulses is equal to half that of the

"real" pulse. Initially, the modes lay on top of one another. Adding the voltages present on each line, we find that the active line has IV

and the quiet line has OV, corresponding to the pulses launched on

the lines.

Figure 2-5b shows the voltages on the lines after the pulses have

traveled a short distance. The modes no longer lay exactly on top of

each other. Assuming that the even mode has a higher velocity, we

see that it is slightly ahead of the odd mode. The even and odd

pulses on the quiet line do not exactly cancel each other any longer,

so we have a pair of noise pulses appearing. Also, the pulse on the

active line has spread out. Figures 2-5c to 2-5d show the pulse as it

travels further down the microstrip lines. If the lines are long

enough, the even and odd modes will completely separate into two

positive pulses on the active line and a positive and negative pulse

on the quiet line.

Recall, that velocity is defined as

where c is the speed of light. So, the velocity of a given mode is related to the effective dielectric constant of that mode, ere or ero. If

we can manipulate the effective dielectric constants of the modes, we

can manipulate their relative velocities. Gilb [1] showed that by

adding additional layers to the traditional single substrate microstrip structure, efe and ero can be made to equal each other. The effect of

1 c (35) v

2 2

this is to make the velocities of the two modes equal, thereby

eliminating forward crosstalk as described above.

A quick way of determining if a given combination of dielectrics and

their relative thicknesses will produce a structure where the modal

velocities are equal would be helpful. Under quasi-TEM conditions,

where the frequency dependence of v is negligible, this can be done

in the following manner. Setting the velocities in (33) and (34) equal

to one another, we find

So, when the ratio of the even to odd mode capacitances is equal to

the ratio of the odd to even mode inductances, the velocities of the

two modes will be equal and forward crosstalk will be minimized.

With this in mind, we must find a way to relate the even and odd

mode inductances and capacitances, Le,0 and Ce,o, to the inductance

and capacitance matrices for the structure. Consider again the propagation constants for the even and odd modes, Ye and Y0,

1 1 Ve VLeCe VLoCo V°

or,

Ce L (36)

Cq Le

Yc=Ye = ± V ( a + b ) = ± ^ / ( Y + Y r a ) ( Z + Z m ) (29)

(30)

and our definitions for Y and Z,

Zi = jwLn ( 6 )

Z2 = jcoL22 ( 7 )

2 3

Zm = jcoLn =jcoL2i

Yi =jcoCn

Y2 = jcoC22

Ym = -jcoCi2 = -jcoC2i

If we substitute (6) - (11) into (29) and (30), we find

Ce = Cn -1C12I

C0 = Cii + |Ci2[

Le = Ln + L12

L0 = Ln - L12

( 8 )

(9)

(10)

(11)

(39)

(40)

(41)

(42)

These expressions make intuitive sense if we look back to Figure 2-3.

The even mode shows magnetic (inductive) coupling between the

two conductors, but no electrical (capacitive) coupling. The odd mode

displays the opposite property—electrical (capacitive) coupling, but

no magnetic (inductive) coupling. If we substitute (39)-(42) into

(36) we find the following relationship,

Cn - C12

Cn + C12

L l l - L 1 2 L l l + L 1 2

or

rat - 1 rat - 1

rat + 1 L r a t + 1

(43)

where Crat Cn C12

L11 and Lrat = For (43) to be true, Crat = Lrat- So,

to determine what combination of materials and thicknesses will give

2 4

us a structure that minimizes forward crosstalk, we look at the ratio

of the first row of elements in the L and C matrices.

L is independent of the dielectric properties of the media. Because

we are dealing with non-magnetic materials, L is only a function of

conductor geometry. That is, it is dependent upon the conductor

width, thickness, seperation, and height above the ground plane only.

So, for a given conductor geometry, Lrat is fixed. Therefore, to satisfy

(43), it is necessary only to manipulate the dielectric permitivities

and thicknesses.

Throughout this development, all relative permitivities, er, were

assumed to be frequency independent constants. For high

frequencies this is not true. At some point, the frequency dependence of er cannot be ignored and dispersion effects must be

included for an accurate analysis. Let fg denote the maximum frequency for which er can be considered a constant. To produce

reliable results, then, one must be careful to apply this analysis only

when the contributing frequencies are less than fg. fg is

approximated by means of the empirical equation [8]

where ZLO is the characteristic impedance of a lossless line in free

space, h is the height of the conductors above the ground plane (in millimeters), ereff is the effective relative permitivity of the

structure, and Zl is the characteristic impedance of a lossless line. fg

is in gigahertz.

For example, a typical characteristic impedance for some of the structures discussed in the next chapter is ZL=80Q . Figure 2-6 shows a microstrip structure with the conductors located 0.66mm

(26mils) above the ground plane, the same height as those in next

(44)

2 5

chapter. Substituting these numbers into (44) yields fg=4.8GHz.

Therefore, all of the frequencies that make a significant contribution

to the signal and crosstalk waveforms must be less than or equal to

4.8GHz.

h = .66mm

7/7/77/7////////77/7 Figure 2-6 Microstrip structure

Assume a 50MHz signal with a magnitude of 5V, a 50% duty cycle,

and a risetime/falltime of 1.0ns is launched on the active line.

Crosstalk is proportional to the time derivative of the signal. Figure

2-7 shows this signal pulse along with its derivative. The significant

harmonics of both waveforms must fall below fg = 4.8GHz.

Since both waveforms are periodic with a frequency of 50MHz, their

fourier transforms will contain discrete frequency components at

f0 = 50MHz intervals. Therefore, the waveforms can require up to f 7s" = 96 harmonic components and still fall within the stated limit. to It is known that the signal waveform can be described with fewer

than 96 harmonics (generally, 5 is sufficient). If the derivative

(crosstalk) waveform can also be described with fewer than 96

harmonics, than this analysis is reliable for this situation.

2 6

5V Signal

1 0 9.0 10 20 time (ns)

Derivative

time (ns)

-5

Figure 2-7 50MHz signal and its derivative, fo=50MHz, tr=tf=l.0ns,

The nth fourier component of the derivative waveform is given by

nci)0§ sin -z—

c » = ( 4 5 )

2

where K is a constant. Using (45) we determine that the fourier

coefficient of the 96th harmonic is C96 = K(.04). This value is small

enough that any higher harmonics can be neglected. Since both

waveforms can be described by 96 or fewer harmonics, the analysis

is valid.

2 7

CHAPTER 3

RESULTS AND DISCUSSION

3.1 Software

Three steps were required to produce the results in the following

sections. First, in order to determine Crat and Lrat» inductance and

capacitance matrices had to be calculated for the considered

geometries. Second, these L and C matrices had to be converted into

useful transmission line circuits. Third, the effect of these circuits on

input signals had to be simulated.

The first of these steps was completed using a program called

UAMOM. UAMOM was developed at the University of Arizona. As

input, the program accepts a description of the two-dimensional

cross-section of a structure and assumes that the structure is infinite

in length. UAMOM assumes a TEM wave propagation mode, and uses

the method of moments to solve Lapace's equation in two

dimensions. Using the concept of total charge, UAMOM calculates the

capacitance matrix, C, of the the n-conductor system. Qj is the free

charge PUL on the ith conductor due to a 1 volt potential on the jth conductor when all other conductors are grounded. Cajr is then

calculated, where Cajr is the capacitance matrix for the system when

all relative dielectric permitivities are set equal to one. The

inductance matrix, L, is then found from the relationship

L = HOEO(CAIR)"1 (46)

where |io and eo are the free space permeability and permitivity,

respectively, and (Ca,,.)"1 is the inverse of the matrix Cair.

UAMOM has a weakness that must be taken into account when using

its data. When adjacent dielectrics have relative permitivites that

2 8

are very close to one another, the L and C matrices calculated by

UAMOM are not reliable. For this reason, cases which include

adjacent dieletrics whose difference in relative permitivity values is

less than or equal to one were not considered for simulation.

The circuit simulations were accomplished using a SPICE-type

simulator. Figure 3-1 shows the circuit model used. The

transmission lines are terminated with their independent characteristic impedance, ZQ, i.e., the characteristic impedance of each

line when considered by itself.

(fwdxtk )% R=Zo

Figure 3-1 SPICE model for transmission line simulations.

Like many other SPICE versions, this simulator only contained

models for ideal transmission lines. Coupling effects between

multiple lines were not included. This shortcoming was overcome by

building transformation networks on either end of the ideal SPICE

transmission line. A program, written by Udy Shrivastava, based on

the work of F. Chang [4] was used to create these networks.

2 9

ii(O.t) id <0,t) VJ(l,t)

vd i(l,t)

O) D)

Figure 3-2 SPICE model for n coupled transmission lines, [3].

A set of n coupled, lossless transmission lines can be modeled as two

transformation networks in conjunction with a set of n decoupled

single transmission lines [4], [3], Figure 3-2. The transformation

networks take the form of two identical congruence transformers

located on either side of the ideal transmission lines. To begin, the

method assumes a TEM mode of wave propagation and uses the

generalized telegraphists' equations (1) to describe the voltages and

currents on the lines, [4]. Next, the coupled voltages and currents are

transformed, converting the system into a set of uncoupled voltages

and currents propagating down their individual lines. We accomplish

this by replacing v(x,t) and i(x,t) with

v = M yVd (47)

3 0

i = Miid (48)

where M v and Mi are n x n constant matrices, and substituting these into (1). This gives us

_a_rvd(z,t)i _ r o Ld"| a_rvd(z,t)i a z L i d ( z , t ) J _ " L c d o J a t L i d ( z , t ) J < 4 9 >

Vd and id are now decoupled and Ld and Cd are the modified

inductance and capacitance matrices that describe this new

decoupled arrangement. The time delay and characteristic

impedance matrices can be calculated from Ld and Cd as follows,

I Dd = (LdCd)2 (50)

i Zd = (Ldcd)2 Cd-' (51)

where Dd is the time delay matrix, Zd is the characteristic impedance

matrix, and both are diagonal. Now by applying the values in the Dd

and Zd matrices to n SPICE transmission lines, and using the

networks at both ends of the lines to transform the voltages and

currents from coupled space to uncoupled space, we can simulate n

coupled transmission lines. The following algorithm describes how to

determine the values for circuit, [3],

1. Given the number of lines n, compute the eigenvalues of matrix LC, A,j.

2. Compute the matrix My = [Mjj] of right eigenvectors of LC.

3. i= 0.

4. i = / +1; compute the control law for each dependent source of

the tranformation network using the following equations, (see

Figure 3-3):

3 1

vsi(x,t) = nMijVdj(x,t) - vdj(x,t)

isi(x,t) = . 2 Mijid;(x,t) - idj(x,t) i=l-»n J J

( 5 2 )

( 5 3 )

where either x=0 or x=l, 1 being the length of the line. 5. Compute the characteristic impedance Zdj and the time delay

per unit length Dd, of the ith line using (50)-(51).

6. If i<n go to Step 4; else stop.

" (o.ty Vsi (0,t)

-o-

Vi isi (0,t)(] ^ Vdi (0,t)

Idi (0,t) —• 0

Vsi (I ,t) Idi (I ,t)

-•—4 o— ii (i ,t)

Vdi (I ,t) (j )isi (I ,t) Vi (I ,t)

Figure 3-3 Detailed model for the ith line [3],

3.2 Geometries

Three geometries are examined here. In all of them, conductor

thickness, spacing, and height above ground is kept constant to

maintain a consistent inductance matrix throughout. The only

changes occurring are changes in dielectric type and placement.

The first geometry is a typical microstrip structure, Figure 3-4. The

substrate consists of a single dielectric extending from the ground

plane to the bottom of the conductors. Above the substrate is air.

y/t

h=26mil t=2.25mil wl=w2=2.5mil s=1.25mil

Figure 3-4 Single dielectric substrate geometry.

The next geometry is a microstrip structure with a substrate

consisting of two dielectrics, Figure 3-5. The total substrate extends

from the ground plane to the bottom of the conductors. The height of

the interface between the two substrate dielectrics and the

permitivity of each of the substrate dielectrics are allowed to vary.

The total substrate height remains constant. Again, air is above the

s u b s t r a t e .

iMt®


Figure 3-5 Double dielectric substrate geometry.

The final geometry has three dielectrics, Figure 3-6. Below the

conductors, the substrate consists of three distinct dielectric layers. The height and permitivity of the bottom layer, e 1=3.8, is kept

constant. The middle layer is always air, e2=1.0. The height of the

interface between the top substrate layer, E3, and the middle

3 3

substrate layer, e2, is allowed to vary, as is the permitivity of the top

l a y e r . A c a p w i t h t h e s a m e p e r m i t i v i t y a s t h e t o p s u b s t r a t e l a y e r , e 3 ,

is located over the substrate and the conductors such that the

conductors appear to be encased in a single dielectric. Air is located

above the cap.

air

M f V ////////////////////


Figure 3-6 Triple dielectric substrate geometry with buried conductors.

3.3 Family of curves and SPICE simulations

After calculating the inductance and capacitance matrices for the different geometries, sets of curves showing Crat versus er as a

function of dielectric thickness were produced. Using these curves,

we determined which combinations should minimize forward and

backward crosstalk and then simulated several of these cases.

Figure 3-7 shows the Crat curve for a single dielectric substrate. This

graph predicts, unsurprisingly, that substrates with lower

permitivities will have less crosstalk. Figures 3-8 and 3-9 support this conclusion. The substrate with er = 3 has a lower level of

forward crosstalk than the substrate with er = 10. However, a

significant amount of backward crosstalk is observed in both cases.

3 4

Next we present sets of Crat curves for the double dielectric substate,

Figures 3-10 to 3-12. Because the addition of a low permitivity dielectric decreases the effective er of the substrate, all of the points

which have a low permitivity dielectric beneath a high permitivity

one will show a lower level of forward crosstalk than their single

high permitivity dielectric counterpart. As the value of Crat gets

closer to Lrat, the difference in the even and odd mode velocities

approaches zero and the forward crosstalk disappears. This trend is

illustrated in Figures 3-13 and 3-14, where we have chosen to simulate two points from the family of curves for Er2 =10 Figure 3-

13 represents the point located at eri =3 and hi = 10.4, and Figure 3-

14 is from the point £rl =3 and hi = 13.0. The forward crosstalk

decreases as we move from Figure 3-13 to 3-14, but there is no

signifcant change in the backwards crosstalk. The same trend is s h o w n i n F i g u r e s 3 - 1 5 a n d 3 - 1 6 , w h e r e e r 2 = 8 .

The cases shown in Figures 3-13 through 3-16 all have Crat greater

than Lrat. When we cross over the Lrat line such that Crat becomes

less than Lrat, the backward crosstalk disappears, see Figures 3-17

through 3-20 The forward crosstalk increases as we move away

from the Lrat line. If we choose a pair of dielectrics and select their heights such that Crat ^ Lrat, we can minimize both forward and

backward crosstalk.

In all of the simulations discussed thus far, the transmission lines

had approximately matched terminations at both ends of the quiet

line and at the receiving end of the active line as shown in Figure 3-

1. If the terminations are not matched, we would expect forward

crosstalk to reappear. Reflections due to a mismatch on the active

line are like newly lauched signals, producing both near end and far

end crosstalk noise. A reflection occurring at the receiving end of the

active line will induce near end crosstalk at the receiving end of the

quiet line. Since that is where we measure forward crosstalk, we see

3 5

noise reappearing there, Figure 3-21. Mismatches on the quiet line

will permit multiple relfections of any voltages induced on the line,

Figure 3-22. Neither Figure 3-23 nor 3-24 shows crosstalk for a

mismatched termination. This was a case where both the backward

and forward crosstalk were negligible. Without either of these noise

sources, there was no mechanism available to increase the crosstalk.

Simulations were also completed for triply coupled lines to show the

effect of adding a third line. In each case, the line terminations were

approximately matched for the three individual lines. The addition

of the third line had a similar effect whether or not the doubly

coupled model had exhibited backward crosstalk. When a signal is

impressed on the center line, Figure 3-25, the crosstalk on the two

outer lines is identical. Figure 3-27 is a case where Crat was greater

than Lrat for the doubly coupled lines. For the case shown in Figure

3-28, Crat was less than Lrat for the for the doubly coupled lines.

Because the surrounding lines affect the impedance of the individual

microstrip lines, our terminations are not truly matched. This is

shown by the fact that the output of the middle lines needs multiple

reflections to build up to its steady state value.

When we impress the input signal on one of the end lines, Figure 3-

26, we see backward crosstalk on line 2 and forward crosstalk

appearing on line 3, Figures 3-29 and 3-30. The addition of a third

microstrip line makes it necessary to use three modes to describe all

the possible signals on the lines. However, in choosing the dielectrics

and their thicknesses in this example, only two modes were

considered. If the middle line is active, Figures 3-25, 3-27 and 3-28,

modes that approximately resemble the symmetric and anti

symmetric even and odd modes are excited. The crosstalk resembles

that for the doubly coupled cases. However, if one of the outside

lines is the active line, the modes describing the signals on the outer

3 6

lines do not resemble the even and odd modes so forward crosstalk

is not minimized.

The Crat curves for the triple dielectric buried microstrip does not

indicate any cases where the forward crosstalk will be eliminated.

The layer of air in the substrate reduces the Crat to such a degree

that, for this conductor geometry, it is always less than Lrat- This

complete mismatch between Crat and Lrat might be removed by

either changing the air layer to some dielectric or by changing the

conductor geometry.

3 7

2 o

1.55-

1.5-

1.45-

1.4-

1.35-

1.3-

1.25-

1.2-

1.15-

1.1- rrrr fTT

2 3 4 5 6 7 8 9 1 0 e1

Lrat

h=26

Figure 3-7 Crat vs. er for a single dielectric substrate with conductors located h=26.0 mils above the ground plane.

Input - - Backward Crosstalk

Output — — Forward Crosstalk

5

4

3

o > 1

0

j —J —J

I 1

F \ \

\ \ \

1

\_ X_

Lf \J V

O) O) CT) |

a Oi o) o> o> CT) CT)

Lii LLI LU LU LU LU LU LU LLJ LLJ LO O LO O LO o LO O in O

•»— CM CM CO Time (s)

CO in

Figure 3-8 SPICE plot for 2 microstrip lines with a single dielectric substrate. er = 3, length=60cm.

3 9


Output -— Forward Crosstalk

JL ^4 -N/ £7"

<D O) 2-(0

-1

\ 1 i

I I I I V I I I I I I I I I I I I I I O +

LU O

Oi o> O) O) O) O) C T ) 1 O) <y> o>

LU LLI LU LU LLJ LU LU LU LU LU m O m O in O in o m O

(M CM 00 CO in Time (s)

Figure 3-9 SPICE plot for 2 microstrip lines with a single dielectric substrate. er = 10, length=60cm.

4 0

re u . o

1.55

1.5

1.45

1.4

1.35

1.3

1.25

1.2

1.15

1 . 1

.J i

>

#

/ • " t

/

* /

• -X

3

'<-4 r, f' / 9 t . % •'/

4—

•i 7 w

e; 2=1 C

2 3 4 5 6 7 8 9 1 0 e1

Lrat

h1=2.6

h1=5.2

h1=7.8

h1=10.4

hi=13

h1=15.6

h1=18.2

h1=20.8

h1=23.4

Figure 3-10 Crat vs. eri for a double dielectric substrate. er2=10>

conductors are located h=26.0 mils above the ground plane.

4 1

1.55

(0 o

ffl

e2 =9

rm rm rm rm

Lrat

h1=2.6

h1=5.2

h1=7.8

h1=10.4

hi=13

hi =15.6

hi =18.2

hi =20.8

hi =23.4

Figure 3-11 Crat vs. eri for a double dielectric substrate. 6^=9,


4 2

1.55

1.45-

1.35 CO

o

1.25-

TTTT

e1

Lrat

h 1 =2.6

h1=5.2

h1=7.8

h1=10.4

h 1 = 13

h1=15.6

h 1 =18.2

h1=20.8

hi =23.4

Figure 3-12 Crat vs. eri for a double dielectric substrate. £r2=8.


4 3


Output --— Forward Crosstalk

i J

r

W=r "\

x_ _

XT •S3

M i l I I I tt nrr tt I I I tt II I tt

o +

LU O

CD O) O) CD LU UJ LU LU 10 o m o

1- T— cvj

a) I LU m c\j

CD Oi o> CD 1 O) LU LU UJ UJ LU o LO o m o CO CO LO

Time (s)

Figure 3-13 SPICE plot for 2 microstrip lines with a double dielectric substrate. erl =3, er2 =10, hi = 10.4, length=60cm.

44



/ /

r '

t i i i

1

i i \

\

1 1

1 *

v _ —• -•»

.

1 1 1 1

Q) ^ o> 2 w o >

0

o +

LU O

a> o> O) 1 CD O) cr> CD 1

ill LLl LU LU LU LLl LU io O in o in O in

t— t- CM CM CO CO

Time (s)

CD LU O

a I LU lO

cn LU O in

Figure 3-14 SPICE plot for 2 microstrip lines with a double dielectric substrate. erl =3, er2 =10, hi = 13.0, length=60cm.

4 5



5-

4- •f

a> ^ O) 2-CO o >

1-

0-

t=;

v___ V

-1 I I I tt tt

o +

LU

o> i LU in

i i i i i i i i t

0 ) 0 ) 0 )

LU 111 LLI O lO o

CM

O) I LU m OJ

a> l LLI O CO

O) I LU in CO

Time (s)

t I I I I I I I I O) O) O) LLJ LU LU o in o t ^ m

Figure 3-15 SPICE plot for 2 microstrip lines with a double dielectric substrate, erl =3, er2 = 8, hi = 15.6, length=60cm.

4 6


Output — Forward Crosstalk

1 1 i i 1 1 1 1 1 1 i i 1 1 1 i i 1 1 1 1 1 1 1 1 1 1 1 i 1 1 i 1 1 1 1 — 1 1 1 1 O) o> o 1 cp O O) O) 1 O) cp O) LLI LLI LLI LLI LLI LLI LU LU LLI LLI LO O m O lO O in O in O

T— •<— CM CM CO CO Tj- in Time (s)

Figure 3-16 SPICE plot for 2 microstrip lines with a double dielectric substrate. eri =4, ej-2 = 8, hj = 23.4, length=60cm.

4 7



Q) ^ O) 2 & o >

0

-1

/ i

i

• 1

t 1 i i

i i 1 i 1 1

o +

111 o

o> CT> o> 1 Oi O) O) Ol |

o> O) CD LLI LLI LLI LLI LLI LLI LLI LLI LLI LLI in O in O in O in O m O

T— CM CM CO CO "<fr in Time (s)

Figure 3-17 SPICE plot for 2 microstrip lines with a double dielectric substrate, erl =4, er2 = 10, hi = 20.8, length=60cm.

4 8



A

I I 1 1 1 / 1

O "

1

/ I 1

i

i

0 "

1 1

1

1 " 1 1 1 1 1 1 1 1 1 1 1 1 o +

LLi O

CJ> o> O) i

O) q> O) O) t

O) <J> O) UJ LLI LLI LLI LLJ LLI LU LLJ 111 LLi U) O m o in O in o in O

V— CM CM CO CO m Time (s)

Figure 3-18 SPICE plot for 2 microstrip lines with a double dielectric substrate. eri =3, er2 = 9 hi = 15.6, length=60cm.

4 9



i i

i

i 1

1

1 i i

i h_

o +

LU O

O) o> o> 1 a CD <J) O)

| O) cp a

LLI LLi LU LU LLI LLI LU ih LU LLI in o in o in O in o in o

T~ T— CVJ CM CO CO in Time (s)

Figure 3-19 SPICE plot for 2 microstrip lines with a double dielectric substrate, erl =3, er2 = 10, hi = 15.6,, length=60cm.

5 0



1 1

i i i

I | 1

I 1 i n

o +

LLI O

O) i LU m

a O) o 1 O)

i O) O) C> CD

til UJ LU LLI LLI LLI LLI UJ o LO O m O to O in

CM CM CO CO

Time (s)

Figure 3-20 SPICE plot for 2 microstrip lines with a double dielectric substrate, erl =3, £r2 = 10, hi = 18.2, length=60cm.

5 1



© - J o> - f <o •

I 2 i '

1-

o-

. ..

-1 111—11 > o +

LU O

i i i i i i i 11 11 i i i tt I I I II I I o> o o

1 q> 9 o> O)

| Oi <J) o>

LU LLJ LU UJ LU LU LU LU 111 LU o in o LO O m o in O T- CM CM CO CO in

Time (s)

Figure 3-21 SPICE plot for 2 microstrip lines with a double dielectric substrate. erl =3, er2 = 10, hi = 13.0, length=60cm. Active line is terminated into approximately 2.5Zo. (Figure 3-14 shows that this case had backward crosstalk when the terminations were approximately matched.)

5 2


Output -• — Forward Crosstalk

2 3 0) O) (0 — 2 o * >

1

0

-1

—{ r / /

—1—

\. . 4-i

T i /

a

1 i v. _>v

: \

L -i.

-»• —v. —% w— — *,

o +

LU O

o> en O) 1 O) O) CD O)

1 CJ) CT)

LU ULl LU LU LU LU LU LLl LLl LU in O LO o in O un o lO O

T— "i— C\J CM CO CO in Time (s)

Figure 3-22 SPICE plot for 2 microstrip lines with a double dielectric substrate. erl =3, er2 = 10, hi = 13.0, length=60cm. Quiet line is terminated into approximately 2.5Zo on both ends. (Figure 3-14 shows that this case had backward crosstalk when the terminations were approximately matched.)

5 3



8

7

6

5

0) ** D) £ 3 o >

2

1

0

-1

1 r I

j 1 1

j 1 i \

! 1 1 1

I !

: i U

i ' 1

11 M 1 1 1 1 1 1 1 1 1 1 1 1 • 1 1 1 • • • I o +

LU O

CD o> O) 1

o> CD o> O) 1 CJ) CD CT)

LU LU LU LU LU LU LU LU LU LU o in O in O in O m o

•*— C\J CM CO CO xT in Time (s)

Figure 3-23 SPICE plot for 2 microstrip lines with a double dielectric substrate. erl =4, er2 = 10, hi = 20.8, length=60cm. Active line is terminated into approximately 4Zo. (Figure 3-17 shows that this case had no backward crosstalk when the terminations were approximately matched.)

5 4



5

4

S 3 <D O) (0 — 2 o * >

1

0

-1

l i 1 a

1 «

/ i

1

o +

111 o

o> o> o> 1 Oi CJ) CJ) Oi

1 a <ji o> 111 LU LLI LLI LLI LLI LU LU UJ LU in O un O in o in o in O

t— t— CM CVJ CO CO M- TJ- m

Time (s)

Figure 3-24 SPICE plot for 2 microstrip lines with a double dielectric substrate. erl =4, er2 = 10, hi = 20.8, length=60cm. Quiet line is terminated into approximately 4Zo on both ends. (Figure 3-17 shows that this case had no backward crosstalk when the terminations were approximately matched.)

5 5

R=Zo (bkdxtk(1) ) (fwdxtk(1) ) < R=Zo

(°hD R=Zo

R=Zo- (bkdxtk(3) )

1-

(fwdxtk(3) ) R=Zo

Figure 3-25 Triply coupled transmission lines. Signal is input to the

center line.

5 6

Backward Crosstalk 1 Output

—— Forward Crosstalk 1 Backward Crosstalk 2

Input Forward Crosstalk 2

o : i

n

u

I I II

V

I I I I I I I I I I

A,'

x

l l l l

7

V

IT I I I

r S

o +

LU O

O) •

111 in

O) o> O) cn 1

O) O) o> LLJ LU LU LU LU LU LU O LO O LO O LO O

t— CM CM CO CO

1 1 1 1 1 M 1 1 1 1 1 1 1 o> LLJ LO

O) LLJ O in

Time (s)

Figure 3-27 SPICE plot for 3 microstrip lines with double dielectric substrate. Input and output signals on center line. erl =3, er2 = 10, hi = 13.0, length=60cm.

5 7

Backward Crosstalk 1 Output

— Forward Crosstalk 1 Backward Crosstalk 2


o> • O) O) cn O) i

O) O) O) O) 1

<j> LU LU LU LU LU LU UJ LU UJ UJ

O in o in o in o in o CM CM CO CO in

Time (s)

Figure 3-28 SPICE plot for 3 microstrip lines with double dielectric subs tra te . Input and output s igna l s on center l ine . e r l =4 , er2 = 10, hi = 20.8, length=60cm.

5 8


Output Backward Crosstalk 2

Backward Crosstalk 1 — . - - Forward Crosstalk 2

5-

4-

3-

2 2. G) D> (0 % 1->

0-

- 1 -

- 2 -

o +

LU O

TT TT

JL

TT

f

TT

-m/

y"

-TT

X

TT I I I I T o O) CD CD O) cp CD | o CD CD

LU LU LU LLI LU LLI LU LU LLI LJJ un o m O in O m o m o T— CM CM CO CO in

Time (s)

Figure 3-29 SPICE plot for 3 microstrip lines with double dielectric substrate. Input and output signals on outside line. erl =3, er2 = 10, hi = 13.0, length=60cm.


Output Backward Crosstalk 2

Backward Crosstalk 1 -— Forward Crosstalk 2

I I I I o> o> o>

1 O) O) o O) i CD Oi G)

LU LU LU UJ LU LU LU LU 111 LU lO O m o LO O LO O m O

t- •*- CM CM CO CO in Time (s)

Figure 3-30 SPICE plot for 3 microstrip lines with double dielectric subs tra te . Input and output s igna l s on outs ide l i ine . e r \ =4 , er2 = 10, hi = 20.8, length=60cm.

6 0

•

mm.

R=Zo

R=Zo (bkdxtk(2) ) (fwdxtk(2) ) R=Zo

R=Zo (bkdxtk(3) ) (fwdxtk(3) ) R=Zo

Figure 3-26 Triply coupled transmission lines. Signal is input to the end l ine .

6 1

CM

O t"

O

1.4

1.35

1.3

1.25

1.2

1.15

1.1

1.05

1

•l.

S; s

5s*

=3.e 3 e; 2=1. 0 h I

TTTTJ

=d.t> na=40.u

lllll llllllllllllllll 11 11

L11/L12

h2=5.2

h2=7.8

h2=10.4

h2=13.0

h2=15.6

h2=18.2

h2=20.8

h2=23.4

O ' - w n ^ f i n t o N o o a * o

e 3

Figure 3-31 Crat vs. er for a triple dielectric substrate with conductors located h=26.0 mils above the ground plane.

6 2

CHAPTER 4

CONCLUSIONS

The triple dielectric buried microstrip geometry was motivated by

single chip packaging scenarios where we have the package leads

encased in some material (usually plastic or ceramic) and mounted

on PCB board. There is usually a small airgap between the PCB board

and the package. Trying to remove this airgap by adding some other

material between the board and package is not very practical from a

manufacturing and cost point of view. Whether or not reducing the

conductor height would remove the forward crosstalk should be

investigated. Size considerations are already pushing for smaller,

thinner packages. If indeed this did reduce or eliminate forward

crosstalk, it would be yet another argument for thinner packages.

The double dielectric substrate method could be useful in multichip

modules (MCM) or RF packaging. Both of these areas utilize

traditional microstrip structures. Design curves can be used to help

select the substrate materials. Once the materials are selected,

design curves can be used to determine optimum height ratios for

the two dielectrics.

The combination of a material that has a high dielectric constant with

one that has a low dielectric constant is likely to have an optimum

height ratio that would eliminate forward crosstalk. Two classes of

materials used widely in packages today fit that description-

ceramics and polyimides.

A typical ceramic, Alumina, with a dielectric constant of

approximately 9 and a polyimide with a dielectric constant of

approximately 4 are good candidates for eliminating forward

crosstalk. Their use, however, presents some interesting challenges

6 3

to other disciplines. Different thermal properties may cause

reliability problems. Alumina has a thermal expansion coefficient of approximately 60 x 10"7/°C and a thermal conductivity of

approximately 18W/m-K°, while those same properties for polyimide are 500 x 10*7/°C and .2W/m-K° [7].

During processing, alumina is cured at a much higher temperature

than polyimide. If the alumina must be attached to the polyimide,

this is a major problem. However, if the polyimide is attached to the

alumina, the problem can be avoided. These two cases may sound

identical. They are not. The difference is essentially in which

material we start with.

To illustrate the difference, imagine we are building a MCM. MCMs

very often have multiple signal layers, so the substrate is built from

the bottom up,

metallization-*dielectric-* signal lines-* dielectric-* metallization....

The top signal layer will be our double dielectric substrate microstrip

structure. This would have to be built up as

metallization-*low dielectric-* high dielectric-* signal lines

or

metallization-*polyimide-*alumina-*signal lines.

This means that we will try to attach the alumina (which must be

cured at a high temperature) to the polyimide (which might be

damaged at high temperatures. Perhaps if we only have one signal

layer, as in some RF modules, we could get around the problem by

turning the substrate upside-down. Starting with the alumina, we

could attach a polyimide and then the metallization (for. the ground

6 4

plane). Turning the substrate over again, we could attach the

microstrip lines on top of the alumina.

The growing importance of RF and multichip modules makes further

research into these thermal and manufacturing issues a reasonable

investment. Extending this method to develop design curves which

account for more than two conductors is a useful project for future study.

6 5

REFERENCES

[1] J. Gilb, C. Balanis, "Pulse distortion on multilayer coupled microstrip lines," IEEE Trans. Microwave Theory Tech., vol. MTT-37, no. 10, pp. 1620-1628, 1989.

[2] K. C. Gupta, R. Garg, I. J. Bahl, Microstrip Lines and Slotlines. Dedham, MA: Artech House, 1979.

[3] F. Romeo, M. Santomauro, "Time-domain simulation of n coupled transmission lines," IEEE Trans. Microwave Theory Tech., vol. MTT-35, no. 2, pp. 131-137, 1987.

[4] F. Chang, "Transient analysis of lossless coupled transmission lines in a nonhomogeneous dielectric medium," IEEE Trans. Microwave Theory Tech., vol. MTT-18, no. 9, pp. 616-626, 1970.

[5] P. Rizzi, Microwave Engineering, Passive Circuits. Englewood Cliffs, NJ: Prentice Hall, 1988.

[7] R. R. Tummala, E. J. Rymaszewski, Microelectronics Packaging Handbook. New York, NY: Van Nostrand Reinhold,1989.

[8] R. K. Hoffmann, Handbook of Microwave Integrated Circuits. Norwood, MA: Artech House, 1987.

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