Antony Zegers

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science

Graduate Department of Electrical and Computer Engineering University of Toronto

Copyright @ 2001 by Antony Zegers

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Abstract

High-Fidelity Broadside Couplers

Antony Zegers

Master of Applied Science

Graduat e Depart ment of Electrical and Comput er Engineering

University of Toronto

2001

The goal of this project is to characterize and design high-fidelity broadside couplers

for use in digital systems. The Ltype contactless connectors currenly in use distort the

coupled signal such that signal reconstruction must be carried out at the receiver. A high-

fidelity coupler would preserve the shape of the digital pulse so that this reconstruction

wodd not be necessary. The coupler under investigation is of broadside stripline configu-

ration and uses a conductive connection to accomplish the coupling. This report explains

the theory behind the operation of such a coupler, introduces a design methodology, and

examines design case studies providing cornparisons with previous work.

Acknowledgement s

1 wodd like to thank Professor K. G. Balmaih for his mgidance during the course

of this research. This research vas financially supported by the Naturai Sciences and

Engineering Research Council and by Norte1 Networks. 1 would also like to thank my

friends in the Electromagnetics group for their assistance and advice, and my- famifa for

their love and support.

Contents

1 Introduct ion 1

1.1 O v e ~ e w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Background 5

2.1 Basic Coupler Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

. . . . . . . . . . . . . . . . . . . . 2.2 Bachvard Electromagnetic Coupling 8

. . . . . . . . . . . . . . . . . . . . . 2.3 F'orward Electroma-etic Coupling 14

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Conductive C o u p h g 18

Coupler Design 23

3.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

. . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Conductive Coupler Theory 24

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Design Relations 29

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Matching 29

3.3.2 Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Loss 40

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Directivity

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.5 Fidelity 51

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Design Procedure 54

4 Coupler Simulation 57

4.1 Simulation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.1.1 Frequency-Domain Analysis . . . . . . . . . . . . . . . . . . . . . 57

4.1.2 Time-Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . 60

4.2 Design Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.2.1 18 dB Coupler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.2.2 25 dB Coupler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5 Conclusions 70

. 5.1 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5.1.1 Design Improvements . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.1.2 Physical Realizability . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.1.3 Alternative Uses for the Device . . . . . . . . . . . . . . . . . . . 73

References 75

List of Tables

3.1 The Effect of Design Parameters on Coupled-Signal Amplitudes . . 28

3.2 The Effect of Design Parameters on Coupler Performance . . . . . . . . . 54

4.1 Design Parameters for an 18 dB High-Fidelity Broadside Coupler . . . . 62

4.2 Design Parameters for a 25 dB High-Fidelity Broadside Coupler . . . . . 66

List of Figures

1.1 A typicd Gtype coupler in microstrip confi,gwation . . . . . . . . . . . . 2

1.2 The broadside coupler layout that was explored in this research . . . . . . 3

. . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Coupled transmission lines 6

2.2 The eqiUvalent circuit for an infinitesimal section of coupled line . . . . . . 7

. . . . . . . . . . . . . . . . . . . . 2.3 Even-mode and odd-mode excitations 9

. . . . . . . . . . . . . . . . 2.4 Even-mode and odd-mode equivalent circuits 10

. . . . . . . . . . . . . . . 2.5 Pulse propagation through a backward coupler 13

. . . . . . . . 2.6 The s-parameter plot for a fornrard electromagnetic coupler 16

. . . . . . . . . . . . . . 2.7 Layered dielectric structure for forward coupling 17

. . . . . . 2.8 A pulse propagating through a forward electromagnetic coupler 19

. . . . . . . . . . 2.9 A resistive directiond coupler made with resistive strips 20

. . . . . . . . . . . . . . . . . . . . . 2-10 Broadside conductive coupler layout 21

2.11 Fornard coupling equivalent circuit . . . . . . . . . . . . . . . . . . . . . . 22

. . . . . . . . . . . . 3.1 Dimensions and physicd parameters of the coupler 24

. . . . . . . . . . . . . . . . . . . 3.2 A simplified conductive coupling mode1 26

. . . . . . . . . . . . . . . . . . . 3 -3 Even-mode and odd-mode capacitances 31

. . . . . . . . . . . . . . . . . . . . 3.4 Line width versus dielectric constant 32

. . . . . . . . . . . . . . . . . . . . . . . . 3.5 Line width versus line spacing 34

. . . . . . . . . . . . . . . . . . . . . 3.6 DC equivalent circuit of t he coupler 36

vii

3.7 Coupling versus conductance . . . . . . . . . . . . . . . . . . . . . . . . . 39

. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Loss versus conductance 42

. . . . . . . . . . . . . . . . . . . . . . . . 3.9 Directivity versus conductance 50

. . . . . . . . . . . . . . . . . 3.10 The input pulse and its frequency s p e c t m 52

. . . . . . . . . . 3.11 Fonvard-coupled pulse fidelity for different values of C r 53

. . . . . . . . . . . . . . . 4.1 Simulated s-parameters for the 18 dB coupler 63

. . . . . . . . . . . . . . . . 4.2 Time domain response of the 18 dB coupler 64

. . . . . . . . . . . . . . . 4.3 Çimulated s-parameters for the 25 dB coupler 68

. . . . . . . . . . . . . . . . 4.4 Time domain response of the 25 dB coupler 69

viii

Chapter 1

Introduction

The goal of this project is to design a high-fidelity broadside c.zoupler. As digital circuits

continue to increase in speed, they can no longer be approxima-.ted as quasi-static electric

circuits, and full elect romagnetic analysis must be undertaken. Circuit board connections

will behave as transmission lines with distributed parameters- A major problem is the

connection of branches to transmission lines. These branches c a a produce reflections and

Erequency-dependent line loading. These problems have prev-iously been addressed by

using an Ltype electromagnetic coupler as described in a pr-evious master's thesis by

Peter Aaen [II. A typicd Ltype coupler is shom in Figure 1 .1.

The Ltype coupler is quite effective, but it has the disad--vantage that the coupled

signal consists of large signal spikes corresponding to the edges of the original signal.

Thus the signal must be reconstructed from these edges. The - goal of this project is to

develop a coupler wit h high fidelity, i.e. such that the coupled sEgnal will retain the shape

of the input pulse. This feat requires a coupler that has a w ide bandwidth to retain the

many frequency components, and is low in dispersion so t h a c the various components

maintain the proper phase relationship t hat makes up the sign.-al.

Microwave coupled-line theory is a very well developed field that has been a subject

of rnuch research over the past fifty years. Coupled transmission lines are very basic

Coupled Port

Input Port

Figure 1.1 A typical L-type coupler in microstrip coniî,mation.

and usefiil microwave circuit components. They are used for many applications such

as directional couplers, filters and baluns. The book "RF and Microwave Coupled-Line

Circuits" by Mongia et al. [2] provides a very good oveMew of the present state of

coupled-line theory and applications. Although the use of coupled lines in microwave

circuits is very well developed, there has been very little research into the use of coupled

lines for digital circuits. A directional coupler suitable for digit al pulses requires time-

domain characterization and performance assessment. Traditional coupled-line theory

focuses on frequency-domain andysis with operation at a certain kequency or over a

limited bandwidt h. Even high-bandwidt h microwave couplers are usually unsuit able for

digital systems due to dispersion or other effects that have an impact on time-domain

performance. A good example of this is the class of broad-band couplers investigated by

Levy [3]. In order to design a high-fidelity digital coupler, a new approach focused on

time-domain performance is required.

The goal of creating a high-fidelity time-domain coupler ras hrst addressed in a

master's thesis by Micah Stickel [4]. That thesis explored the concept of a resistive

directional coupler using resistive strips between the two main lines to provide a direct

coupling connection.

This research pro j ect continues the investigation of high-fidelity digital couplers. A

stripline geometry is used rather than a microstrip structure. The coupler consists of

broadside striplines with a layer of conductive material between them to provide the

required conductive coupling connection. The geometry of the coupler is shom in Fig-

ure 2.2. This basic geometry was decided upon early in the research program in order

to complement Wcah Stickel's findings by estendhg his coplanar-coupler resdts. This

broadside configuration also provided several attractive features such as good control over

different even-mode and odd-mode parameters, rigorous numerical analysis made possi-

ble by analyzing the structure separated into inhnite layers, and int eresting possibilities

for e4xtending the use of the design into areas such as material characterization. There

are many more characteristics of this configuration which will be discussed at greater

lengt h in the follotving chap t ers.

Backward Coupled Signal Foward Coupled Signal

Ground Plane

Figure 1.2 The broadside coupler layout that was eqiored in this research.

The guiding concept of this project is the postdate that a high-fidelity broadside

coupler could be useful in a high-speed digital system. Possible applications include, for

example, using many couplers with weak coupling dong a transmission line to provide a

point-to-multipoint distribution of the digital signal. The coupler should also be directive

so that it could discriminate between signals propagating in different directions on a line.

1.1 Overview

This report is divided into five chapters. Chapter 2 introduces coupler theory and the

reasoning behind the fundamental design of the broadside high-fidelity coupler. Chapter 3

goes into more detail explaining the theory of the high-fidelity broadside coupler. The

relationships between design parameters and performance are e.xplored analytically, and

t hese analyt icaI relations are compared tvit h results obt ained by full-wave elect romagnetic

simulation. Chapter 4 explains the numerica, methods used to analyze the full-wave

electromagnetic behaviour of the coupler. Design case-studies are also introduced in

this chapter. The last chapter, chapter 3, surnmarizes the findings of this research a d

provides ideas for possible future extensLons of it.

Chapter 2

Background

This chapter will introduce the theoretical underpinnings of coupled line theory and

e+.cpand on them to provide an intuitive concept of coupled line behaviour. Coupled-

mode analysis and normal-mode analysis will be described and these treatments will be

used to explain the phenomena of both forward and bacba rd directional coupling. The

suitability of these couplers for digital systems will be discussed and the resistive forward

coupler will be introduced.

2.1 Basic Coupler Theory

Coupled transmission lines consist of three conductors (usudy two transmission lines

and a ground plane) in proximity to one another. For the purposes of this discussion,

two uniform transmission lines will be defined such that they form a four-port network

as s h o m in Figure 2.1.

In this case, a voltage source V, is fed into port 1 and al1 four ports are terminated

in the intrinsic impedance of the system Zo. If a voltage appears at port 3, then this is

knovm as the backnrard coupled signal, and a voltage appearing at port 4 is called the

fonvard coupled sipal.

This thesis wiU refer to forward and backward couplers. A backnrard coupler is one in

=O 3 coupled line segment r:

Figure 2.1 Coupled transmission lines.

which the input power will be transmitted to port 3, with very Little appearing at port 4,

and a forward coupler is the opposite, wïth the input power coupling primarily to port 4.

In a backward coupler, port 3 would be called the coupled port and port 4 would be

called the isolated port. In a forward coupler, these designations would be reversed wïth

port 3 called the isolated port and port 4 being the coupled port. In both cases, port 1

is referred to as the input port and port 2 is called the through port.

In order to describe quantitatively the behaviour of couplers, certain measures of their

performance have been defined, for example in the book by Pozar [5 ] . The first of these

is the coupling factor. The coupling factor describes how much of the input power is

tïansferred to the coupled port. In decibels it is defuied as

PC C = 10 log,, - P r

where Pi is the input power to the coupler, and P, is the coupled power. P, would be

the power at port 3 in the case of a backward coupler and the power at port 4 in the

case of a forward coupler.

Another very important figure of merit for couplers is the directivity. This quantity is

an indication of the coupler's ability to isolate forward and backward waves. The direc-

tivity is a measure of the ratio of coupled signal to isolated signal. It is mathematicdy

expressed in decibels as

1 c D = 10 log,, - pi

where, once again, P, is the coupled power and Pi is the power at the isolated pod.

The operation of coupled transmission lines can be analyzed mathematically by con-

Figure 2.2 The equivalent circuit for an infinitesimal section of coupled iine.

sidering an equivalent lumped-element circuit, as shown in Fiawe 2.2. This analysis Rias

first canied out by Oliver [6] and Firestone [7]. The equivalent circuit describes an in-

hitesimal section of the coupled line. The interaction between the two lines is though

the capacitance between the lines Cm and the mutual inductance Lm. The currents and

voltages dong this section of coupled lines are fully described by the following set of

partial differential equations:

T t should be noted that this model assumes lossless transmission lines and also assumes

a linear isotropic medium such that L12 = L21 = Lm and CL? = C21 = Cm. If these

equations are solved, four independent solutions for the voltages and currents will emerge.

The solutions correspond to two distinct modes, each of which c m propagate in both the

positive and negative z directions. These distinct modes are called the normal modes of

the coupler and are labeled as the c mode and the T mode. Thus the actual voltage at

any point on the coupler is given by the superposition of both the forward and bacha rd

traveling c and n modes.

There are two common methods for malyzing coupled Line circuits knonm as normal-

mode theory and coupled-mode theory. The normal-mode theory, as introduced above,

provides an exact method of analysis and is the better known theory. A pair of coupled

lines can support two independent normal modes which are characterized by having their

currents in-phase and anti-phase- For the special case of symmetric lines, these modes

are the even and odd modes.

Coupled-mode theory, on the other hand, makes some approximations in order to

simplie the analysis [2]. The lines are assumed to be "weaklf' coupled which means

that the intrinsic impedances of the individual lines are affected very Little by the presence

of the coupling. In this case there is very little coupling in the bach~a rd direction and

most of the signal is coupled in the fornard direction.

2.2 Backward Electromagnetic Coupling

The vast majority of previous research and implementation of coupled transmission lines

has dealt with bach~ard-coupled lines. This is because, when two transmission lines are

placed in close proximity to one another, they will naturally produce coupling in the

bach~ard direction, as described by Oliver [6]. This section will delve into the theory of

backward coupling using normal-mode analysis.

For the sstke of simplicity and clarity, symmetric transmission lines will be analyzed

using even and odd mode analysis. It should be noted, however, that normal-mode

analysis is also valid for asymmetric coupled lines and this analysis can be e-xtended to

include them.

A set of coupled transmission lines forms a four-port network. When one or more

sources are attached to the ports of the network, then waves traveling in both directions

are created on each of the lines. The incoming and outgoing waves at each port are

related to each other in a manner described by the s-parameter matrix of the system.

+- v, 3 coupled line segment 4 -

I

(a) even mode

elecmc wail

3. 2

(b) odd mode

Figure 2.3 Even and odd mode excitations. Superposing these two excitations will yield a coupler excited by Vg at port 1.

In the generic coupler shown in Fiame 2.1, it can be seen that there will be many

simplifications in the s-paxameter relationships of the s i sa l s due to the symmetrical and

reciprocd nature of the system. For exampie, the relationship of an outgoing signal at

port 2 to an incident signal at port 1 would be the same as the relationship of an outgoing

signal at port 1 to an incident signal at port 2,

Due to these symmetries, it can be s h o m that if two equal in-phase sipals are

exciting ports 1 and 3, then equal in-phase signais are produced at ports 2 and 4. This is

s h o m in Figure 2.3(5t). This type of excitation is called even-mode excitation. Similady,

if equal anti-phase sources are driving ports 1 and 3, then equd anti-phase voltages will

appear at ports 2 and 4. This is called odd-mode excitation and is shown in Figure 2.3(b).

We c m now see that this particular superposition of even-mode and odd-mode esci-

tations will simply yield a situation where port 1 is excited with Vg m d the remaining

ports are each terminated with the impedance Zo. This situation arises because the

excitations at port 3 are in opposite phase and wiil cancel each other when superposed.

What this means is that the behaviour of the four-port coupled-line circuit c m be fully

coupled Line segment - - , , , , , - , , , , - - - , - - - - magnetic wall

(a) even mode

(b) odd mode

Figure 2.4 Even-mode and odd-mode equivalent circuits. The coupled lines can be analyzed simply as transmission lines with individual characteristic impedances Zo, and Zoo respectively.

characterized by analyzing taro independent two-port devices. Each of the normal-mode

circuits simply consists of a section of transmission line with a voltage source $4 and terminated in impedance 2 0 .

The even mode circuit is shown in Figure 2.4(a). It consists of a section of transmission

line with characteristic impedance Zo, terminated with impedances of Zo and driven by

the source $V,. In general, Zoe is not equal to Zo and thus the input signal is reflected

at the interfaces a t each end of the transmission line. The h s t interface where reflection

occurs is at the junction between the transmissio~ lines and the coupler at ports 1 and

3. This first interface can be seen in the diagram at the left end of the coupled line

segment labeled as port 1. Reflection will also occur a t a second interface which is at the

right-hand end of the coupled line se,o;ment.

At the left end of the coupled-line segment, the signal on the input line will be reflected

with a voltage reflection coefficient of

Similady, the odd mode circuit has an intrinsic impedance of Zoo and will reflect the

input signal at port I with a voltage reflection coefficient of

If we want to match the coupler to the impedance of the surrounding system (Zo), then

we will choose parameters such that there is no reflected signal a t port 1. Sirice the

reflected signal at port 1 is the superposition of the even-mode reflection and the odd-

mode reflection, these two signals must cancel each other. This means that r, = -ïe

or

Solving for Zo, we get the condition necessary for matching a coupler [8] :

If this condition is satisfied, then the input signal to the coupler will not be reflected at

the input port. \mat is interesting to note a t this point is what is happening at port 3.

Since incident waves of the two modes are in opposite phase at port 3, the reflected signals

will not cancel each other but rather will add together to produce a signal at port 3 which

is contra-directional to the input signal at port 1. This is a back~azd coupled signal! It

should be noted that if one does not want a coupled signal at port 3, the o d y way to

eliminate it, while maintaining the matched condition at port 1, is to let Zo, = Zoo = Zo.

Of course this explanatiori. nas o d y considered the reflections at the h s t interface and

the second interface must also be taken into account. The waves incident a t the second

interface will also reflect in a manner similar to the r e f l ~ r t l m at the fitst interface. But

because the waves are nom traveling dong the coupled segment and reflecting off of

20, rather than the other way around, the reflection will be of the opposite s ip . This

means that while the reflections on the first (bottom) line still cancel each other out,

the reflection on the top line will arrive at port 3 delayed by twice the time it takes to

propagate the length of the coupler, and will be of the opposite sign compared to the

first reflection. If the coupler is excited with a sinusoidal voltage, then the maximum

amount of backnard coupling c m be achieved when the retuming wave is delayed by half

a wavelength. This means that the physical length of a coupler for maximum backward

coupling is X/4. It is dso interesting to note that for a matched coupler, the even and

odd signais will remain at the same amplitude and opposite sign a t port 4 and thus they

will cancel each other and there Nil1 be no forward coupling. Of course this is assuming

that they remain in phase, and it will be shown in the nedut section that matched fom-a~d

coupling can occur if there are different even-mode and odd-mode phase velocities.

\Vit h t his descript ion of backward couplers, it becomes fairly intuitive to understand

what happens in the case of a digital pulse. Since the baclavard coupled pulse a t port 3

is created by normal-mode reflections from both ends of the coupler, the coupled signal

will consist of two pulses, one positive and the other negative, separated by twice the

propagation delay of the coupler. This scenario has been simulated and the result c m

be seen in Fiopre 2.5. In addition to these two pulses, a backward coupler with more

coupling mil1 create several more pulses which decrease exponentially in amplitude due to

multiple back-and-forth reflections within the coupler [6]. These are usually very small,

however, and cannot be seen in the exarnple shown. What can be seen, however, are

very small signals leaving ports 1 and 4. These signals are due to very slight mismatches

between the coupler and the connecting transmission lines- This is becaxse equation 3-10

is not satisfied perfectly.

This example is a good illustration of why bach~a rd coupling is not suitable for a

high-fidelity digital coupler. In any coupler in which the coupling occurs over an extended

region, different components of the signal will be delayed by different time intermls and

thus the signal will be dispersed. It is more desirable to have a situation in which the

delay for d l of the signal is equal. Intuitively, it seems that a forward coupler would

accomplish this because al1 of the components of the signal would be traveling along

(a) Porl 1 -Input Pulse

1 . . .

O 0 5 1 1.5 2 25 3 3.5 4 @) Port t - Rellmon

1

1 -I

I I I I , 1 O 0.5 1 1.5 2 25 3 3.5 4

(c) Part 2 - Thmugh-Pulse

, I I 1 I I

O I

0.5 1 1 .S 2 25 3 3.5 4 (q POR 3 - 6aOrward-Cgupled Signai

0.2 I 1

-0.2 I i 0.5 I 1.5 2 2 5 3 3.5 4

(e) Port 4 - ForwardCoupied Signal 0.2 1 I I

Figure 2.5 Pulse propagation through a backward coupler. The baci-i~ard coupled signal (plot d) consists of b o puises, one reflected Erom each end of the coupler.

together through the coupler, and no change in direction would occur which could make

the path lengths different. In other words, since the signal enters one end and eAxits at

the other, there will be a single path length for the signal which is equal to the length

of the coupling region. The following section nill e-uplore the corresponding theory of

fonvard electromagnet ic coupling.

2.3 Forward Electromagnetic Coupling

In the previous section, it was shown that the even and odd mode signals aniving at

port 4 have equal amplitudes in a matched coupler but, since they are in opposite phase

at port 4, they will cancel and no forward coupling will occur. However, this explmation

relies on the fact that the even and odd modes propagate with the same phase velocity,

causing them to remain in opposite phase al1 the way through the coupler until they

arrive at port 4. If the modes travel with different phase velocities, however, t hey will

not remain in opposite phase and thus will not completely cancel each other at port 4.

This results in forward coupling! So by varying the difference in phase between the two

normal modes arriving a t port 4, the level of forward coupling c m be controlled. There

axe three parameters that afFect the phase difference at port 4 and thus the level of

forward coupling. These parameters are the difference in phase velocities of the modes,

the length of the coupler, and the frequency at which the coupler is operating.

Of course this phase difference between the modes does not only occur at port 4 but

also will manifest itself a t port 2, which is the through port. However the situation at

port 2 is the reverse of what is happening at port 4. Normally when the modes arrive

in phase, they will add constructively at port 2 to form the through signal leaving the

coupler. However, when phase shifts are introduced and the sipals become out of phase,

they will start to interact destructively at port 2 and the through signal will become

weaker. So, as the phase shift between normal modes is increased, a signal will appear

and begin to grow at port 4 as the signal at port 2 gets weaker. The net effect is that

the input power is coupled to the forward port-

It should be noted that backward coupling will still occur if there are impedance

differences between the normal modes. For a forward coupler to have high directivity it

is therefore necessary to reduce the bacha rd coupling by equalizing the odd and even

mode impedances. Usually, the way to equalize these impedances is to space the Lines

farther apart, thus reducing the interaction between them. Forward coupling c m remain

strong, however, as this couphg is created by differences in phase velocity between the

modes and thus loosely coupled Lines can achieve quite good fornard coupling.

It is interesting to consider what happens when the coupler is long enough for a

relative phase shift between the two modes of rr radians (equivalent to a differential line

length of X/2) to be reached at the far end of the coupler. When this happens, the modes

arriving at port 4 will be exactly in phase and Rrill add up to the full input voltage. The

signals at port 2, by contrast, will be completely out of phase and thus e l 1 cancel each

other completely. m a t this means is that full O dB coupling can be achieved with a

fonvard coupler as long as the coupler satisfies the equation

where Ltot is the length of the coupling region and P, and P, are the propagation constants

for the even and odd modes respectively. It is interesting that loosely coupled lines can

achieve full power transfer if there is a difference in phase velocity between the even and

odd modes and if the coupling region is sufficiently long. The corollary of this is that,

for a . q symmetric forward coupler, there will be a certain frequency at which there is

full power transfer to the coupled port.

A plot of s-parameters versus fiequency for a typical forward coupler is shown in

Figure 2.6. In this plot we can see that there is still backward coupling by the sl3 curve

which rises to about -10 dB. It also is not perfectly matched as the sll curve also rises

to about -10 dB similarly to the sis curve. The interesting plots, however, are the curves

F r e q u e n c y 2 . 0 G H z / D i V

Figure 2.6 The sparameter plot for a forward electromagnetic coupler. The circuit simulated was in a broadside stripline configuration wïth dielectric of permittivity E, = 9.8 between the two coupled lines and e, = 2.2 between the lines and ground. The coupling region is 5 cm long. The curves are labeled by: Osil, 0 ~ 1 2 , V S ~ J , AS^^.

of SI* and ~ 1 4 - TVe c m see that s l 4 rises to almost full coupling at about 5 GHz at the

same frequency where s i 2 is a t a minimum. This graph also illustrates that maximum

forward coupling typically occurs at higher frequencies, or at longer coupler lengths for

the same frequency, than maximum bachward coupling.

For asymrnetric couplers, full power transfer is not achieved because the two normal

modes do not add to full power a t port 4, and do not fully cancel at port 2. This

fact is used to create wide-band fommd couplers [ Z ] . The coupler ni11 have the widest

bandwidth at the top of the sl4 cuve where the curve is level. Therefore, if one wants

to create a wide-band fornard coupler at any arbitrary level of coupling, the widest

bandwidth c m be obtained if the device is operating a t the point of maximum coupling.

Any coupler which is in a non-homogeneous medium in which the modes are not

TEM will have different even-mode and odd-mode phase velocities and thus can achieve

ground plane dielectric 1

input signal

I I

coupled signa1

Figure 2.7 Layered dielectric structure for forward coupling.

dielectrîc I I I 1

fonvaxd coupling. This effect has been used to build forward couplers on microstrip such

as the one described by Ikalainen and Matthaei [9]. The different dielectric constants

of the media affect the propagation constants of each mode differently and thus create

fomard coupling. If one considers the broadside stripline coupler geometry that this

thesis is investigating, it becomes apparent that certain distributions of materid ni11

mauimize the difference in phase velocities between the modes and will thus lead to strong

fomard coupling with short couplers. In a broadside coupler configuration, odd-mode

excitation rvil concentrate most of the electric field lines between the two transmission

lines whereas during even-mode excitation there will be less electric field between the

two lines (since they are excited to the same potential) and more of the field Line will be

concentrated between the transmission Lnes and the ground planes. It t herefore follows

that significantly different propagation constants between even and odd modes can be

created if different dielectrics are layered as shown in Figure 2.7. The dielectric medium

is layered such that dielectric 2 between the two lines has perrnittivity different than the

two outer regions with dielectric 1. If the dielectric is configured in continuous layers like

this, then the structure is quite convenient since it can be readily aiialyzed using well

known layered structure analysis algorithms .

I I gound plane I

Once again, as with the backward coupler, we can also understand the propagation

of a pulse through the coupler using even and odd mode analysis. To gain an intuitive

understanding of what is happening when a pulse travels through the forward coupler,

one simply has to visualize what wiU happen w h e n the even and odd mode pulses arrive

at the far end of the coupler at different times. At port 4 the even and odd mode

pulses are of opposite polarity and therefore u_suaUy cancel each other. In a fonvard

coupler, however, the two pulses will not arrive simultaneously so the front edge of the

h s t a- iiving pulse and the trailing edge of the second pulse RriU not be cancelled. If the

relative shift of the two pulses is not very large Pthen parts of the pulses will overlap and

cancel. The net effect of this is a positive and a negative spike of voltage with cancelled

signal between them as shown in Piave 2.8-

The through signal (port 2) is also affectecl by the pulse not being aligned. In the

case of the through pulse, the lack of a l i b ~ e n t ; will manifest itself as lowered levels at

the edges of the pulse. It will look like a "step-" a t half of the full pulse height where

the even and odd mode pulses are not adding tagether. As the phase shift of the pulses

increases, as in longer couplers for example, th% step would become larger and larger

until the signal h a l l y breaks into two separate pulses.

Once again we can see that this coupling nnechanism will not be able to produce

high-fidelity coupling for digital pulses. Because the coupling mechanism relies on phase

velocity difference and shifts in the modes, any eoupling that occurs will introduce dis-

tortions to the signal.

2.4 Conductive Coupling

Since neither forward nor bachard electromagneitic coupling have been found suitable for

provïding high-fidelity coupling, a novel coupling mechanism must be used. The concept

of using a conductive connection to provide the coupling fbst arose out of the idea that

it would be necessaq to provide a direct-curent- connection to the coupled signal.

The only known previous work on high-fidelnty digital coupling was done by Micah

(a) Port 1 - Input Pulse I ,

I I I I I O 0.5 1 1.5 2 25 3 3.5 4

(g Port 1 - Rafleam

O 0.5 1 1 5 2 2 5 3 3.5 4 (c) Part 2 - Thrwgh-Pulse

I I

1

I t I I O 0.5 1 1.5 2 25 3 3.5 4

(d) Part 3 - Backward-Coupied Signal

O.'" i 1

- 0 5 . . , . I I I I , O 0.5 1 1.5 2 2.5 3 3.5

(el Port 4 - Fwward-Couded Stgnai

Figure 2.8 A pulse propagating through a forward e l e ~ t r o r n a ~ e t i c coupler. The effects of fortvard electromagnetic coupling can be seen in the through-pulse (plot c) where the spreading of the modes creates a "step" at 0.5 V. The unaligned modes also produce two '%pikesn in the fornard coupled signal (plot e).

Coupled Line

1 Main Line

Figure 2.9 A resistive directional coupler made with resistive strips.

Stickel using resistive strips comecting the two coupled lines. A conceptud picture of

this type of coupler is shown in Figure 2.9. This was a time-dornain adaptation of a

frequency-domain design by Jenkins and Cullen [IO]. Stickel's research found that this

type of coupler was able to achieve directional qualities over a wide bandwidth, and

maintain good reproduction of the input pulse at the coupled output port [4].

Using resistive strips is practical for a microstrip structure where the strips are laid

out in an edge-to-edge configuration7 but a different configuration is more suitable for

a broadside layout . Similarly to the forward electromagnetic coupler introduced in the

previous section, it was felt that a layered structure would be appropriate to provide

the conductive connection between the coupled lines. By inserting a layer of conductive

material between the two Iines, a continuous conduciive connection is made. The basic

structure is shown in Figure 2.10.

Although the coupling mechanism of this device is similar to Stickel's coupler, there

are rnany important differences that m r a n t investigation. First of all, the lines are

broadside to each other rather than edge-coupled. This means that the performance pa-

rameters will be difTerent. It was felt that these differences would be valuable to explore

as they could provide the basis for implementing couplers for different applications. An-

other significant difference is that the resistive connection is in the form of a continuous

layer ïather than in discrete elements. This is significant when considering t heoretical

modeling of the coupler. Stickel used discrete elements, each cont aining one conduc-

--

insulating material ground plane

conductive material

ground plane I i

input signal coupled signal

I insulating material

I I

Figure 2.10 Broadside conductive coupler layout -

tive connection, to create a transmission line mode1 for the system. The analysis of the

broadside coupler will be different since it consists of a contuiuous conductive connection.

The broadside layered structure has some useful properties for designing a coupler.

As mentioned in the previous section, using continuous layers of dielectric, which are

modeled as i nh i t e layers for numerical simulation, allows for the use of well established

simulation algorithms to mode1 the structure. It was also felt t ha t continuous layers

could be convenient for physically building the circuit. For example, the coupler could

be built by sandwiching the conductive material between two microstrip substrates. In

a multi-layer circuit board, it may also be convenient to build structures which consist

of uniform layers.

Since the broadside conductive coupler structure used in this project consists of a

continuous couplinp region, it is best ~mderstood by regarding it as a continuous whole

rather than by breaking it up into segments. The easiest way to understand the cou-

pling mechanism is as a combination between transmission line theory and static circuit

principles. In this overview, it will be assumed that the conductivity of the conductive

layer is quite small compared to the intrinsic impedance of the coupler. Having high

conductivities complicates the analysis and will be discussed in more detail in the next

chapter.

For the forward traveling pulse, the input signal and the coupled signal will remain

in the same position with respect to each other as they travel together dong the length

Figure 2.11 Fornard conductive coupling equivalent circuit.

of the coupler. Since the power of the input pulse is being coupled to the output pulse

dong the whole length of the coupler, the forward coupling circuit c m be rnodeled as

a resistance corresponding to the entire length of the coupler connecting the input and

output ports. This mode1 is s h o m in Figure 2.11. The value of Rf, is determined by the

resistivity of the conductive layer multiplied by the separation of the lines, and divided

by the area of the coupling region.

The b a c b a r d coupled signal, on the other hand, travels in the direction opposite

to the input signal. Since the two signals do not remain beside each other, the coupled

signal d l be much lower, but i t will also be stretched out in time. Essentially, the height

of the b a c h ~ a r d pulse will be determined as if there is a much higher resistance in the

equivalent circuit, but the signal will be distorted to become much wider.

Therefore we c m see that the frequency-independent nature of the conductive con-

nection forms a pulse at the forward coupled port which is the same width and shape as

the input pulse, and that the b a c h a r d coupled pulse will be lower in amplitude than

the forward coupled pulse. From this superficial look at forward conductive coupling, it

seems that it should satis& the requirements for a high-fidelity directive coupler. The

following chapter will delve more deeply into the behaviour of the conductive coupler and

characterize the behaviour in order to allow for the design of high-fidelity couplers which

behave in whatever manner is desired.

Chapter 3

Coupler Design

This chapter deals with the performance of the coupler and how it can be controlled by

varying the physical design. The measures of coupler performance are introduced and

then the relationships between the performance and the physical parameters of the device

are discussed and explained. This understanding of coupler performance is then used to

corne up with a design procedure for creating a coupler which wil l behave according to

given specificat ions.

3.1 D efinit ions

A diagram of the general dimensions of a broadside conductive coupler is shown in Fig-

ure 3.1. The structure consists of two ground planes on the top and bottom of the

structure Mth two broadside coupled lines in between. The coupled lines are spaced

evenly between the ground planes. The dielectric medium which ms the space is divided

into three layers, with the middle layer possessing some conductivity, a. The width and

length of the coupled lines as well as the spacing of the layers are defined by the symbols

shown in the diagram.

The dielectric constants of the dielectric layers are denoted in the figure by €1 and

€2. However, for the majority of the couplers investigated in this project, the dielectric

Centre conducting Iayer

Figure 3.1 Dimensions and physical parameters for the broadside conductive fcmard coupler.

constant was kept uniform throughout the coupler and in these cases will be referred to

as 6,.

There are several characteristics of coupler performance. Some of these characteristics

are general rneasures that can be used to characterize any coupler. These include the

degree of coupling, the directivity, and the extent to which the coupler is matched to

the surrounding circuit. Other performance rneasures are specific to high-fidelity digital

coupling. Pulse fidelity is a measure of how closely the shape of the coupled pulse matches

that of the input pulse. Energy loss is also a characteristic of conductive couplers.

Because currents will travel through the conductive dielectric, energy will be lost to

ohrnic dissipation and it is usu- desirable to keep this loss as low as possible-

Conductive Coupler Theory

The previous chapter of this thesis introduced the theory behind forward and bachard

electromagnetic coupling, as weil as introducing conductive coupling. The waveforms

that appear at each of the ports of a conductive coupler will be composed of various

amounts of each of these types of coupling. I t was previously noted, however, that

only the coupling caused by the conductive connection between the lines will produce a

high-Edelity signal at the forward-coupled port. Because of this, a high-fidelity coupler

should be designed such that conductive coupling is the dominant form of eneroT transfer

between the lines. This design goal will impose several constraints on the desis of the

coupler-

Conductive coupling can best be understood by k s t considering the case where the

conductivity between the two coupled lines is very low. In this case the resistive loss in

the conducting region ni11 be very low and it becomes possible to make approximations

that simplify understanding of conductive coupling. It will be assumed that the s ipals

traveling on each line do not lose energy to resistive dissipation or through couplhg to the

other line. Of course it is necessary for the input signal to lose some energy to produce

a coupled signal at the output port. But in this case of low conductivity, the coupled

energy will be very small compared to the input energy and therefore the energy lost

fi-om the input signd will be insignificant compared to the input energy-.

Of course in a practical design of a high-fidelity conductive coupler, these approsima-

tions may not prove to be valid. Thus one of the primary goals of this project is to get

an idea of when these approximations are valid. It is also important to understand how

deviations from this simplified model will manifest themselves in the performance of the

coupler.

But fkst the simplified model must be understood. A conceptual diagram of a simpli-

fied forward coupler is s h o m in Figure 3.2. This diagram shows the input signal traveling

from left to right through the coupler on line 1. This signal entered the coupler a t port 1

and will leave as the through pulse at port S. Also shown are the fornard and backward

coupled signals on line 2. The purpose of this diagram is to illustrate how the forward

and backward coupled signals are generated from the input signal through conductive

coupling.

Backward Coupled Pulse Forward Coupled Pulse

Line 2

n- Line L

(a) Pulses at time to

Backward Coupled Pulse - Forward Coupled Pulse

P L Line 2

n Line 1

1 \ Input Pulse

(b) Pulses at time to f At

Figure 3.2 This is a simpiified mode1 of conductive coupling- The waveforms in these figures represent voltage distributions on each of the coupled lines a t two snapshots in time. The voltage on line 2 has been decomposed into the forward-coupled signal and the bacbard-coupied signal which are differentiated by their directions of travel. The actual voltage on line 2 will be the sum of these two waveforms. As time passes and the input pulse travels along the coupler, the forward coupled puise wiU increase in amplitude while retaining the same Rridth as the input pulse, whereas the backward coupled pulse will not add to its amplitude but will grow wider.

Since the forward-coupled signal is traveling in synchronism with the input signal,

energy transfer will add to the amplitude of the fornard-coupled signal for the entire

length of the coupling region. As tirne progresses, energy transfer to the fomard-coupled

pulse will add to its amplitude. This means that for forward coupling the distributed

nature of the coupling does not need to be taken into account. In other words, the

coupling region can simply be considered as a resistor corresponding to the total DC

resistance of the coupling region connecting the two lines together. This resistance can

be calculated according to the equation

where S, L, W and a are d e h e d in Figure 3.1. This means that the strength of the

fomwd conductive coupling will increase with increasing coupler length, width, and

centre layer conductivity and the coupling Fvill decrease with more distant line spacing.

The situation is quite different, however, in the case of the backward coupled signal.

In this case, the coupled signal is traveling in a direction opposite to the input signal.

Since the pulses do not remained aligned, the energy from the input signal Rrill couple to

the bachward coupled signal over a very wide region and therefore the bach-ard coupled

signal will be very spread out. The duration of the conductively coupled bachward

pulse is dependent on the length of the coupler, in fact it will be equal to twice the

propagation time over the length of the coupler. This is because the input pdse and

the bacbard pulse will couple over the length of the coupler as both are traveling in

opposite directions. The energy transfer from the input pulse to the bachward-coupled

pulse will always be occurring at the trading edge of the backward-coupled pulse and

t herefore as t ime progresses, the backward-coupled p d s e increases in durat ion, but the

amplitude of the pulse does not increase. Because the coupling is spread out like this, the

amplitude of the backward coupled pulse will be much lotver than the forward coupled

pulse. The equivalent resistance that determines the amplitude of the backward coupled

signal will therefore be much larger than the equivalent value for the forward coupled

Table 3.1 The Effect of Design Parameters on Coupled-Signal Amplitudes

II Electromagnetic Couplirg 1 Conduct ive Coupling

Parameter I/ Bachard 1 Fornard

Note: 7 means an increuse, while \ means a decrease.

w / i L /

Pulse Duration f

signal. Figure 3.2 shows why the fommd-coupled pulse will be the same duration as the

input pulse, whereas the backward-coupled pulse will have a Ionger duration and lower

amplitude t han the fora-md-coupled pulse.

B a c b a r d

The general characteris tics of fornard and bacha rd coupling for both electromagnetic

and conductive coupling have now been discussed and axe summarized in Table 3.1.

The conductive coupling behaviour in this table corresponds to the low-loss case for

the coupler, and would be difFerent once the conductivity (a) increases beyond a certain

point. For example, once losses become dominant, sign3cant energy will be lost to ohmic

dissipation and the coupled signals will begin to decrease. More detailed descriptions for

specific performance parameters and discussion of higher-loss cases are presented in the

next section.

Fornard

N P

no change

no change

N/A

f

no change

7

no amplitude change

longer duration

/

/"

/

no amplitude change

Ionger duration

3.3 Design Relations

In this section, each of the performance measures wïll be discussed in tum. The relation-

ship between the performance and the design parameters will be explored with the go&

of understanding how to design a coupler with the desired performance.

3.3.1 Matching

Matching of a device deals with the practical fact that the device must be connected to

a surrounding circuit which has a certain characteristic impedance associated with it.

Essentially, it is usually desired that the impedance seen rvhen looking into the device

corresponds to the characteristic impedance of the surrounding circuit. This means that

there d l not be reflections from the device due to interfaces with the outside connections.

Looking at the coupler in terms of normal mode theory, it was shonm that the even-

mode and odd-mode impedances must sa t ise Equation 2-10. Since both Zo, and Zoo

depend on H, S, W and E, when these parameters are varied, their values must be con-

strained such that Equation 2.10 is satisfied. For example, if the spacing of the coupled

lines is chmged, the Mdths of the lines must be altered in order for the coupler to remain

rnatched.

The values of Zo, and Zoo can more easily be related to the values of the components

in the equivalent circuit shom in Figure 2.2. In this case, Zo, and Zoo are given by

and

where the variables L I , Lm, Cl and Cm are defined in Figure 2.2. T t should be noted

that these equations apply to the case of a symrnetric coupler such that LI = L2 and

Cl = C2.

When looking at the even and odd modes of coupled transmission Lines, it is usefd

to dehne equivalent capacitances for each mode. These equivalent capacitance networks

are shown in Fiove 3.3. During the odd-mode excitation, since the two lines have equal

and opposite potentids, an equivalent electric w d (short circuit) can be placed between

the lines and the capacitance SC, will be added to Ci making the equivalent odd-mode

capacit ance

The even-mode equivdent circuit, on the other hand, has an equivalent magnetic wall

(open circuit) between the lines and therefore Cm does not &ect the even-mode capaci-

tance. The even-mode equivalent capacitance is therefore

These equivalent capacitances are useful because they can be used to reduce the even

and odd mode characteristic impedances to the following form [2]:

and

where vpe and v, are the phase velocities of even and odd mode signals respectively, and

Ce and Co are the even-mode and odd-mode equivalent capacitances. If the coupled lines

are in a homogeneous medium, then

where c is the speed of light and E, is the dielectric constant of the medium.

It is now useful to define two new quantities, the capacitances Co, and Co,. These will

be defined, respectively, as the even-mode and odd-mode capacitances of the coupled lines

obtained when the dielectric constant of the surrounding medium is replaced by unity.

Open Circuit I I I

Short Circuit

- --

~ r o u n d - -

(a) Even-mode (b) Odd-mode

Figure 3.3 Representations of a line wïth either an open circuit (magnetic d l ) in the case of the even-mode circuit, or a short circuit (electric wall) in the case of the odd-mode. These electric and magnetic walls account for the s-vmmetry wïth the other coupled line which would be located above the electric and magnetic waUs.

They âre therefore related to the even-mode and odd-mode equivalent capacitances, Ce

Equations 3.8 and 3.9 can then be substituted into Equations 3.6 and 3.6 in order to

yield the espressions

and 1 zoo = (3.11)

c*Coo

which describe the even and odd-mode characteristic impedances in terms of the geomet-

ric parameters Co, and Co, and the dielectric constant of the medium. These expressions

are useful because they separate the effect of the dielectric substrate fiom the variables

Coe and Cao which depend only on physical dimensions. The even-mode and odd-mode

chaxacteristic impedances both Vary inversely with the square-root of the dielectric con-

stant of the substrate material.

To understand how difFerent design decisions will manifest themselves in the coupler,

it is important to remember that the even and odd mode characteristic impedances must

Figure 3.4 This is the relationship between line width (IV) and dielectric constant (6,) such that the coupler remains matched to 500. The other dimensions are kept constant at B = lmm and S = 0.8mm.

satisfy the matching condition given by Equation 2.10. For example, if the dielectric

constant of the medium is increased, then the capacitances Co, and Co, must be lowered to

ensure that the coupler remains matched. This is most easily accomplished by decreasing

the line width of the coupled lines. Figure 3.4 shows a plot of line width versus dielectric

constant for a coupler that is matched to 5052. The plot shows that increases in dielectric

constant will require narrower line widths in order to keep the coupler matched. The

data for this plot was generated with the transmission line simulator Linecalc.

When modifying physical dimensions, the relationships between them are more corn-

plicated- A good example of this can be seen by considering variations in the spacing

of the coupled lines (S) when the overall spacing between the ground-planes (B) is kept

constant. Varying line spacing in this manner will affect two capacitances. It will affect

the capacitance between the lines and ground (Ci), and the mutual capacitance between

the lines (Cm). These capacitances are manifested in Equations 3.10 and 3.11 in the

capacitances Co, = Cl/€, and Co, = (Ci + ~C,)/E,. If the line spacing is increased, and

no other parameter is varied, then Cm svill decrease as the lines become fa.rther apart,

whereas Cl will increase as the line get closer to the ground planes- It is therefore not

immediately obvious how varying the line spacing will affect the matching and the other

variables of the coupler.

It is useful to consider two es-treme cases for line spacing in order to gain an intuitive

understanding of how it will affect the coupler design. The first case is for very smail

values of line spacing. WXen the line spacing is very small, the mutual capacitance

between the lines will be much greater than the capacitance between each line and the

ground planes. Also, when the lines are close together, small variations in line spacing

will have a si,o;nificant effect on the mutual coupling, but will only change the capacitance

between the lines and growid very slightly. If a very close line spacing is increased, then

the mutual capacitance between the lines will decrease and the capacitance between the

Lines and ground (Cl) will not change significantly. In order to keep the coupler matched

to the characteristic impedance of the surrounding circuit: the line width must then

be increased to increase the mutual capacitance of the lines, thus compensating for the

increased spacing between the Lines. Therefore, when two coupled lines are spaced very

closely together, line spacing and line width must be increased together in order to keep

the coupler matched to the characteristic impedance Zo.

The situation is quite different when the lines are spaced far apart and the Line

spacing is approaching the ground-plane spacing. In this case the lines are very close to

the ground planes, Le. H is very much smaller than S, and therefore the capacitance Cl

will be much larger than Cm. This means that the odd-mode capacitance wil l approach

the same value as the even-mode capacitance.

This means that the even and odd mode characteristic impedances will also approach

each other when the line spacing approaches the same value as the ground plane spacing

and therefore the backward electromagnetic coupling will approach zero. In order to

Figure 3.5 This is the relationship between line width (W) and line spacing (S) such that the coupler remains matched to 50Q. This example uses a substrate with a dielectric constant of 2.2 and the ground plane spacing (B) is kept constant a t Imm.

maintain matching for large coupler spacings, the width of the lines must be decreased

as the lines approach the ground plane in order to maintain a constant value for the

capacitance Cl. This means that increasing the line spacing requires narrowing the lines,

Mth the line width approaching zero as the line spacing approaches the ground plane

spacing.

By observing both of these extreme cases together, we c m see that for both very small

line spacings, and for very large line spacings, the width of the lhes will tend towards

zero. This means that there must be a maximum value for line width somewhere between

these two extremes. A plot of line *dth versus line spacing can be seen in Figure 3.5 in

which the line width tends towards zero at both extremes of line spacing, and achieves

a maximum of about 0.6 mm between these extremes. This plot is for a particular value

of dielectric constant of the substrate, and using different dielectrics would simply move

the curve up or down on the W axis according to the curve shown in Figure 3.4.

The importance of ensuring that the coupler is matched to the surrounding circuit

imposes constraints on the coupler's design. The main parameters that can be varied

in order to affect the performance of the coupler are the coupledl line spacing, the Iine

nridth, the length of the coupling region, the dielectric constant of the substrate, and the

conductivity of the centre layer of dielectric. The coupler's length e l 1 not affect matching

and c m thus be varied independently at WU. The conductivity of the central region also

mill not affect matching significantly for the small values of conductÉivity that will be used

for a high-fidelity conductive coupler. The remaining three parameters, however, affect

matching sim@ficantly. They cannot be varied independently of each other but Rrill be

constrained as has been discussed in this section.

The coupling factor of the coupler refers to the ratio of the couplied signal to the input

signal and is usually expressed in dB. The coupling factor is t radi t iondy defined at a

certain fiequency or over a certain bandwidth and can be calculated using Equatioo 2.1.

However, This equation is not appLicable for digital pulses. Since the digital pulses are

time-domain signals, the coupling shouid be defined with respect t~ O the total energies in

each signal. For this reason, the coupling in decibels wiil be defined as

where El is the input energy and E4 is the energy at the forwaxd-ccoupled port.

As rnentioned earlier, for the low loss case of a conductive coupder, the couplinp Ievel

can be calculated using the DC resistance of the coupler, Rfo,, in the equivalent circuit

shown in Figure 2.11. This circuit has been redrawn in F i b ~ e 3.6 in order to make the

analysis of the coupling strength more understandable. This circinit is a DC equivalent

circuit of the coupler which allows quasi-static analysis of forward- conductive coupling.

It cannot be used to calculate the backward conductive coupling Level. It also does not

take into account the bacbard electromagnetic coupling.

Figure 3.6 This is the equivalent DC circuit of the conductive coupler. It is equivalent to the circuit s h o w in Figure 2.11- The resistor Rfo, is the total resistance of the central dielectric Iayer.

The instantaneous power of the the signal at port

where Zo is the impedance of the port and v,(t) is the

n at my instant t is given by

(3.14)

instantaneous voltage at that port

at any time t. From this e.upression, the total energy of the signal can be obtained by

integrating the power over the duration of the pulse. This yields

where tl and t2 represent the beginning and the end, respectively, of the time period over

which the signal's energy is being measured and En is the total energy at port n for that

time period.

If the input at port 1 is a rectangular pulse with a voltage amplitude of VI, the integral

of equation 3.15 will become a multiplication of the square of the voltage level and the

duration of the pulse. This is ex-pressed as

where Tp is the duration of the pulse. The coupled energy at port 4 can similarly be

expressed as

where is the voltage amplitude of the rectangular pulse at port 4. This allows the

CHAPTER 3. COUPLER DESIGN

energy coupling factor of Equation 3.13 to be expressed as

where VI is the amplitude of a pulse traveling along the transmission line attached to

port 1. A theoretical value for coupling can be obtained by evaluating the voltages VI

and V4 in the quasi-static equivalent circuit for the coupler s h o w in Fi,we 3.6.

Because of the resistive c o ~ e c t i o n between the two ünes, the input impedance of the

coupler at port 1 will be different kom the characteristic impedance of the transmission

line, and some of the input signal Nill be reflected with a voltage reflection coefficient of

where Zin is the impedance of the coupler looking in a t port 1. Due to this voltage

reflection? the voltage K R will be lower than VI. The voltage Kn can be expressed as

The voltage .en is the voltage that will couple across the resistor RI,, so the ratio of V4

to K R is obtained by voltage division between the two resistances Zo at ports 3 and 4 in

parauel, and the resistance Rfw This leads to the equation

By combining Equations 3.20 and 3.21, the

This is then substituted into Equation 3.18

ratio of V4 to Vl

to obtain the energy coupling factor in deci-

bels:

This equation assumes that there is no electromagnetic coupling occurring in the

coupler. If there is any backward electromagnetic coupling taking place, however, some

energy wïll be reflected at each end of the coupler causing the forward-coupled signal to

be at a lower level. The amount of energy reflected from each normal mode of excitation

is given by the reflection coefficients in Equations 2.7 and 2.8. Each normal mode of the

coupler is excited with sources of amplitude ;v,. Looking a t the coupled line of the cou-

pler, one sees that the junction at port 3 will refiect a voltage of amplitude $4 (r, - r,), and similarly that the junction at port 4 will reflect a (r, - r,) proportion of the volt-

age. Tlierefore, to take the effect of backward electromagnetic coupling into account,

the e.qression for voltage coupling level given in Equation 3.22 must be multiplied by

(1 - (L - r*)), Yie lbg

1 Cv = - (1 - re + r,)

2 (3.24)

where Cv is the coupled voltage amplitude relative to the input voltage. The decibel

coupling value d l then become

Plots comparing these theoretical coupling values to values obtained kom fd-wave

electromagnetic simulations are presented in Figure 3.7. These plots consider a coupler

where the dimensions are kept constant while the conductivity of the middle dielectric

layer is varied in order to change the coupling strength of the coupler. The coupler for

this example is in a medium of dielectric constant 2.2 and has a ground-plane spacing of

Imm. The coupled Iines are separated by a distance of 0.4mm, t h e Mdth of the lines is

0.6m.q and the length of the coupling region is 5 0 m . The d u e s for even-mode and

odd-mode characteristic impedance were calcdated using Linecalc and were found to be

20, = 70.418 and Zoo = 37.345 respectively.

The theoretical values of coupling in Figures 3.7(a) and (b) are calculated from the

transmission-fine mode1 using Equations 3.24, and 3.25 respectively and are represented

by the dashed lines in the plots. The data from the full-wave simulation for coupling

level in Figure 3.7(a) was obtained by using the voltage amplitude of the pulse at port 4.

(a) Coupled signal level in volts for a one volt input pulse

(b) Coupling in terms of decibels of total signal energy

Figure 3.7 These plots show the coupling level both in terms of voltage Ievel and in decibeis. The dashed line is the coupling level predicted using transmission-iine theory, whereas the points are da ta £rom full-mave simulation of the circuit. The values for voltage level are obtained by using the voltage amplitude of the coupled pulse which was generated from an input pulse of one volt amplitude. The decibel values are obtained from the total energy of the coupled pulse by using the area under its voltage versus time plot.

Because the input pulse had an amplitude of one volt, simply looking at the forward-

coupled pulse in the time-domain plots of the pulses would give the coupling level.

The plot in Figure 3.7(b) is obtained using a different method. The energy integ-ral

of Equation 3.15 t ~ a s carried out by numericdly summing the squares of the voltages

over a wide range (4 ns) of the tirne-domain simulation data using Matlab. Once the

total energies at the input port and at the fonvard-coupled port are determined, the

coupling is calculated using Equation 3.13. This method will represent the total energy

in any randomly shaped signal and will therefore represent not only the energy in the

conductively coupled pulse, but wiU also include the energy of any spurious voltages that

are present.

Both the plot using coupled signal levels and the data from the energy calculations

match very well with the t heoreticd predictions from transmission-line t heory. This

indicates that the transmission-line mode1 for fomard coupling is valid and should be

useful in the design of high-fidelity conduc tive couplers,

3.3.3 Loss

Conductive couplers are inherently lossy because they rely on a resistive connection to

transfer energy from the input to the coupled port. Whenever any enereT is coupled,

some of it will be lost to ohmic dissipation in the conductive region. For a practical

coupler it is desirable to keep the losses as low as possible so that both the through

signal and the coupled signal retain as much energy as possible.

There are two main types of loss to take into account when considering the loss of

the broadside conductive coupler. The h s t of these is simply the DC resistive loss of the

conductive connection between the two coupled lines. This DC loss can be understood

by looking at the equivalent DC circuit for the coupler shown in Figure 2-2. The loss

can be calculated as the proportion of energy that is dissipated in the resistor Rb,

compared to the total energy put into the circuit. The value for the resistor Rh, c m be

calculated based on the conductivity of the centre layer and coupler dimensions according

to Equation 3.1. The total conductance can be similarly calculated with the equation

where Gtot is the total conductance comecting the two coupled lines, L, W, and S are

the coupler dimensions s h o m in Figure 3.1 and a is the conductivity of the central

conductint; layer. Since the DC loss is dependent on the total resistance comecting the

two coupled lines, the loss nrill be aifected by varying any of the circuit dimensions or by

varying the conductivity of the central dielectric Iay-er.

When the conductance of the centre layer is low, the loss will d s o be very low and the

loss will increase linearly with increases in the conductance. However, as losses increase,

the value of the conductance will become comparable to the characteristic impedance

of the circuit. For example, a typical characteristic impedance of 50R is equivalent to

a conductance of 0.02 Siemens. This means that as the conductance of the coupler

approaches 0.02 Siemens, the loss will be significant and tvill begin to deviate from a

straight line. This c m be seen in Figure 3.8 nrhich shows the variation of loss Rrith

conductance for a conductive coupler. The data for this graph was obtained from full-

wave simulations of a coupler with a dielectric constant of 2.2. The conductivity of the

centre layer was varied while the circuit dimensions were kept constant. The coupler had

a ground plane separation of Imm, a line separation of 0.4mm7 line of width 0.6mm7 and

the total length of the coupler m a s 50mm.

The purpose of this plot is to show that if it is desired to keep l o s in the coupler

below a certain level then the conductance must be kept below a corresponding value.

For example, in order to keep the loss below thirty percent, then the total conductance

of the coupler will be constrained to be lower than 0.1. This restriction will in turn

constrain the possible choices for the design parameters of the coupler. For example, if

one Mshes to increase the length of the coupler, this may raise the conductance above the

desired level and it will have to be compensated for with another parameter. In this case,

Figure 3.8 Increasing the conductivity of the centre layer of dielectric will cause the energy loss in the coupler to increase in a marner which is roughly linear for very low conductivities, but which gradually c u v e s domward and levels off as the total conduc- tance of the coupling region becomes comparable to the characteristic impedance of the system. The horizontal mis represents- the total conductance between the two lines, and a line has been drawn at a conductan~e of 0.02 Siemens nrhich corresponds to 50 ohms. This plot is for a coupler with dimensions B=imm, S=0.4mm, W=0.6mm, L=50mm, and nith a substrate of dielectric consgant 2.2.

increasing the coupler length could be compensated for by lowering the conductivity of

the centre conducting layer.

The second type of loss to consider is the frequency-dependent loss in the conductive

dielectric. For ainy electromagnetic field in a lossy medium, a current tvill Bow according

to the equation

where J i s the curent density at a p a n icular point, o is the conductivity of the medium,

and Ë is the electric field at that point. Substituting this relationship into Maxwell's

curl equation for H

v x H = j w B + J (3.28)

From this equation it can be seen that the ratio of a to WC wi11 determine whether the

conductivity (a) Rill have a s m d or a large effect on electromapetic fields that exist in

the medium. For o << (we), the conductivity of the medium has a negligible effect and the

material is considered low-loss. As the conductivity increases and becomes comparable in

value to we, it will start to significantly affect electromagnetic fields in the medium and

significant conduction currents will flow. What is important to note here is that it is not

the value of conductivity alone that determines whether the material is lossy, but rather

it is the ratio of conductivity to the dielectric constant of the medium multiplied by the

angu1a-r frequency of the e l e c t r ~ m a ~ e t i c oscillation. This means that the lossiness of the

material d l vary for different frequencies. The concept of a high-fidelity coupler is that

fidelity c m be achieved by reducing or eliminating frequency-dependent behaviour. The

fact that this loss is frequency-dependent implies that if it becomes ~i~onificant it may

adversely affect the fidelity of the coupled signai.

This Ioss is also dependent on the dielectric constant of the medium. As the dielectric

constant increases, the ratio of conductivity to the dielectric constant of the medium mul-

tiplied by the anodar frequency of the electromagnetic oscillation will decrease, making

the material less lossy. This means that having a substrate of higher dielectric constant

twill reduce the frequency-dependent loss.

An interesting experiment that can be performed to demonstrate the difference be-

tween the two types of loss that have been discussed in this section involves placing a

region of lossy material in the presence of a transmission line. If the lossy material does

not make contact between the transmission line and ground, then it will not cause any

loss for a DC voltage on the line. However, a time-varying excitation of the transmission

line wiU create electromagnetic fields in the lossy material which in turn cause electric

currents to flow. This will result in ohmic losses which dissipate the energy of the signal

that is traveling on the transmission line.

This section has discussed which parameters affect the loss in a high-fidelity conduc-

tive coupler and how these losses may affect other aspects of the coupler's operation. The

desire to keep loss at a certain level RilI impose constraints on the design of the coupler.

Loss is also tied in with other aspects of the coupler performance and will therefore be of

interest when considering performance measures such as coupling strengt h and fidelity.

D irectivity

Directivity of the coupler refers to the level of the fomaxd coupled pulse relative to the

bacbard coupled pulse. Tradit ionally, direct ivity is defined over a certain bandwidt h

around the operating frequency of the coupler. For the purposes of this project, however,

the coupler does not operate at only one frequency, but couples time-domain signals.

The directivity tvill be evaluated for digital pulse sigmh by looking at the total energy

at each port as was done with coupling. Sirnilar to the case for coupling, the e,upression

for directivity using the total signal energy is

which yields a decibel value comparing the coupled-port energy (E4) to the isolated-port

energy (&).

Since the directivity is determined by comparing the total energies at the coupled and

isolated ports, in order for one to gain an intuitive understanding of what affects direc-

tivity, it is valuable to understand what mechanisms produce both the bacha rd coupled

pulse and the forward coupled pulse. In a conductive coupler, coupling arises from both

electromagnetic interaction and from the conductive comection. The total coupled signal

at each port will therefore be a combination of electromagnetic and conductive coupling.

Let's begin by looking at the backward-coupled signal. It will be composed of an

e1ectromagneticdly coupled component and a conductively coupled component. The

amplitude of the electromagnetic coupling can be calcdated from the even and odd mode

impedances of the coupler to get the reflection coefficients for the transmission-line to

coupler junctions at either end of the coupler. This yields a voltage level of $b(r,-ro) for

the puise reflected from the fht transmission-line to coupler interface. In the case of low

electromagnetic coupling, Rihich should hold true for most practical forward conductive

coupler desiPs, multiple reflections can be ignored. Assuming that the loss is also

low, the pdse reflected from the second coupler to transmission-line interface will have

the same amplitude, but wiU be of opposite sign. Figure 2.5 shows what backcard

electromagnetically-coupled pulses RTill look like in the case of no conductive coupling.

With a one-volt input pulse, the energy in each of the bacbard-coupled pulses will be

1 1 2 - [- (L - L)] Tp (3.31) 20 2

where Tp is the duration of the pulse and Zo is the port impedance. With the previously

stated assumptions, the energy for each of the pulses is equal, and therefore the total

energy of the backward elec tromagneticdly coupled signal is

1

This is not the total energy at port 3, however, because there will also be a contribution

to the voltage from the conductive connection.

The bacba rd conductively coupled signal can be thought of in the same way as the

forward conductively coupled signal with the coupler length and pulse duration inter-

changed. In other words, in the case of the backwatd conductively coupled signal: the

amplitude of the coupled pulse is dependent on the duration of the input pulse, whereas

the duration of the coupled pulse will be determined by the length of the coupler. A

new variable R k c k w-ill be dehed which is the equivalent resistance to determine the

amplitude of the backward-coupled pulse. The equation for the backward conductively

coupled signal is the same as that for the forward signd with the exception that Rf,, is

replaced by R b a c k -

The value of Rback can be eqlained by considering a thought e-xperiment in which

the conductive connection between the h e s is divided into discrete resistors connecting

the two lines- If these resistors are very f x apart, then the bachward-coupled signal wïll

be composed of discrete pulses with gaps between them. The time delay between the

leading edges of two successive pulses d l be equal to twice the propagation time between

two consecut ive resistors. As t hese resistors are brought closer together, the pulses t hat

comprise the bacbard coupled signal will also approach each other. When the resistors

reach a certain pro.vimity to each other, the pulses that make up the backwaxd-coupled

signal will no longer have a gap between them and form a long continuous pulse.

At this point, the distance between the resistors Rill be such that the propagation time

between them is equal to one half of the duration of the input pulse. This situation

corresponds to the case when the conductive connection is continuous. The resistance

of each of these resistors will determine the level of the backward conductively coupled

pulse and therefore is equal to The value of each of these resistors is equal to

the resistance of the chu& of conductive material corresponding to its segment of the

coupler. This resistance c m be calculated using the equation

where vp is the speed of propagation of the pulse and Tp is the duration of the input pulse.

Using the relation of u, to the dielectric constant of the medium given in Equation 3.8,

one obtains the following expression:

R b a c k

What this indicates is that the level of backward conductive coupling increases with

increasing pulse duration, line width, and dielectric conductivity, but decreases when

the line spacing or the dielectric constant of the medium is increased. Using the same

reasoning as for the fornard conductive coupling, one h d s that the level of bach~ard

conductive coupling is @en by

Since bachward conductive c o u p h g occurs over the entire length of the coupler, and

the input and backward coupled pulses are traveling in opposite directions, the duration

of the backward coupled puise is equal to twice the time a signal takes to travel one

coupler length. Therefore the duration of the bachard conductively coupled pulse is

and therefore the energy of the conductive component of bachward coupling is

1 1 ' 20 2 &,d = - [ ( ) 2z0 2 +Zo) ] Tbark back

Now that these energies c m be calculated, the total energy of the signal at port 3 can

be found sirnply by adding them:

In the case of the fornard-coupled signal, if the dielectric medium is homogeneous

there should not be any forward electromagnetic coupling and the signal will be made up

entirely of the conductively coupled pulse. The amplitude of the forward conductively

coupled pulse is given in Equation 3.24. For a one-volt input pulse this means that the

energy of the fornard-coupled pulse can be expressed as

This expression together with Equation 3.39 can be substituted into Equation 3.30 to

calculate theoretical values of directivity.

It is interesting to note that spacing and width of the lines affect forward conduc-

tive coupling and backward electromagnetic coupling in the same mariner. Making the

lines wider, or placing them closer together has the eEect of increasing the conductivity

connecting the two lines together and thus increasing the forward conductive coupling.

However, this will also increase the capacitance between the two lines and thus increase

the backward elect romagnetic coupling similarly. This means t hat changing the line

width or spacing will not change the directivity significantly.

The conductivity of the centre layer is a parameter that affects backward and forward

conductive coupling similarly. If bachard electromagnetic coupling is the dominant form

of bachward coupling, then increasing the conductivity can increase the directivity by

increasing the fornard coupled signal while the bachard coupled signal remains relatively

constant. However, once it reaches a certain level, the conductive backward coupling

Nill become comparable to the bachard electromagnetic coupling and increasing the

conductivity will simply increase both the backward and forward coupled signals by

similar arnounts. Thus there exists an optimal level of conductivity which, once exceeded,

will not result in significant increases in directivity.

The final parameter is the length of the coupler. This parameter affects bachxvard

electromagnetic coupling by increasing the time separation between the two reflected

pulses, but does not affect their amplitudes. Similarly, for the backward conductive

coupling, it alters the length of the coupled pulse but does not increase its amplitude.

For the forward coupled pulse, since everything remains in phase, increasing the length

of the coupling region will add to the amplitude of the coupled pulse. This indicates that

increasing the length of the coupler is an effective way of increasing its directivity.

Plots of directivity versus centre-layer conductance for two different coupler geome-

tries are shown in Figure 3.9. The upper curve, which is a solid line, represents the

directivity for a coupler with dimensions B=lmm, S=O.Gmm, W=0.43mm, L=100mrn,

and with a substrate of dielectric constant E, = 5. This line was plotted according to the

equations presented in this chapter. The square dots are the directivities for this geom-

etry that were obtained from ml-wave electromagnetic simulations using Sonnet. These

values were calculated by taking the ratio of the total energy in the fornard-coupled

signal to the total encra in the backward-coupled signal. These simulated values cor-

respond well to the cuve predicted using the simplified theory. This coupler reaches a

maximum directivity of approximately 3 dB.

The lower curve, which is shown as a dashed line, represents a coupler with dimensions

B=lrnm, S=0.4mm7 W=O.Gmm, L=SOmm, and with a substrate of dielectric constant

2.2. The dashed Line is the directivity predicted from the sirnplified theory, and the

small stars are the values obtained from full-wave simulations. The directivity of this

coupler remains below O dB which means that there is more energy appearing at the

backward-coupled port that there is at the fomaxd-coupled port.

As conductivity is varied, the level of backward electromagnetic couphg will remain

constant. This is why the directivity increases drarnatically with conductance at low

conductance levels. However, as the conductance rises, the backward conductive coupling

will becorne sioonificant compared to the bacLvard e l e c t r ~ m a ~ e t i c coupling, and when

the conductive coupling becomes dominant, the directivity wi11 remain vir tudy constant

as the conductance is varied. In order to be able to design a coupler with high directivity,

it desirable to have this 'leveling off' of the directivity curve occur a t as high a level as

possible. The height of the flat part of the directivity cuve is determined by the ratio

of forsvard conductive coupling to bacha rd conductive coupling. This ratio remains

constant as conductance is varied. The ratio can be increased by increasing the length

of the coupling region, or by shortening the duration of the input pulse.

Another factor that can limit the directivity is loss in the coupler. Once the con-

ductance reaches a certain level, coupling will reach a maximum and further increases

in conductance will cause more energy to be lost to ohmic dissipation rather than being

coupled. If the backward electromagnetic coupling is too high, then as the conductance

is increased this lossy region will be encountered before the coupler reaches an optimal

level of coupling. It can be seen that lowering the ratio of electromagnetic coupling to

Figure 3.9 This plot shows how directivity is affected as the conductivity of the cen- tre layer is varied for kvo different coupler geometries. The solid line represents the directivity calculated from the simplified theory according to Equation 3.30 for a coupler Rrith dimensions B=lmm, S=O.Gmm, W=0.43mm, L=lOOmm, and with a substrate of clielectric constant e, = 5. The square dots are the values of directivity for this geom- etry obtained from Full-wave Sonnet simulations. The dashed line shows the directivity predicted from the simplified theory for a coupler with dimensions B=imm, S=0.4mm, W=O.Gmm, L=5Omm, and with a substrate of dielectric constant 2.2. The small stars represent the values of directivity corresponding to this geometry obtained from full-wave Sonnet simulations.

O - -

* * * *c - -. - -, . - . - .+_ . - . - . 35. - . - . _;+ -_-- - - - . - . - - - - - -

-

-

-

-20

-25

-30

1

I

- Ï - 1

42 1 - -

- 1 I 1 1 1 I

O 0.01 0.02 0.03 0.04 0.05 0.06 0.07 conductance (S)

conductive coupling wïll result in higher possible directivities. One of the charact erist ics

of the broadside coupler layout, however, is that these two types of c o u p h g are closely

linked- If one attempts to d t e r the conductance between the two lines by varying the

line spacing or line width, the capacitance between the two lines d l Vary similarly to

the conductance. For example, if one attempts to lower the electrornagnetic coupling by

spacing the lines farther apart-, the conductance will also become lower. The length of

the coupling region is the only dimension that can increase fomard coupling wïthout also

similarly increasing the backwxd coupling.

In the theoretical analysis, during the derivation of the expression for E3-: ohmic

loss was assurned to be negligible. This caused some discrepancy with the simulated

directivity that can be seen in the lower cuve in Fi,we 3.9. At low conductivities, the loss

Fvill be very small and the theory and simulated values do indeed correspond very closely.

As the conductivity is increased, however, the discrepancy becomes more noticeable.

The loss of bach~axd coupled signal energy causes the full-svave Sonnet simulations oE

directivity to be higher than the simplified theory predicts. However, as conductivity

is increased even further, the theoretical and simulated values begin to approach eacb

ot her again. This is because at higher conductivities, the backward conductively coupled

signal, whose theoretical value does not neglect loss, will become dominant.

3.3.5 Fidelity

The motivation behind this research was to create couplers that can couple a digital

signal with high fidelity. This means that the coupled signal should be the same shape

as the input signal. Fidelity is a measure of how similar the shape of the coupled pulse

is to the shape of the input pulse. The reason that conductive coupling was chosen as

the coupling mechanism is that it is inherently high-fidelity. Because of this the coupler

usually has a high fidelity, but extreme design parameters can cause deviations from ideal

behwiour that may result in degraded pulse fidelities.

tirne (ns) Frequency (GHz)

(a) Input pulse (b) Fourier transform af input pulse

Figure 3.10 The input pulse and its frequency spectrum. The solici line in plot (a) is the undistorted input pulse with a complete frequency spectrum. The dashed line in plot (a) shows the input pulse when i t bas been reconstructed from a frequency spectrum that was truncated at 20 GHz as shom in plot (b).

If a digital pulse is analyzed in the frequency domain, it c m be seen that the pulse

consists of many fiequencies. A plot showing a pulse in the time damain dong with

its frequency spectrum is shom in Fi-gure 3.10. It c m be seen that the energy of the

pulse cornes mostly from frequencies wïthin a certain range. In order for the coupler to

have high fidelity, it is necessary that the frequencies in this range are coupled with equal

strength, and that the phase relationships between the frequencies are preserved. In other

woïds, the coupling shodd be independent of frequency. Any frequency dependence will

result in distortions to the coupled signal. As was discussed in Section 3.3.3, frequency-

dependent losses WU be dependent on the conductivity and the dielectric constant of the

centre dielectric layer. The value of 2 will give an indication of the frequency dependence

of the coupler. Figure 3.11 contains plots showing the coupled pulse for different values

of E, showing how fidelity is negatively adfected.

(a) Input pulse

I I I

O 0.5 1 1.5 2 2 5 3 3.5 4 rime (ns)

(b) Coupled signal with = O.OlS/m

(c) Coupled signal Nith = 0.04S/m

Tirne (ns)

(d) Coupled signal with

Figure 3.11 Fomard-coupled pulse fidelity for different values of z. Plot (a) shows the pulse that entered the input port of the coupler, and plots (b), (c), and (cl) show the forward-coupled signal. These plots were generated from full-wave Sonnet simulation of a coupler with a dielectric constant of 10 and conductivities ranging from 0.1 S/m to 1.0 S/m

Table 3.2 The Effect of Design Parameters on Coupler Performance

Note: / means an increase, white \ means a decreuse.

Parameter

0 i"

s i" 6 7

L i "

3.4 Design Procedure

Using the relationships between the design parameters of a coupler and its performance

I

that have been discussed in this chapter, a design procedure will be introduced. This

design procedure should allow a coupler to be designed to meet given performance re-

Coupling

7

\

\

i"

qiiirements. A summaq of how design parameters affect the coupler performance is

s h o m in Table 3.2, It should be noted that this table is very simplified. For example,

directivity is show= to increase with increasing conductivity, but as was discussed pre-

Loss

i"

\

\1

/"

viously, directivity will increase significantly at low conductivities but beyond a certain

point increases in conductivity d l not cause sibp.ificant increases in directivity. More

Directivity

1

1

/"

1

det ailed dependencies were discussed in Section 3 -3.

Fidelity

\

\

i"

no change

The design procedure is as follows:

1. The first step is to decide on d u e s for the ground-plane spacing and the dielectric

constant of the substrate. The choice of ground-plane spacing is somewhat arbitrary

as different spacing wïll simply result in a scaling for other components of the

coupler. For the dielectric constant of the medium, higher values tend to resulc in

better directivities and are therefore preferable. This choice will also have to take

practicd considerations of possible materials into consideration

2. The next step is to decide on an acceptable level of backwârd coupling. The dimen-

sions of the coupler must be chosen so that the backward electromagnetic coupling

falls below this level. Values of Iine spacing (S) and line Mdth (W) can be chosen

to meet this requirement. These values will also have to be chosen such that the

coupler rernains matched to the characteristic impedance of its port. Larger line

spacings will result in less b a c h a r d electromagnetic coupling, but WU also simi-

lady lower fornard conductive coupling levels. Therefore the Line spacing should

be as close as possible while maintaining the backnrard electromagnetic coupling

below an acceptable level.

3. Now it's time to choose the value for the conductivity of the centre dielectric layer.

This will primarily afTect the level of forward coupling and the pulse fidelity. For low

conductivities it will not have a significant effect on the backward-coupled signal

since the back~a rd electromagnetic coupling will be much larger than the backward

conductive coupling. However, as the conductivity increases, the backward conduc-

tive coupling m-iU become more significant. Because of this relationship, increasing

the conductivity will not result in significant increases in directivity beyond a cer-

tain point. It will simply increase both the forward-coupled and bacbward-coupled

signal levels and the loss of the coupler. For this reason, conductivity should usually

be increased until it has increased the directivity as much as possible. Increasing

the conductivity will also lower the pulse fidelity and should be kept low enough to

maintain an acceptable fidelity.

4. Once the conductivity has been chosen, the only parameter left to choose is the

physical length of the coupler. Increasing the coupler length will result in increased

forward coupling without aEecting the level of backward coupling. Therefore in-

creasing the length of the coupler will increase its directivity. A coupler length can

now be chosen such that the desired levels of forward coupling and directivity are

attained. Increasing the coupler length will also increase the loss of the coupler (by

raising the total conductance), Coupler length c m be seen as a 'last resort" for

conductive couplers since it is the only parameter that can significantly increase

directivity without having an adverse impact on some other aspect of the coupler's

performance.

5 . AU that remains now is fine-tuning the coupler. The conductivity of the centre

layer may have caused some rnismatch between the coupler and the surrounding

circuit. To remedy this, the line width c m be adjusted until the coupler is matched

as weil as possible to the characteristic impedance of the circuit.

Chapter 4

Coupler Simulation

4.1 SimulationMethod

The coupler designs in this project were analyzed numerically using a full-wave moment-

method technique of electromagnetic analysis. This generated frequency-domain network

parameters which were convolved with the freqriency spectrum of the input pulse yielding

the coupler's response to that input pulse. These fiequency-domain responses were then

converted to the time-domain using inverse Fourier transforms. These numerical elec-

tromagnetic simulations are a very valuable tool because they provide an analysis that

t &es into account every possible coupling mechanism and electromagnet ic interaction in

the structure.

4.1.1 Frequency-Domain Analysis

The numerical technique used to characterize the physical structure of the coupler is a

technique based on the method of moments. The method of moments is a mathematical

procedure for solving linear equations of the form

where L is a linear operator, g is the excitation (a known function) and f is the response

(the unknown to be determineci). The rnethod of moments can be used to reduce the

functional equations of field theory to matrïis equations in a procedure introduced by

Harrington [Il, 121. To solve the field equations, f is expanded into a series of functions

such that

where cr, are constants and f, are called the basis functions. For an exact solution to the

problem, Equation 4.2 MU be an infinite summation. For practical applications, however,

the sum will be h i t e yielding an approximate solution. This sum is then substituted

back into Equation 4.1 and the inner product is taken with a set of testing functions.

This will yield matrix equations which can be solved to find the values of a,. Then f is

f o n d from Equation 4.2. When the testing fhctions are equal to the basis hc t ions ,

this is known as Galerkin7s method.

The set of equations in matrix form that the method of moments produces can be

solved using a computer program. This d o w s large or complicated structures which

can not easily be analyzed analytically to be accurately characterized. The particular

program used for this project was the Sonnet software [13]. The algorithm used by

Sonnet is based on a Galerkin technique that was developed in 1986 by Rautio and

Harrington [14]. This technique was developed as an extension of an analysis of planar

waveguide probes done by Hariington [15]. The algorithm used by Sonnet deals with

planar structures inside a metal box. The fields in the box are e-upressed as a sum of

waveguide modes. The algorithm does a full three-dimensional analysis which talies into

account all three-dimensional fields as well as currents.

A particular trait of the Sonnet software is that the subsectioning of the circuit must

be done to fit onto a grid of uniform dimensions. This is because it uses a fast Fourier

transform technique that sums waveguide modes to determine a convolved Green's fimc-

tion. This technique is described by Rautio and Harrington in [16]. The actual subsec-

tions used in the analysis may be larger than the grid size, but they must conform to

the grid layout. This c m be problemattic for circuits with irregulaz shapes or with small

features because a very fine grid d l h.-ave to be used resulting in much longer computa-

tional times. For this project, however,, Sonnet was suitable since the coupler structure is

composed of large rectangular segments. Sonnet also proved capable of handling multiple

dielectric layers with varying properties.

The coupler was analyzed in the keequency domain to yield s-parameters for all four

ports of the coupler at a particular Eequency, In order to be able to convert these

into time-domain descriptions, it as mecessary to simulate the coupler at many different

frequencies. The simulations were perhrmed at uniform frequency intervals over a certain

range of frequencies. This required tzhe selection of a suitable fiequency range, and

fiequency "step". The range of simu1at;ion frequencies was decided on by considering the

input pulse and its frequency spectrum as shown in Figure 3.10. The energy of the input

pulse is composed of a range of frequerncies with a peak at O Hz, and lobes of decreasing

amplitude as the frequency is increasetd. In Figure 3.10(b), the Fiequency spectrum is

truncated at 20 GHz. A pulse recons-ztructed from this truncated frequency spectrum

is shown as a dotted line in Figure 3-10(a). The reconstructed pulse will show some

distortion which varies depending on w:-here the frequency spectrum is truncated. In this

case, it ras decided that simulating up to 20 GHz was an acceptable range. Using input

pulses of different durations d l also ; affect the choice of frequency range since wider

pulses will have narrower spectra and wice versa. Wider pulses can therefore have their

frequency spectra truncated at a smaller value with a comparable level of distortion.

The interval between simulation frequencies must also be chosen. In this case the

criterion for deciding an appropriate ffrequency step is that it must be small enough

to convey significant features of the frequency response. For example, if the frequency

response has narrow spikes at certain Bfrequencies, and the intemal between simulation

frequencies is comparable to or larger than the width of these spikes, then the spikes

might not be visible in the simulation. An appropriate frequency step can be determined

visually by looking a t a plot of the simulated frequency response. If the c u v e appears

smooth, then the frequency step is fine enough, but if it appears jagged and discontinuous,

then it is probably too coarse. Beyond a certain point, however, decreasing the interval

between frequency steps does not result in si,~ficant improvements in accuracy. If nem

frequency points are added and they simply fall almost directly between existing points,

then no new information is added as these points could simply have been determined by

interpolation. For this pro ject a fiequency step of 0.1 GHz was found to be satisfactory.

Simulation of the coupler using a moment-method technique will chzacterize the coupler

in the frequency domain. In the case of this research, the simulation ras used to calculate

s-parameters for the four ports of the coupler. These s-parameters describe ~ L L U ~ the

behaviour of the coupler in the frequency domain. However, this project is concerned

with the time-domain behaviour of the coupler in a digital system. In order to analyze

the coupler's performance with digital signals, it is necessary to convert the frequency-

domain s-parameters into a time-domain behaviour. This was done by considering how

the coupler would respond to a digital input pulse.

At any particular frequency, the relationship between an input voltage and an output

voltage at any two ports is given by the s-parameter relating the two ports. For example,

if a wave of amplitude Vl is incident on port 1, then the signal leaving port 2 is of

complex amplitude s l z . VI. The s-parameters describe both the amplitude and phase

relationships of the voltages- To find the output at a given port with a pulse input at

port 1, the frequency spectrum of the pulse (show. in Figure XlO(b)), is multiplied by

the appropriate s-parameter spectrum. The product of these two spectra will be the

spectrwri of the signal a t the output port. The frequency spectrum of the signal at

the output port can then be converted to the time domain through an inverse Fourier

transform. The real part of the inverse Fourier transform will be the signal at the output

port. This multiplication in the fkequency domain is equivalent to a convolution of the

input pulse with the impulse response of the coupler.

4.2 Design Case Studies

To provide an example of the type of coupling performance achievable with a high-fidelity

broadside coupler, two couplers have been simulated and are presented here. The h s t

esample is a coupler that svas designed on a substrate of dielectric constant E , = 5 and

has a coupLing strength of -18 dB. The second has a lower dielectric constant of E , = 2.2,

and a coupling strength of -25 dB.

4.2.1 18 dB Coupler

The physical dimensions and other design parameters of this coupler are presented in

Table 4.1. The coupler v a s designed to be comparable to the 20 dB stripline coupler

presented by Stickel [4]. This coupler has a slightly higher coupling factor of -18 dB.

The frequency-domain results of the simulation are shown in Figure 4.1. The plot of

si1 (plot (a)) indicated the amount of reflection at the input. It is below -15 dB through

most of the frequency range indicating that the coupler is fairly well matched. It n*ould

be possible to improve the matching somewhat by fine-tuning the width of the coupled

lines. In this particular coupler, the lines were left at the width calculated during the

initial design which still results in good matching. Oscillations of about 0.66 GHz c m

also be seen in this plot. These oscillations correspond to frequencies where length of the

coupler is a multiple of X/4 and the reflections from each end of the coupler add either

cons t ruc t ively or dest ruct ively.

Figure 4.l(b) shows s i 2 which corresponds to the through signal. It stays very Bat

t hroughout the frequency range indicating that the through signal will not be distorted.

Table 4.1 Design Parameters for an 18 dB High-Fidelity Broadside Coupler

Constant

Conductivity

The level of s i 2 is about -5 dB indicating t h a t the through signal d l have about one

third the power of the input.

The bachaxd-coupled response is shom in Figure 4.l(c). This plot also has oscilla-

tions of fkequencies where the length of the coupler is equal to X/4. Finally, s l 4 , which

corresponds to the forward-coupled signal, is shown in Figure 4.l(d). This plot shows a

very flat frequency response indicating that the forward coupling should be high-fidelity.

It can also be seen that the fine for s14 is about 3 dB higher than the sl3 plot which

means that the coupler e l 1 have a directivity of 3 dB.

0.2 S/m

The predictions of time-domain behaviour based on the s-parameter plots are con-

firmed by the time-domain plot shown in Figure 4.2. The energies of the s ipa l s at each

port were measured by integrating the squares of the voltages over the time period s h o m

in the plots (4 ns). This calculation was done numerically using Matlab. The energies

in each of the signals, e-qressed as a percentage of the input energy, are 3.8% in the

reflected signal, 34.4% in the through signal, 0.68% in the backniard-coupled signal and

1.37% in the forward-coupled signal. This means that 59.7% of the input signal energy

was lost to resistive dissipation. The ratio of signal energy at the coupled port to the

energy a t the isolated port indicates that the coupler has a directivity of 3.04 dB.

Compared to Stickel's 20 dB stripline coupler, this coupler lias about 2 dB more

coupling, but the loss is significantly higher and the directivity is Zonier. Stickel's coupler

had a resistive loss of 21.5% and a directivity of 7.5 dB. An explmation for the lower

performance can be found by looking at the plot of the bachvard-coupled signal (plot (d)).

Coupler Length

lOOmm

Ground Plane

Spacing

lrnm

Line Spacing Line Widt h

0.6m.m 0.43mm

(a) sll - reflection (b) s ~ 2 - transmission

(c) 513 - bachvard coupling (d) sl4 - f o m w d coupling

Figure 4.1 These show the s-parameters f?om O to 20 GHz for the 18 dB coupler. These s-parameters are the ratio of the voltage of the signal leaving each port to that of the signal entering at port 1. These plots show that the s-parameters of the high-fidelity port (ports 2 and 4) are relatively flat as fiequency varies.

(a) Pwt 1 - Inpot Pulse I t

O 0.5 1 1.5 2 25 3 3.5 4 (b) Port 1 - Relleaion

1 1 I b I

I

L t I I I l O 0.5 1 1.5 2 25 3 3.5 4

(dl P M 3 - Backward-Cwpled Signal 0.15

O 0.5 1 1.5 2 25 3 3.5 4 Time (ns)

Figure 4.2 This is the time domain response of the 18 dB coupler with a pulse input. The coupler has a directivity of 3.04 dB and a coupling factor of -18 dB. The coupler bas a substrate of E , = 5 and has a centre layer conductivity of o = 0.2S/m. The coupler's dimensions are: L = lOcm, S = 0.6mm, LV = 0.43mrn, and B = Imm.

In this design, the bachaxd-coupled signal has a large spike indicating electromagnetic

coupling which accounts for most of its energy. The level of bachward conductive coupling

can be seen as the raised voltage bettveen the electromapetically-coupled pulses. The

pulse response of Stickel's coupler does not contain these pulses indicating that there is

little, if any, electromagnetic bachard coupling. A visual observation of the fornard-

coupled pulse shows that this coupler has higher pulse fidelity than Stickel's design. The

frequency response of Stickel's coupler varies more with frequency indicating that the

pulse will be distorted. This can be seen in his tirne-domain plots of pulse propagation

as a smoothing out of the fomard-coupled pulse.

4.2.2 25 dB Coupler

The design parameters for the 25 dB are presented in Table 4.2. This coupler was

designed using the same conductivity (o = 2.0 S/m) in the centre layer as the 18 dB

coupler. However, because the lines are spaced farther apart and are narrower, the

coupling is weaker.

The frequency-domain s-parameter plots are shown in Figure 4.3. The oscillations

in the sll and ~ 1 3 plots are wider in frequency than they were in the case of the 18 dB

coupler. This is because the dielectric constant of the substrate in this case is lower and

therefore the frequencies at which the coupler length is equal to multiples of X/4 will be

lower. In this case the oscillations me about 1 GHz as opposed to 0.66 GHz as they were

in the case of the 18 dB coupler. The sll cuve stays below -25 dB in the higher parts of

the kequency range but is significantly higher at low frequencies rising to -10 dB at DC.

Comparing the sll curve in this case to the sll c u v e for the 18 dB coupler, one can see

that in this case the variation of sll with frequency is more prominent than it is in the

case of the 18 dB coupler. This indicates that this coupler is more frequency-dependent

than the 18 dB coupler and therefore will have worse fidelity.

Plots (b) and (d) which correspond to the transmitted signal and the forward-coupled

Table 4-2 Design Parameters for a 25 dB High-Fidelity Broadside Coupler

signal are very flat through most of the frequency range, but also have frequency depen-

dence at lower frequencies. This frequency dependence is slightly more pronounced t han

in the case of the 18 dB coupler. Looking at the plots of s i 4 and 513 , it can be seen that

the level of the forward coupling is about 3 dB higher than that of the bachard coupled

signal indicating that the directivity should be about 3 dB.

The time-domain behaviour of the 25 dB coupler is shown in Figure 4.4. The per-

centages of energy at each port, calculated in the same manner as for the 18 dB coupler,

are 2.27% in the reflected signal, 28.19% in the through signal, 0.148% in the backwaxd-

coupled signal, and 0.293% in the fomard-coupled signal. The amount of loss in this

coupler is 69.1% of the input energy. The directivity of this coupler, calculated by com-

paring the total energies at the forward-coupled port and the backward-coupled port, is

2.96 dB. An interesting aspect of this coupler's time-domain performance is the reduced

pulse fidelity of the fornard-coupled pulse. The increased frequency dependence which

was seen in the s-parameter plots causes more distortion to the forward-coupled pulse.

This illustrates the point that for the same centre-layer conductivity, the coupler set in

a substrate of lower dielectric constant will have lower pulse fidelity.

These examples illustrate the high-fidelity coupling that can be achieved with a broad-

side conductive coupler. By comparing the two coupler examples presented heïe, it can

be seen that fidelity will Vary with different design parameters. The two designs pre-

sented here both have virtually the sarne directivity of 3 dB, and the same conductivity

in the centre layer of dielectric, but the coupler with higher dielectric constant has no-

~r

Dielectric

Constant

2.2

B

Ground Plane

Spacing

lmm

O-

Conductivity

0.2 S/m

S

Line Spacing

0.8m.m

L

Coupler Length

l0Omm

W

Line Width

0.25mm

ticeably better pulse fidelity. The most sibg.ificant limitation of this layout is that the

bachard electromagnetic coupling strength and the conductive coupling strengt h are

closely linked, This linkage imposes a limitation on the directivities that can be achieved

with a broadside conductive coupler.

(a) si1 - reflection

(c) 813 - b a b a r d coupling

(b) SI? - transmissiori

(d) 514 - fomaxd coupling

Figure 4.3 These show the s-parameters £rom O to 20 GHz for the 25 dB coupler. These s-parameters are the ratio of the voltage of the signal leaving each port to thac of the signal entering a t port 1.

(a) Port 1 - Input Pulse r I I

Figure 4.4 This is the time domain response of the 25 dB coupler nith a pulse input. The coupler has a directivity of 2.96 dB and a coupling factor of -25 dB. The coupler has a substrate of E, = 2.2 and has a centre Iayer conductivity of a = 0.2S/m. The coupler's dimensions are: L = lOcm, S = 0.8mm, W = 025mm, and B = Inmi.

1 t t I I I l O O 5 1 1 5 2 2 5 3 3.5 4

(e) Port 4 - FamardCaipled S~gnal

0 0 6 -

z004- i3 $0.02 >

r

- - - a

&.

0-

Chapter 5

Conclusions

This project tvas aimed at investigating a coupled-line structure that could provide high-

fidelity coupling for digital signals- Alt hough coupled-line structures are quite cornmon

in microwave devices, very little research has concerned itself with providing high-fidelity

coupLing in the time domain. The only previous work to address this problem was Stickel's

research which led to this project. One of the goals of tliis project was to investigate

methods with which coupled lines could be used to produce high-fidelity coupling, focus-

ing specifically on the case of broadside stripline couplers. Different coupLing mechanisms

were evaluated, and it was concluded that forward conductive coupling is the most a p

propriate mechanism to produce the non-frequency-dependent performance required for

high-fidelity coupling.

The broadside conductive coupler structure was analyzed analytically in order to

determine the relationships between design parameters and the coupler's performance.

This theoretical analysis was also compared to Ml-wave simulations of the coupler and

was found to be consistent with these simulations. The strength of the high-fidelity

forwaxd coupling is dependent on the total conductance of the conductive layer between

the coupled lines. It was aIso found that couplers with a substrate of higher dielectric

constant tend to have better pulse fidelity- The directivity of the coupler has a more

complex relationship w-ïth the design parameters since it depends on both electromagnetic

coupling md conductive coupling. When electromagnetic coupling is the dominant source

of backward-coupled s i s a l energy, then the directivity will be directly related to the

conductance of the centre layer in the same manner as the coupling strength. However,

if conductive coupling is the dominant source of the backward signal, then the directivity

is directly proportional to the ratio of the propagation time of the signal through the

length of the coupler to the pulse duration. Because of this dependence, once bachward

electrornagnetic coupling has been reduced as much as possible, the only ways to increase

directivity are to either increase the length of the coupler, or to use a pulse of shorter

duration. This usually results in very long physical lengths for the high-fidelity forward

coupler.

It is desirable that a high-fidelity forward coupler be designed such that the electro-

magnetic backward coupling is minimized in relation to the conductive component of

the coupling. In the broadside stripline coupler layout, minimizing electromagnetic cou-

pling is accomplished by increasing the separation between the coupled lines. Increasing

this separation, however, will also similarly decrease the conductive coupling strength.

This means that it is diEcult to get into a region where directivity can be significantly

improved. In order to accomplish significant increases in directivity, it would be neces-

sary to somehow reduce or eliminate the linkage between electromagnetic and conductive

coupling.

The purpose of this research was to investigate high-fidelity coupling which would

be suitable for digital systems. Broadside conductive couplers were demonstrated to be

capable of coupling a signal having the same shape as the input sipal . The broad-

side coupler layout was found to be limited by the linkage between electromagnetic and

conductive coupling which restricts the directivity of the coupler. In order to achieve

high-fidelity coupling, a flat frequency response is desired. A conductive coupling mecha-

nism is able to achieve this non-hequency-dependent operation and thereby couple digital

pulses ~ 4 t h high fidelity.

Another bd ing of this project is that the Sonnet electromagnetic simulation softwaxe

is well suited to solving the broadside conductive coupler structure. A lot of time was

spent looking into the operation of numerical electromagnetic simulators because prob-

lems were encomtered using some softm-aze packages that had trouble dealing Rrith the

unusual structure of the coupler. It seems that dielectric layers with different conductivi-

ties can present problems to certain algorithms. The algorithm used by Sonnet, however,

had no problem simulating a structure with dielectric layers of arbitrary conductivities.

A further advantage was the large number of references available for Sonnet that permit a

thorough understcuiding of the numerical methods used in the softwae. This cm be very

useful in determinhg the range of validity of its results. Sonnet does have constraints on

the meshing of the circuit to be simulated, but for this particular project that was not

an issue.

5.1 Future Work

5.1.1 Design Improvements

One aspect of the coupler's performance with improvement possibilities is its directivity.

The primary effect that degraded the directivity of the broadside conductive coupler was

the large electromagnetically-coupled signal that appeared at the isolated port. A method

for lowering this undesirable signal without also lowering the coupled signal energy would

be very appealing. The most prornising concept is to place some shielding between the

two coupled lines, such as another metal lai-er. It would be necessary to have a break in

the shielding for the conductive connection to remain between the two coupled lines. If

the electromagnetic coupling could be reduced independently of the conductive coupling

then significant directivity gains could be made. Another idea would be to suppress

the backward electromagnetic coupling through line tapering or some other metbod.

However, this is problematic as it tends to result in longer couplers and also may spread

out the backward-coupled signal, but leave it wïth the same amount of energy.

One of the initial motivations for pursuing the broadside structure for the coupler was

to be able to include layers of novel materials between the coupled lines. An interesting

possibility for e-xtending the design of the coupler would be to use a semiconducting

material between the coupled lines. This would allonr the properties of the coupler to be

controlled by varying a DC bias curent between the lines. This could allow the coupling

to be "switched" on or off.

5.1.2 Physical Realizability

The greatest obstacle to physicdy building the coupler would be hd ing a suitable con-

ducting dielectric material for the centre layer of the coupler. There are many conductive

materials available in the marketplace, but often a measure of the characteristics which

are important to a high-fidelity conductive coupler are not k n o m by the manufacturer

or are not available. Another limitation is that the materials are usually not available

with a wide range of properties, and the properties may Vary from sample to sample.

An exarnple of a feasible material is Eccosorb V F [17]. The technical bulletin describ-

ing the material indicates that it has a dielectric constant of 37 at 8.6 GHz, and a volume

resistivity that c m range from 5 to 50 %cm. This material has also been characterized

more fully by Leesa MacLeod showing variations in conductivity and dielectric constant

over a wide range of frequencies [18]. There are also many more partially conductive di-

electric materials available, often intended for use as microwave absorbers of attenuators.

Many of these materials could be applicable to a broadside conductive coupler.

5.1.3 Alternative Uses for the Device

A very interesting area of future research would be to extend the use of the broadside

conductive coupler structure t o applications other than high-fidelity coupling. An in-

teresting possibility would be to use it for material diagnostics. If an unknom Iayer of

mat-erial were inserted as the centre layer of the coupler, electric and magnetic properties

could be deduced by rneasuring the s-parameters of the device. This could be very useful

for measuring t h e properties of films or other flat materials.

Another interesting extension of the device would be t o use it as a directive via

connecting different layers in a circuit board. This could be done by cutting a long

narrow slot in t he ground plane separating two layers in the circuit board. Inserting a

conductive material in this dot to connect two transmission lines would allow power to

be coupled between them.

References

[l] P. H. Aaen, "Short printed-circuit couplers and vias," M.A.Sc. thesis, Department

of Electrical and Cornputer Engineering, University of Toronto, 1997.

[2] R. Mongia, 1. J. Bahl, and P. Bhaxtia, R F and Microwaue Coupled-Line Circuits.

Artech House, 1999.

[3] R. Levy, L~a.nsrnission-line directional couplers for very broad-band operation,"

Proceedings of the IRE, vol. 112, pp. 469-476, March 1965.

[4] M. S tickel, "Broadband high-fidelity directional transient couplers," M. ASC. t hesis,

Depart ment of Electrical and Cornputer Engineering, University of Toronto, 1999.

[5] D. M. Pozar, Microwave Engineering. John Wiley and Sons, Inc., 2 ed., 1998.

[6] B. M. Oliver, "Directional electromagnetic couplers," Proceedings of the IRE, vol. 42,

pp. 1686-1692, November 1954.

[7] W. L. Firestone, "Analysis of transimission line directional couplers," Proceedings

of the IRE, vol. 42, pp. 1529-1538, October 1954.

[8] E. M. S. Jones and J. T. Bolljahn, "Coupled-strip-transmission-line fihers and di-

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pp. 75-81, April 1956.

[9] P. K. Ikalainen and G. L. Matthaei, "Wide-band, fomaxd-coupling microstrip hy-

brids with high directivity," I E E Transactions o n Microwave Theorg and Tech-

niques, vol. 35, pp. 719-725, August 1987.

[IO] A. Jenkins and A. L. Cullen, L'Resistive four-port directional coupler," IEE Proceed-

ings, vol- 129, pp. 94-98, 19&2.

[Il] R. F. Hnrrington, "Nfatriu methods for field problems," Proceedings of the IEEE,

vol. 55, pp. 136-149, February 1967.

[12] R. F. Harrington, Field Compatat ion by Moment Methods. Malabar, Florida: Robert

E. Krieger Publishing Company, 1968.

[13] Sonnet Software, Inc., Sonned User's Manual - Volume 1, 1999. release 6.0.

[14] J. C. Rautio and R. F. Harrington; "An electromagnetic tirne-harmonic analysis of

shielded microstrip circuits,?' IEEE Transactions o n kficrowave Theory and Tech-

niques, vol. 35, pp. 726-730, August 1987.

[15] R. F. Harrington, T h e - H a m o n i c Electromagnetic Fields. New York: McGraw-Hill,

1961. section 8-11.

[16] J. C. Rautio and R. F. Harrington, "Results and experimental verification of an elec-

tromagnetic analysis of microstrip circuits," Transactions of the Society for Com-

puter Simulation, vol. 4, pp. 125-155, April 1987.

(171 Emerson & Cuming, "Eccoso~b VF ." Technical Bulletin 2-16, September 1980.

[la] L. MacLeod, "Compact travelling-wave electrostatic discharge simulator," M.A.Sc.

thesis, Department of Electrical and Computer Engineering, University of Toronto,

1993.