RF crosstalk in InP based Transmission Lines

Institutionen för systemteknik

Department of Electrical Engineering

RF Crosstalk in InP(Indium Phosphide) based

Transmission Lines

Master thesis performed in Electronic Device

by

Mahboobeh Khosravi Nahouji

LiTH-ISY-EX--13/4712--SE

August 2013

RF crosstalk in InP based Transmission Lines

...

...

Master thesis in Electronic Device

at Linköping Institute of Technology

by

Mahboobeh Khosravi Nahouji

...

LiTH-ISY-EX--13/4712--SE

Supervisor: Professor Spartak Gevorgian

Chalmers University

Examiner: Dr. Behzad Mesgarzadeh

Linköping University

Presentation Date 2014/08/21

Publishing Date (Electronic version)

Department and Division

Department of Electrical Engineering Electronic Device

URL, Electronic Version http://www.ep.liu.se Publication Title

RF crosstalk in InP based Transmission Lines

Author(s)

Mahboobeh Khosravi Nahouji Abstract

Currently two main tracks are considered for integration of photonic circuits. Silicon based integration may be more cost effective; however implementation of some functionalities like laser, is problematic. In contrast InP offers complete solution of photonic integration including laser diodes.

Additionally, much higher speeds may be anticipated from InP based integration. As in the case of ordinary integrated circuits, attempts to increase degree (density) lead to undesired coupling-crosstalk between the components. Three types of cross coupling may be clearly distinguished: optical, RF(electric) and thermal. Each of them has its specifics, physical mechanisms and methods of analysis. Modeling RF crosstalk will be in the focus of this project.

To drive active components, such as laser and photodiodes, conducting tracks are integrated with photonic components. In multichannel photonic IC chips these tracks become very dense leading to strong parasitic electrical couplings between them. This crosstalk becomes more problematic in high speed photonic IC chips where the frequency of the RF signals (modulation, detection) is in the range up to 10GHz and beyond. Thus modeling of the crosstalk between RF tracks (also between RF and DC) is of prime importance. This is the main task of the project. A further task is analysis of the crosstalk using developed models and considering designs allowing reduced cross coupling.

Number of pages: 40 Keywords

PICs, Transmission line, RF Crosstalk, Microstrip, Coplanar waveguide, Coplanar stripline, Parallel plate waveguide Language

English

Other (specify below)

Number of Pages Type of Publication Licentiate thesis  Degree thesis Thesis C-level Thesis D-level Report

Other (specify below)

ISBN (Licentiate thesis)

ISRN: LiTH-ISY-EX--13/4712--SE

Title of series (Licentiate thesis) Series number/ISSN (Licentiate thesis)

I

Abstract

Currently two main tracks are considered for integration of photonic circuits. Silicon based

integration may be more cost effective; however implementation of some functionalities like laser, is problematic. In contrast InP offers complete solution of photonic integration including laser diodes.

Additionally, much higher speeds may be anticipated from InP based integration. As in the case of ordinary integrated circuits, attempts to increase degree (density) lead to undesired coupling-crosstalk between the components. Three types of cross coupling may be clearly distinguished: optical, RF(electric) and thermal. Each of them has its specifics, physical mechanisms and methods of analysis. Modeling RF crosstalk will be in the focus of this project.

To drive active components, such as laser and photodiodes, conducting tracks are integrated with photonic components. In multichannel photonic IC chips these tracks become very dense leading to strong parasitic electrical couplings between them. This crosstalk becomes more problematic in high speed photonic IC chips where the frequency of the RF signals (modulation, detection) is in the range up to 10GHz and beyond. Thus modeling of the crosstalk between RF tracks (also between RF and DC) is of prime importance. This is the main task of the project. A further task is analysis of the crosstalk using developed models and considering designs allowing reduced cross coupling.

II

Acknowledgement

It was impossible to do this project without the invaluable supervision of my supervisor Professor Spartak Gevorgian. So hereby I would like to appreciate all his guides, advices and helps during doing the thesis.

It was my pleasure and my great opportunity to have all the helps, consideration and cooperation of my Examiner Dr. Behzad Mesgarzadeh, not only before starting the thesis when his great guides helped me to get the chance to take this thesis, but also during the thesis. So I am really thankful of him.

I am deeply grateful to my beloved family and my dearest sister Maryam Khosravi whom their company, attention and supports have been always the best encouragement for me to follow my studying and goals and to overcome the difficulties.

At the end I would like to thank all my dear friends for their supports, helps and the whole nice and memorable moments they created for me during my master education.

III

Abbreviations

ACPW

Asymmetric Coplanar Waveguide

CPS

Coplanar Strip line

CPW

Coplanar Waveguide

EMP

Electromagnetic Pulse

GaAs

Gallium Arsenide

InP

Indium Phosphide

LiNbO

3

Lithium

Niobate

MS

Microstrip line

OEO

Optical-to-Electrical-to-Optical

PIC

Photonic Integrated Circuit

PLC

Planar Lightwave Circuit

PPW

Parallel Plate Waveguide

RF

Radio Frequency

Si

Silicon

T

Thickness

TE

Transvers Electric

TEM

Transvers Electric and Magnetic

TFMS

Thin Film Microstrip

TFPPWG

Thin Film Parallel Plate Waveguide

TM

Transvers Magnetic

IV

Table of Contents

Abstract

... I

Acknowledgement

... II

Abbreviations

... III

Table of contents

... IV

Thesis outline

... 1

Chapter1: Introduction to PICs

... 2

1.1

Photonic integrated circuit

... 2

1.1.1 The differences and similarities between photonic integrated circuits and

electronic integrated circuit ... 2

1.1.2 Benefits of PICs ... 3

1.1.3 Substrate ... 3

1.2

Optical Waveguides

... 4

1.3

RF lines in PICs

... 5

1.3.1 Transmission line model ... 6

1.3.2 Different types of integrated transmission line ... 7

1.4

Travelling wave modulator

... 10

1.4.1 Electro-optic modulators ... 10

1.4.2 Travelling wave modulator structure ... 11

1.5

Crosstalk in PICs

... 11

1.6

Objectives

... 11

Chapter2: Crosstalk in coupled microstrips

... 12

2.1

Substrate and cross section of the microstrips

... 12

2.2

Microstrip transmission lines with reduced crosstalk

... 14

2.2.1 Regular thin film parallel-plate waveguide(TFPPWG) ... 14

2.2.2 Twisted parallel-plate waveguide ... 16

2.3

Conclusion

... 18

Chapter3: Crosstalk in coupled CPS

... 19

3.1

Substrate and cross section of the CPS

... 19

V

3.3

Dependences of the crosstalk on the coupling length

... 21

3.4

Dependences of the crosstalk on line spacing

... 22

3.5

Conclusion

... 23

Chapter4: Crosstalk in coupled CPWs

... 24

4.1

Substrate and cross section of the strips

... 24

4.1.1 Asymmetric CPW ... 24

4.1.2 Symmetric CPW ... 27

4.2

Coupled coplanar waveguides

... 28

4.3

Bends in coplanar waveguides

... 29

4.3.1 Model ... 29

4.3.2 Results of 90

o

_{bend ... 32}

4.3.3 Parameter size dependences ... 34

4.4

Conclusion

... 35

Chapter5: Conclusions

... 36

1

Thesis Outline

Chapter 1 includes a general introduction over Photonic Integrated Circuits (PIC) and their specifications and benefits over Electronic integrated circuits. In this also chapter different types of optical waveguides and RF lines in PICs, specification of different types of transmission lines as well as crosstalk between transmission lines are explained.

Chapter 2 represents a cross section preview for microstrip transmission lines and afterwards in order to investigate the crosstalk between coupling microstrip lines, results of performed

simulations in ADS momentum are shown and outcomes of simulations for different length and distances between lines are studied. Then the new designs for microstrip lines (TFPPWG and Twisted parallel plate waveguide) are introduces and their performance are compared with the regular microstrip lines in order to investigate a solution for decreasing the crosstalk between this type of transmission lines.

Chapter 3 comprises the same investigations and issues as it has been described in above for microstrip lines but for coplanar strip lines (CPS) which is another type of transmission lines. Chapter 4 besides the simulation results for crosstalk between coupled symmetric and

asymmetric coplanar waveguides (CPW) represents an analytic model for Bends in this type of transmission lines. Then the validity analysis of the proposed model is carried out by comparing the results with the ADS Momentum simulations for 90 degree bend.

2

Chapter1:

Introduction to PICs

1.1

Photonic integrated circuit

Photonic integrated circuits are devices on a planar substrate in which light is guided from one optical device to one or more other optical devices. They are also called planar light wave circuits (PLC) or integrated optoelectronic device. The technology used in them is called integrated optics.

1.1.1 The differences and similarities between photonic integrated circuits and

electronic integrated circuit:

Main difference between PIC and electronic integrated circuits is in the type of materials which is used to fabricate the IC.

While silicon (Si) is the most dominant material which is used in fabrication of electronic ICs, PICs are fabricated with a variety of substrate such as silicon (Si), Gallium Arsenide (GaAs), Lithium Niobate (LiNbO3) or Indium Phosphide (InP) and Silica-on-Silicon.[1,2]

The next difference between PICs and electronic integrated circuits is the type of primary devices which are used in integration of any of them.

Electronic ICs integrate many resistors, capacitors, inductors and transistors while PICs integrates optical components such as lasers, modulators, multiplexers/de-multiplexers, photodetectors, filters and optical amplifiers. [1]

Furthermore, in photonic integrated circuits data is transferred through photons while in electric ICs electrons are the carriers of data.

PICs also like the electronic ICs can have both the hybrid and monolithic integrations. In monolithic integration all the devices, both active and passive components, and their interconnections are mounted on the same substrate, all the photonic functions are implemented on a common substrate. The restriction here is limitation in using non- semiconductor components which cannot be incorporated in this method.

In hybrid integration, multiple individual single-function optical and electrical devices are fabricated into a single package and interconnections of these individual devices are done by wires or optical couplings. Here unlike monolithic integration, there is no constraint to use non-semiconductor components as well. [1]

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Figure 1.1: illustrates the both described models of integration

1.1.2 Benefits of PICs

Photonic integrated circuit provides significant advantages such as reduction in power consumption, cost and size of the device as well as improving reliability by packaging many optical devices and functions into a single chip.

It also provides the possibility of integrating electronic components along with optical devices which results in optical-to-electrical-to-optical (OEO) transformation in the optical systems. So it extols both system flexibility and functionality.

PIC ICs are more robust and have lower sensitivity to interferences comparing to electronic ICs which are so vulnerable to decays when they are for example exposed to electromagnetic pulses (EMP).

Since light is the source of transferring data in photonic integrated circuits, a huge amount of data is transferable at a very high speed, so they have a higher data rate. This is an advantage which makes these devices suitable for optical fiber communications.

1.1.3 Substrate:

Different materials such as silicon (Si), silicon on silicon, lithium niobate (LiNbO3), gallium

arsenide (GaAs) or indium phosphide (InP) can be used as substrate in manufacturing of transmission lines in photonic integrated circuits.

Although silicon based integrating of tracks might be more cost effective, among the various mentioned materials, InP is a critical one which is used in both photonic and high speed

electrical instruments. Higher speed of electrons in InP comparing to Silicon substrate makes it a suitable alternative for manufacturing of high speed devices in photonic and optoelectronic areas.

InP also has the capability of being grown as an epitaxial substrate to create another materials which can be used in fabrication of photonic system. Growth of InP on silicon and its approach to fabricate devices like LEDs, lasers, solar cells, and other optoelectronic devices for optical

4

1.2 Optical Waveguides

In PICs optical waveguides are used as interconnections between optical components. Optical waveguides are dielectric structure in which infrared or visible electromagnetic waves propagate. .

Optical waveguides have different shapes and geometries depending on the range of frequency and bandwidth they operate in. According to their geometry, waveguides can be categorized as slab (1), strip (2) fiber and (3) waveguides [1,2,3]. Figure1.2 is the illustration of these 3 types.

Figure 1.2: Optical waveguide [1]

An optical waveguide consists of a dielectric material of a specific refraction index which is surrounded by other materials having lower refraction index.

Figure1.3 shows that electromagnetic waves propagate lengthwise in waveguides and are confined by the physical boundaries and geometry of the waveguide.

Figure1.3: a planar waveguide

Three different refraction indexes are also shown in this picture as n1, n2 and n3 where n2 is

related to the core and is bigger than the two other ones. Light waves such as electromagnetic waves tend to propagate where the refractive index is higher.

There are different modes of propagation of electromagnetic waves in waveguides. Two common modes are Transvers Electric (TE) and Transvers Magnetic (TM) modes.

For a typical planar waveguide which is bounded in x direction, waves are propagating along the

z axis as it is clear in figure1.3. In TE mode, electric field lines (Ē) of EM waves are perpendicular

to the direction of propagation and in TM mode the magnetic flux of wave is perpendicular to the direction of propagation.

5

Figure1.4: illustrates the magnetic and electric field propagation in TE and TM modes

Wave propagation in each mode depends on the cutoff frequency; it means that if electromagnetic waves have a frequency smaller than a certain frequency called cutoff frequency, they can’t propagate in a certain mode. So electromagnetic wave propagation in each mode only supports propagation in frequencies above its cutoff frequency.

Wavelength is an important factor to take into consideration:

⁄ (1.1) where is the wavelength and is the velocity of propagation.

According to equation 1.1, wavelength is a function of frequency. As the frequency is increases the wavelength decreases and the thickness of the optical waveguide decreases as well. It means that for lower frequencies thickness of optical waveguides is less than in higher frequencies. It is vital to take it into consideration that for a specific mode if the width of the optical waveguide is too large, then other modes of propagation also may carry in it and cause problems.

Optical waveguides may be used for different applications; some of them are for example in optical fibers where they are used to transmit light in long distances or in optical integrated circuits where they interconnect different optical components.

1.3 RF lines in PICs

RF lines in photonic integrated circuits are electrical type of waveguides or transmission lines used to convey microwave frequency range (between 300MHz~300GHz).

These kinds of transmission lines are metal strips that are fabricated on a dielectric which separate them from a ground plane. They form the connection between different electrical and optical components on photonic circuits.

Here the main propagation mode is transverse electric and magnetic (TEM) mode or quasi-TEM mode, in contrast with other types of optical waveguides such as rectangular waveguides for which the transmission mode of signal are TE or TM modes.

In TEM mode both electric and magnetic field are perpendicular to the path of EM wave propagation and there is no cutoff frequency for the waveguides which support this mode.

6

Figure1.5 shows that for a waveguide to support the TEM waves, it should have at least 2 separate conductors.

Figure1.5: TEM propagation representation

Integrated transmission lines investigated in this thesis support quasi-TEM mode. These are transmission lines like microstrip, coplanar waveguide, etc. more explanation about this mode of propagation is provided in section 1.3.2.

1.3.1 Transmission line model

If we consider a unit length of a transmission line, the equivalent circuit for that is the network shown in figure1.6.

Figure1.6: Schematic representation of a unit length transmission line

In this figure primary constants of the transmission line are shown and can be defined as following:

R is the resistance per unit length L is the Inductance per unit length G is the conductance per unit length C is the capacitance per unit length

Using these parameters characteristic impedance of the transmission line is

√ (1.2) which in the case of low losses is simplified to:

√ (1.3) The propagation constant and the phase velocity are given as:

7

(1.5) Where β=2П/λ is phase constant or phase change.

Characteristic impedance and propagations constant (phase velocity) are important factors to take into consideration in designing a transmission line, it will be explained more in next chapters how to design it in order to have a good design.

1.3.2 Different types of integrated transmission line

In this section, a brief explanation about some RF transmission lines which are of consideration in this these is presented and their structure is described.

The transmission lines which are studied in thesis are microstip lines (MS), coplanar striplines (CPS), coplanar waveguides (CPW).

 Microstrip

Microstrip line structure consists of one single conductor with a specific thickness (T) and width (W) on an insulating substrate and a ground plane on the opposite side of the substrate.

(a) (b)

Figure1.7: microstrip structure (a), field propagation in microstrip (b)

So microstrip transmission line contains two paths for current. Metal conductor and ground plane as the return path of current. They support quasi-TEM mode of propagation.

According to figure1.7 (b), EM waves in microstrip lines propagate in two different mediums including substrate and air; so speed of wave which depends on the permittivity of the dielectric (equation1.3) is different for these two mediums. Consequently there is not a pure TEM mode either in microstrip lines or in any other transmission line with a similar structure.

These are quasi-TEM transmission lines, meaning that for lower frequencies, up to a few GHz they have a behavior like in TEM mode so the analysis and equations of TEM mode can be applied for them but in higher frequencies where dispersions are more, dispersion corrections are required in analysis.

In quasi-TEM transmission lines, we have effective dielectric constant ( ) instead of dielectric constant:

(1.3)

Hence the phase velocity is given by:

8

Using microstrip facilitates the mounting of active components on top of the boards. Microstrip transmission line simplifies the connection between components, they are also cheap and it is possible to integrate it with strip line coplanar waveguide on the same substrate.

Components such as antennas, filters, couplers and power dividers can be provided using microsrip lines.

Since microstrip is not immersed in dielectric is vulnerable to crosstalk and undesired

interferes. This is one of disadvantageous of microstrip transmission line. Additionally they have higher losses and are dispersive.

 Coplanar waveguides (CPW)

This is a full planar strip line composed of a central metal strip of width (S), separated from two other conductors of width (W) which are as ground plane. The separation width is (g) and all the conductors are on the same substrate.

The thickness of substrate (h) is infinite ideally but practically it is chosen in a way that electric and magnetic fields vanish before getting out to the air. But still because of more distribution of EM fields in the air, the effective dielectric constant in CPW is less than that for a

microstrip. This effect results in higher attainable characteristic impedance in CPW.

Figure1.8: CPW structure

However due to the same reason of larger amount of EM field propagation above the substrate, dispersion in CPW is worse than that in microstripline.

Another disadvantage in CPW comparing to microstrip is the concentration of the current in edges is more and ends up in more losses.

CPW on the other hand has many advantageous over microstrip. For example in CPW, thickness of the substrate does not affect the level of parasitic radiation too much, so CPW is not that sensitive to substrate thickness while it is not the same for the microstrip.

The flexibility in choosing the substrate thickness in CPW makes it a good choice specially in high frequency designs.

Another advantage of CPW is that because all its conductors including its ground are on the same side of a dielectric, components can be mounted on it without need to via holes which are used in microstrip line to create the ground connection.

Generally speaking, there are some limitations in utilizing CPW lines because there is a lack of general understanding of how to use them in microwave circuits also because of shortage in its available circuit elements or CAD program to support them.

But still they are used in some application as alternative of conventional microstrip lines. They are used for instance as an energy coupler for medical applications or it is attractive for RF circuit design or to be used in antennas and arrays.

9

 Coplanar strip line (CPS)

Coplanar strip lines consist of two parallel metal strips with thickness (T) and width (W) fabricated on a dielectric substrate of thickness (h). This pair of strips is separated by a slot of width (g) as shown in figure1.9.

Figure1.8 is a cross-sectional view of a typical CPS which also represents E and H field distributions in it.

Figure1.9: CPS structure

CPS has a unipolar and balanced structure which makes it superior to microstip or even CPW transmission lines.

One of CPS advantageous over microstrip is in the process of fabrication. The restrictions

applied by this process on the width and distance between conductors, causes a limitation in the range of possible achievable characteristic impedances. This restriction causes a maximum impedance of 110 ohm for a microstrip while in CPS, the ease of changing characteristic impedance with changing the width or distance between conductors, facilitates having higher characteristic impedances even till 250 Ohm.

Furthermore, its balanced nature simplifies the parallel and serial surface mounting of several active and passive components without need for via holes which end up in increased parasitic elements.

Having the paired structure, CPS not only has all the advantageous of CPW, but also has additional advantage of decreasing the die size for each circuit function which results in more number of circuit functions for each given die size and efficient usage of the wafer area. Consequently it has lower cost.

CPS has a couple of other advantageous. Its balanced structure makes it suitable for designing balanced circuits such as differential amplifiers, mixers, modulators, rectennas and feeds for printed antennas.

Along with CPW it is a good transmission line for solid-state device integration and integrated electro-optic components.

Of its other characteristics are good propagation, small dispersion, comparably insensitive to substrate thickness, small discontinuity parasitics and simple implementation of open- or short-ended strips. [23]

10

1.4 Travelling wave modulator

Travelling wave modulator is a type of electro-optic modulators (EOM). In what follows a brief description of the travelling wave modulators and their structure is provided.

1.4.1 Electro-optic modulators:

Electro-optic modulators are optical devices which are used to control phase, amplitude, polarization and power of a laser beam with an electrical signal. This way, the electrical control signal modulates the mentioned parameters of the beam.

Electro-optic modulators are based on electro-optic effect [26]. According to electro-optic effect definition, electrical field generated by applied electrical signal produces some changes in the optical properties of the material wherein the beam of light and the electrical signal are propagated. These changes affect the refraction index of the material and are translated to different modifications in parameters of the light such as amplitude, phase, frequency, polarization, etc.

Two practical uses of electrooptical modulators are amplitude and phase modulators, as it is depicted in Figure1.10 by applying the electrical field of the propagating microwave or dc signal, the phase of the optical signal varies therefore makes a phase modulator.

One way to make an amplitude modulator is by applying the phase modulator to one of the arms of the Mach–Zehnder interferometer.

Figure1.10: Layout configurations for integrated electro-optic modulators The upper part shows a phase travelling wave modulator. The lower

part shows a Y-Branch travelling wave amplitude modulator [31]

The simplest optical modulator is made from a crystal of some material like lithium niobate where a lumped capacitance is used as the electrodes of propagating electrical signal. Because of the structure of the lumped capacitance configuration, there are some limitations in velocity and bandwidth in high frequencies. So the travelling wave structure can be an alternative in which the path of propagating signal is longer and therefore the problems existed in lumped model such as reflection of the wave and velocity mismatch between electrical and optical signals are managed better.

11

1.4.2 Travelling wave modulator structure

Travelling wave modulator is a kind of electro-optic modulator which is used for wide bandwidth modulations (gigahertz regions). In other words to guarantee the operation of an electro-optic modulator in high speeds, utilizing the travelling wave electrodes is significant. In this design, electrodes are designed as transmission lines, typically as CPS or CPW.

Generally speaking a travelling wave modulator consists of a substrate, e.g. semiconductor material, an optical wave guide for propagating an optical signal within the substrate, and travelling wave electrodes. Electrical signal is propagated along these electrodes and electrical field produced by this propagating signal penetrates the optical waveguide and changes its reflective index, thereby controls the optical signal.

1.5 Crosstalk in PICs:

In photonic or optoelectronic modules, individual blocks and elements are integrated densely to reduce the size and cost. Consequently there are some undesired interactions between these components and the input output data channels.

These undesired interactions or interferences can be categorized into three different groups of crosstalk called:

I. Electrical crosstalk II. Optical crosstalk III. Thermal crosstalk

Crosstalk in photonic integrated circuits is mainly originated between laser and photo diode consisting both electrical and optical interconnects/transmission lines and crosstalk between them.

1.6 Objectives:

In this thesis electrical crosstalk in various types of planar transmission lines such as coplanar strip lines (cps), parallel plate waveguides (ppwg), coplanar wave guides (cpw) and microstrip lines are investigated. Optical and thermal crosstalks are out of the scope of this thesis.

Apart from the analysis of the FR crosstalk attempts are made to design RF lines in such a way that reduces the crosstalk while keeping the high density of integration.

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Chapter2:

Crosstalk in coupled microstrips

In this and next chapters the results of simulations of crosstalks between different types of transmission lines are presented.

In all cases, before analyzing the coupling effects between transmission lines, first single transmission lines with characteristic impedance (Z0) around 50Ω in an acceptable frequency range are designed.

Thickness of the substrate, relative permittivity (dielectric constant, ), and width of strip (metal) are some important parameters to design a transmission line. With changing the width of the metal or strip, the desired effective dielectric constant ( ) and characteristic impedance is designed.

2.1 Substrate and cross section of the microsatips

The considered substrate in this thesis for the analysis of the thin film microstrip transmission lines is InP with a BCB layer. The permittivity of BCB is 2.65 and the thickness is 4.5m. The cross sectional sizes of the strips are shown in Figure2.1. Thin film microstrips of this type are used in photonic integrated circuits where they deliver microwave signals to or from

semiconductor devices like laser and photodiodes.

(b) (b)

Figure2.1: cross section preview of a microstrip transmission line

Designing the microstrip transmission line with the mentioned parameters, results in an about

characteristic impedance. The following graph (figure2.2) shows the best result for in a wide frequency range.

(a) (b)

Figure2.2: (a) Characteristic impedance and (b) effective dielectric permittivity

As seen from Fig.2.2 both the impedance and effective permittivity are characterized with strong dispersion, i.e. frequency dependence. This dispersion is associated with the internal inductance of the strip. The internal inductance is the inductance which is associated due to the penetration

5 10 15 20 25 30 35 40 45 0 50 2.4 2.6 2.8 2.2 3.0 freq, GHz E p si lo n _ e ff W=13um m Port1 Port2 L=2000um h=4.5um BCB InP

13

of magnetic flux into the metal. As much as the frequency increases penetration depth of magnetic flux into the conductor decreases due to the skin effect. This penetration depth (also known as the skin depth) is given by √ where f is the frequency, µ, the permeability and σ (=1/ρ), the conductivity of the conductor [33]. Decreasing of skin depth in higher frequencies means that the impedance increased and similarly when the magnetic fields penetration decreases so the inter inductance is decreased.

When two or more lines are in close proximity the microwave power launched in one (or more) of the lines induces undesired propagating waves in the other liens. This is referred to as a crosstalk.

Figure2.3: strips and arrangements of the ports

S21 in Figure2.3 is the response at port2 due to a signal at port1. It is shown in dB and indicates the amount of power which is received at port2 as the destination.

S31 and S41 are both the microwave power launched from input signal at port1.

It means that a signal launched in port 1 of the primary line, Figure2.3, induces undesirable waves in the neighboring line travelling back and forth. Apart from port 2, the power is

delivered also to the ports 3 and 4, S31 and S41, distinguished respectively as near-end and far-end crosstalk.

In order to study the crosstalk behavior of this transmission line, first the coupling effect of two neighboring microstrip for different lengths and different distances between them is taken into consideration.

Cross section of two coupled microstrip line and simulation results for near-end (S31) and far-end (S41) crosstalk are shown in Figure2.4.

(a)

(b) (c)

Figure2.4: (a) cross section of the microstrip lines used in Momentum simulations, (b) crosstalk changes with changing length (c) crosstalk changes with changing distance between lines

As it is seen in Figure2.4 (a) the thickness of the substrate is 4.5um and the permittivity is 2.65. d is the distance between two lies and as it is seen in Figure2.4 (c), it changes between 30um to 100um. Crosstalk for different length of strips are also analyzed and in Figure2.4 (b).

Port1 Port2 Port3 Port4 S21 S41 S31 BCB d =2.65, t=4.5um

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2.2 Microstrip transmission lines with reduced crosstalk

In this section, new designs of the microstrip lines with reduced crosstalk are proposed and their performances are analyzed.

2.2.1 Regular thin film parallel-plate waveguide (TFPPWG)

First a new type balanced line allowing for reduced crosstalk is identified. Detailed analysis of its performance is described in the following.

The cross section of the proposed thin film parallel-plate waveguide (TFPPW) is shown in Fig.2.5 (a). Like coplanar strip waveguides this line may be designed to be balanced.

(a) (b)

(c)

Figure2.5: (a) PPWG cross sectional preview, (b) its characteristic impedance, and (c) Momentum layout

The substrate consists two layers, InP and BCB. Microstrip lines with this cross section and materials are used in photonic integrated circuits bot to deliver both DC bias and RF signals. The proposed thin film PPWG is similar to microstrip structure in Figure2.1 except for the return path which is implemented as a narrow strip sandwiched between InP substrate and BCB layer. In the case of conventional microstrips, Figure2.6.a, the lines share a common ground plane which increases the crosstalk. In contrast, in the case of PPWGs the return paths of the signal are separated to reduce the crosstalk, Figure2.6.b.

Figure.2.6d and Figure.2.6e compares the crosstalk in coupled PPWs (twin strips) with coupled microstrip lines.Simulations are done for the length equal to 500um for both the microstrip and PPW lines. . The thickness of the BCB layer is set to be 4.5um and strips are made of gold with 1.0um thickness.

(b)

(c) W=16um m BCB h=4.5um InP =13 h=250um BCB BCB Microstrip PPW Coupled Microstrip Coupled PPW S21 D D 14um 14um 13um 13um Coupling length (a)

15

(d) (e)

Figure2.6: (a) Cross section preview of coupled microstrip lines, (b) cross section of the coupled PPWGs, (c) cross coupling and loss, (d) near-end crosstalk, (e) far-end crosstalk

Even though the line losses (S21) are slightly higher for PPW compared to microstrips, the far- end crosstalk of the coupled TFPPWs (S41) is substantially lower compared with the coupled microstrip.

Figure2.7 compares the near and far end crosstalks between coupled twin strips or PPWs and microstrips depending on the distance D between them.

As it is seen from Figure2.7, near-end crosstalk (S31) between PPWs for frequencies below 15GHz and distances between the lines less than 50um is substantially lower compared to the microstrip lines.

Similarly, the far-end crosstalk (S41) is substantially lower in the case of twin lines (PPW) below 15GHz and distances less than 70um.

(a)

(b)

Figure2.7: Comparison between (a)near-end (S31) and (b)far-end (S41) crosstalks vs. distance D between the coupled twin strips and TFMs. The coupling length is 500um

Figure2.8 compares the crosstalks between coupled twin strip and microstrip lines depending on the coupling length (see figure2.5(c)) at 15GHz.

-68 -63 -58 -53 -48 -43 30 50 70 90 S31 ( d B)

Distance Between 2Lines(um)

-80 -75 -70 -65 -60 -55 -50 30 50 70 90 S41( d B)

Distance Between 2Lines(um)

S31 Coupled Microstrip Coupled PPW _Coupled PPW Coupled Microstrip S41 PPWGs @ 30GHz PPWGs @ 15GHz Microstrips @ 15GHz Microstrips @ 30GHz PPWGs @ 15GHz Microstrips @ 15GHz Microstrips @ 30GHz PPWGs @ 30GHz

16

(a) (b)

(c)

Figure2.8: Dependences of the (a)insertion losses S21, (b)near end, S31, and (c)far end, S41, crosstalks on the length of the coupled line sections L . f=15GHz, distance D=30um in all cases.

Here the distance between coupled lines are constant and equal to 30um.

The dependences of the crosstalks on the coupling length are characterized with a typical periodic exchange of the signals between the lines (not shown in figure2.8).

Additionally, for the given distance, D=30um, and below frequency 15GHz, both far and near end crosstalks of the coupled twin strips are lower.

2.2.2 Twisted parallel-plate waveguide:

One of the methods offered in many articles in order to decrease the crosstalk effect between balanced lines, is twisting them. [34]

This method is applied here to PPWs to observe its influence. Detailed information about this structure and its performance is in following.

 Symmetric twisting

Shown in Figure2.9 is the structure of one line PPW with one symmetric twist. In symmetric twist both strips are twisted.

In this picture one twist is applied in the middle of a line with length L. The width of one of the strips is exaggerated in this figure for clarifying the twisting, while both strips have the same width in reality in order to have a balance line.

Figure2.9: PPW preview with one symmetric twist in the middle of line

-4 -3,5 -3 -2,5 -2 -1,5 -1 -0,5 0 200 1200 2200 3200 4200 S21 ( d B) Length(um) S21 @ 15GHz Regular PPWG S21 @ 15GHz Microstip -60 -50 -40 -30 -20 -10 200 1200 2200 3200 4200 S31 ( d B) Length(um) S31 @ 15GHz Regular PPWG S31 @ 15GHz Microstip -85 -75 -65 -55 -45 -35 -25 -15 200 1200 2200 3200 4200 S41 ( d B) Length(um) S41 @ 15GHz Regular PPWG S41 @ 15GHz Microstip L

17

The crosstalk in two regular coupled lines (figure2.10 a) is compared with the crosstalk in two coupled lines where one of the lines has one twist in the middle and the other one is a simple balanced PPW(figure2.10 b).

(a) Figure2.10: (a) Regular coupled PPW, (b) twisting in one of the coupled lines (b)

Results from ADS Momentum simulations for near and far end crosstalks show that twisting utilization in the PPWs is not a suitable way to modify the crosstalk behavior and in fact results in both twisted and regular PPWs are either so close to each other or in some cases the regular PPWs have better results which means that they have lower crosstalk (specially in the case of S41).

These results are available in figure2.11. As it is seen with increasing the distance between two coupled line, results get even worse.

Figure2.11: Comparison between near and far end crosstalks between copled twisted PPW an coupled regular PPW

In order to get more assurance about the results, the simulations are done for different coupling lengths. This results are compared with the results of microstrip lines as well to get the final conculotion. 5 10 15 20 25 0 30 -90 -80 -70 -60 -50 -100 -40 freq, GHz d B (p p w g _ 5 0 0 u m _ d 5 0 _ m o m _ a .. S (3 ,1 )) d B (p p w g _ tw ist e d _ 5 0 0 u m _ d 5 0 _ m o m _ a .. S (3 ,1 )) 5 10 15 20 25 0 30 -100 -90 -80 -70 -60 -50 -110 -40 freq, GHz d B (p p w g _ 5 0 0 u m _ d 5 0 _ m o m _ a ..S (4 ,1 )) d B (p p w g _ tw ist e d _ 5 0 0 u m _ d 5 0 _ m o m _ a ..S (4 ,1 )) 5 10 15 20 25 0 30 -90 -80 -70 -60 -50 -100 -40 freq, GHz d B (p p w g _ 5 0 0 u m _ d 7 5 _ m o m _ a .. S (3 ,1 )) d B (p p w g _ tw ist e d _ 5 0 0 u m _ d 7 5 _ m o m _ a .. S (3 ,1 )) 5 10 15 20 25 0 30 -110 -100 -90 -80 -70 -60 -50 -120 -40 freq, GHz d B (p p w g _ 5 0 0 u m _ d 7 5 _ m o m _ a ..S (4 ,1 )) d B (p p w g _ tw ist e d _ 5 0 0 u m _ d 7 5 _ m o m _ a ..S (4 ,1 )) 5 10 15 20 25 0 30 -100 -90 -80 -70 -60 -50 -110 -40 freq, GHz d B(p p w g _ 5 0 0 u m _ d 1 0 0 _ m o m _ a .. S(3 ,1 )) d B(p p w g _ tw is te d _ 5 0 0 u m _ d 1 0 0 _ m o m _ a .. S(3 ,1 )) 5 10 15 20 25 0 30 -110 -100 -90 -80 -70 -60 -50 -120 -40 freq, GHz d B(p p w g _ 5 0 0 u m _ d 1 0 0 _ m o m _ a .. S(4 ,1 )) d B(p p w g _ tw is te d _ 5 0 0 u m _ d 1 0 0 _ m o m _ a .. S(4 ,1 )) S31 S31 S31 S41 S41 S41

Blue lines: results of twisted PPW red lines: results for regular PPW

D=50um

D=75um

18

Figure2.12: Dependences of the insertion losses S21, near end, S31, and far end, S41, crosstalks on the length of the coupled line.

The dependences of the crosstalks on the coupling length are characterized with a typical periodic exchange of the signals between the lines, figure2.12. Additionally, for the given distance D=50um and frequency f=30GHz, both far and near end crosstalks of the coupled microstrips are lower. In contrast with the outcome from figure2.8, where it is shown that for lower frequencies and smaller distances, crosstalk between coupled tween strips (PPW) is lower compared to the microstrips.

 Asymmetric twisting

Another possible twist to be applied on this type of transmission line is twisting only one side of the line as depicted in figure2.13.

Figure2.13: asymmetric twist in one line PPW

This is Asymmetric twist. Results for symmetric and asymmetric twists are completely compatible so explaining more details is withdrawn.

2.3 Conclusions:

Compared to thin film microstrips (TFMs), tween strip lines (PPW) offer lower crosstalk at lower frequencies and smaller distances between them. Hence they are suitable for densely packed tracks at lower frequencies, while TFMs are preferable for higher frequencies and relatively larger distances between them.

-4,5 -3,5 -2,5 -1,5 -0,5 0,5 200 1200 2200 3200 4200 S21 ( d B) Length (um) -60 -50 -40 -30 -20 -10 200 1200 2200 3200 4200 S 31 ( d B) Length (um) -70 -60 -50 -40 -30 -20 -10 200 1200 2200 3200 4200 S41 ( d B) Length (um) Regular PPWG 1line twisted PPWG

Microstrip 1line twisted

PPWG Regular PPWG Microstrip Microstrip Regular PPWG 1line twisted PPWG

19

Chapter3:

Crosstalk in coupled CPS

In this chapter crosstalk between balanced lines or coplanar strip lines (CPS) are investigated. A large number arrangements of coupled balanced lines is considered and the near and far end crosstalks are analyzed depending on the length of the coupled section and spacing between the lines.

3.1 Substrate and cross section of CPS

The substrate considered in the analysis of the coplanar strip lines includes a 250um thick InP and a 4.5um thick BCB. Strip conductors can be on the same layer or on two different layers. Figure3.1 (a, b) illustrates two different example of these arrangements. Permittivity of each layer (εr) is also represented in this figure.

(a) (b)

Figure3.1: cross sectional view of CPS, (a) both of strips on the same layer, (b) strips are on different layers

The cross sectional parameters and port arrangements for two coupled CPS lines are shown in Figure3.2. Twelve possible arrangements of the strips are considered in simulations (see Table3.1).

(a) Figure3.2: (a) Two couples lines and arrangement of the ports (b) cross sectional parameters

The parameters of lines shown in Figure3.2 are: width of the strips S=20m, gap between two strips 2g=5m, and distance between two coupled lines D= 50m. Strips are 1m thick and made of gold.

The crosstalk between coupled lines depends on the cross sectional arrangement of the lines, the distance, D, between the lines and the length of coupled region. The possible arrangements of the strips are summarized in Table3.1. Table3.1 also includes simulated near and far end crosstalks (S31 and S41 respectively) at three different frequencies.

The cross sectional sizes used in simulation of all twelve arrangements in Table3.1, are equal to the sizes mentioned above.

In column “Line Cross section” of Table3.1, any strip of a line on BCB, is identified by color red and on InP layer is identified by color yellow.

InP BCB =13,t=250um =2.65,t =4.5um InP BCB =13,t=250um =2.65,t =4.5um L Port 1 Port 2 Port 3 Port 4 D S 2g S S 2g S (b)

20 Line Cross Section

S31

Line Cross Section S41 5GHz 10GHz 15GHz 20GHz 5GHz 10GHz 15GHz 20GHz -42.704 -39.961 -39.294 -38.877 -49.207 -46.785 -46.715 -48.317 -42.566 -40.118 -399.955 40.555 -46.338 -43.535 -43.356 -44.905 -42.511 -39.138 -37.009 -34.955 -46.338 -43.535 -43.356 -44.905 -42.324 -39.119 -37,372 -34.994 -45,926 -43.303 -43,574 -45.675 -42.268 -39.945 -40.154 -42.067 -42.278 -42.811 -42.59 -43.518 -41.777 -39.713 -40.619 -43.947 -45.13 -44.334 -46.958 -38.389 -41.699 -38,798 -38.222 -38.893 -44,673 -40.545 -37.24 -33,419 -41.662 -39.881 -41.594 -42.366 -44.629 -40.52 -37.243 -33.493 -41.097 -37.937 -37.179 -37.962 -44.439 -41.578 -40.811 -40.518 -41.061 -38.023 -37.656 -38.805 -44.433 -41.981 -42.003 -43.757 -41.058 -38.021 -37.654 -38.809 -44.317 -43.28 -47.257 -44.68 -39.301 -35.969 -35.265 -36.991 -41.246 -41.634 -41.279 -41.831 Table 3.1 Cross-sectional arrangements and simulated near and far end crosstalks, S31 & S41 values are in increasing order at 5GHz

3.2 Dependences of the crosstalk on the cross sectional arrangement:

As a first step coupled balanced lines with different cross-sectional arrangements of the strips are considered for fixed coupling length, L=2000m, and fixed distance, D=50m, between the lines. The other sizes, s=20m, 2g=5m, are also kept fixed.

Figure3.3 and Fig3.4 show frequency dependences of the near and far end crosstalks for the cross-sectional arrangements shown in Table 3.1.

Figure3.3: Near-end crosstalk (S31)

-45 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 5 10 15 20 S31 ( d b ) Frequency (GHz) 2lin_BCB 2lin_InP 2lin_BCBInP 2lin_InPBCB 1lineBCB_1lineInP BCBBCB_BCBInP BCBBCB_InPBCB BCBInP_InPInP InPInP_InPBCB InPInP_BCBInP BCBInP_InPBCB InPBCB_BCBInP BCB InP InP InP InP InP InP InP InP InP InP InP InP InP InP InP InP InP InP InP InP InP InP InP InP BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB BCB

21

Figure3.4: Far-end crosstalk (S41)

As seen in Figure3.3 and 3.4, depending on the frequency and cross-sectional arrangement of the strips, the crosstalk may change between 5 and 10 dB. Given in Table3.1 are crosstalks at four different frequencies. The comparison shows that for the lowest near end crosstalk (S31) both lines should be on top of the BCB layer (second arrangement in column 1, Table3.1), while for lowest far end crosstalk (S41) both lines should be at the interface between BCB and InP layers (first arrangement in column2, Table 1). Therefore it can be concluded that for CPS lines, cross sectional designs with higher have higher near-end crosstalk (S31) while far-end crosstalk (S41) is decreased with increasing .

The cross sectional arrangements in Table3.1 are listed in the order of increasing crosstalks. Thus the selection of the cross sectional arrangement depends on the PIC requirements imposed on the far and near end crosstalk levels.

3.3 Dependences of the crosstalk on the coupling length

In order to check the dependence of the crosstalk on the coupling length, various lengths of two mentioned configurations in section 3.2 with lowest near and far end crosstalk are designed. The theory predicts periodic exchange of microwave power between the lines. This periodic behavior is clear in Figure3.6. According to theory when the length of line is more than the wave length of microwave signal, exchange of power happen every λ/2. It may be explained

considering Figure3.5 where two lines with length L and voltages V1 and V2 are adjacent.

Figure3.5: Two adjacent lines

Equation3.1 demonstrates this periodic behavior. This equation is a function of electrical length (φ) and voltage coupling coefficientcorresponding to the maximum level of coupling (K).

_√

(3.1) -50 -48 -46 -44 -42 -40 -38 -36 -34 -32 5 10 15 20 S41 (d B ) Frequency (GHz) 2lin_BCB 2lin_InP 2lin_BCBInP 2lin_InPBCB 1lineBCB_1lineInP BCBBCB_BCBInP BCBBCB_InPBCB BCBInP_InPInP InPInP_InPBCB InPInP_BCBInP BCBInP_InPBCB InPBCB_BCBInP V1 V2 L

22

Where .

Figure3.6 shows dependences of the near and far end crosstalks on the coupling length for two cases identified as:

(a) best in terms of lowest near end cross talk, and (b) best in terms of lowest far end cross talk.

According to Figure3.6 (b), when two lines are on BCB, except for the lengths shorter than 1mm, is always S41higher than S31.

The crosstalk becomes stronger where the coupling length is close to resonance length.

(a)

(b)

Figure3.6: Dependence of the cross-talks on the coupling length at 50 GHz for two arrangements of the lines: (a) both lines are on top of BCB, (b) both lines are at BCB/InP interfaces

3.4 Dependences of the crosstalk on line spacing:

As an example, Figure3.7 demonstrates dependences of the near and far end crosstalks for the case where both lines are on top of BCB layer. As one may expect intuitively, the crosstalk decreases linearly with increasing distance between the lines.

-64 -59 -54 -49 -44 -39 -34 0 1000 2000 3000 4000 S-Par ame te rs (d B) Length(um)

Both lines on InP layer

S31 @ 50GHz(2LineInP) S41 @ 50GHz(2LineInP) -60 -55 -50 -45 -40 -35 -30 0 1000 2000 3000 4000 S-Par ame te rs (d B) Length(um)

Both lines on BCB layer

S31 @ 50GHz(2LineBCB) S41 @ 50GHz(2LineBCB) BCB InP BCB InP

23

Figure3.7: Crosstalk vs. distance between the lines

3.5 Conclusion:

Balanced (i.e. CPS) lines are inherently low crosstalk. By proper arrangement of the strips in substrate layers the crosstalk level may be controlled by 5-10dB.

The selection of cross-sectional arrangement depends on the crosstalk requirements imposed by PICs. -50 -48 -46 -44 -42 -40 -38 -36 -34 25 50 75 100 S31 ( d B)

Distance Between 2 lines(um)

Both lines on BCB layer

S31 @ 25GHz S31 @ 50GHz -51 -49 -47 -45 -43 -41 -39 -37 -35 -33 -31 -29 25 50 75 100 S41

Distance Between 2 lines(um)

S41 @25GHz S41 @ 50GHz BCB

24

Chapter4:

Crosstalk in coupled CPWs

Primarily step in this chapter is also designing a single symmetric coplanar waveguides (CPW) and asymmetric coplanar waveguides (ACPW) with acceptable characteristic Impedance. Then the performance of these lines with extended lengths is also considered. The results will be used for interpretation of the crosstalk between adjacent CPWs.

4.1 Substrate and cross section of the strips

4.1.1 Asymmetric CPW

The structure of one line Asymmetric CPW is displayed in figure4.1. This is displaying a general preview of ACPW. There different types of substrate are used in simulations of ACPW.

They are called Oclaro, Silicon nitride and substrate with the single layer of InP. Characteristics and effects of each of these 3 types are considered separately in the following descriptions.

Figure4.1: general preview of a single line CPW

 Asymmetric CPW using oclaro as substrate

Simulated parameters of a single CPW based on Oclaro template, figure4.2, are shown in figure4.3. Cross sectional sizes and different layers permittivity are indicated in figure4.2.

Figure4.2: Oclaro substrate template for a single asymmetric CPW

In figure4.2, the parameters of line are equal to: signal strip 2s=50um, slots g=7um and ground strips w=350 um. The other parameters are also as determined in figure4.2. Length if line is 2000um.

The results of simulations for characteristic impedance and effective permittivity are available in figure4.3. For the given cross sectional sizes of the CPW the impedance is less than 71ohm for frequencies above 15GHz (the violet line in figure4.3(a)).

Substrate

GND Signal g 2S

Semi-insulating InP Substrate, t=250um (σ=0, =12.6)

n-InP, t=2um (σ=3.7E4 S/m, =12.6) Undoped core, t=0.4um, (σ=0, =13)

Implanted p-InP, t=2.4um (σ=0, =12.6) Si3N4, t=0.2um, (σ=0, =7.5) SiO2, t=2.1um, (σ=0, =3.9) GND Signal 2S g W

25

(a) (b)

Figure4.3: (a) Characteristic impedance value for ACPW, (b) effective permittivity

 Asymmetric CPW using silicon nitride as substrate

The other substrate which is considered in this thesis as previously said is Silicon nitride substrate.

Shown in figure4.4 is the cross sectional preview of the single asymmetric CPW with silicon nitride substrate.

Figure4.4: cross sectional preview of asynchronous CPW with Silicon nitride substrate

The parameters for asymmetric CPW shown in figure4.4 are same as Oclaro template with strip 2s=50um, slots g=7um and ground strips w=350um. The other parameters are as in figure4.4 and length of line is also 2000um.

Simulation results for Z0 and εeff are depicted in the figure below (figure4.5).

(a) (b)

Figure4.5: (a) Characteristic Impedance value for ACPW, (b) effective permittivity

Considering figures 4.3 and 4.5, it ends up in some outcomes.

The primary result is that both characteristic impedance and epsilon effective are frequency dependent. 5 10 15 20 25 30 35 40 45 0 50 65 70 75 80 85 60 90 freq, GHz Z _ 0 (H ) 13.76G 71.09 m1 m1 freq= Z_0=71.09413.76GHz H 5 10 15 20 25 30 35 40 45 0 50 1 2 3 4 5 6 0 7 freq, GHz E o si lo n _ e ff (H ) H 5 10 15 20 25 30 35 40 45 0 50 20 40 60 80 0 100 freq, GHz Z _ 0 (H ) 14.53G 65.32 m1 m1 freq= Z_0=65.316 14.53GHz H 5 10 15 20 25 30 35 40 45 0 50 1 2 3 4 5 6 7 0 8 freq, GHz E p si lo n _ e ff (H ) H When thicknessof substrate isdecreased When thicknessof substrate isdecreased Si3N4, t=0.2um, (σ=0, =7.5)

Semi-insulating InP Substrate, t=135um (σ=0, =12.6) g W 2S GND Signal When thicknessof substrate isdecreased When thicknessof substrate isdecreased

26

Also it is observed in these figures that with changing the thickness of substrate, results for characteristic impedance and epsilon effective are changed. The decrement of effective permittivity is the direct consequence of reduction in substrate thickness. Meaning that with decreasing the thickness, more portions of the fields are penetrated into the air and since the permittivity of the air is lower, so the total effective permittivity is decreased as well. This phenomenon ends up in increment of impedance.

Furthermore both Oclaro and Silicon nitride templates include low permittivity layers between the strips and InP substrate, shown in figure4.2 and figure4.4. These layers make the impedance of the lines high, and at higher frequencies cause leakage of the signals into the high permittivity InP substrate. These leakages results in spikes and noises which are seen in characteristic impedance graphs in both figures 4.3(a) and 4.5(a). So areas of frequencies beyond 30GHz are useless areas for these types of substrates where it does not get into a good reasonable result. The mentioned substrate surface waves (waves traveling between different layers of substrate) also cause uncontrollable crosstalk between other components of IC. Generation of the surface waves is especially extensive where the length of the lines (L) is comparable with one coefficient of half wave length of the microwave signals in the line:

( ) Where n=1,2,3,… (4.1)

L and n in the equation above (equation4.1) are physical length of the transmission line and

number of waves respectively. λg is wave length and is equal to:

√

(4.2)

C0 in equation4.2 is the velocity of air equal to 3*108 (m/s).

The frequencies corresponding to the condition ( ) are given by:

√ (4.3)

In fact this is the frequency at which the length is half the wave length (for n=1) and CPW acts as an antenna, so the fields shine in the air and effective permittivity (εeff) is decreased. That is why

it is better to utilize shorter lengths of CPW around 1mm. this frequency is indicated by vertical green arrows in figure4.3(a) and figure4.5(a).

 Asymmetric CPW using InP as substrate

The last type of substrate using in simulations of asymmetric coplanar wave guides (ACPW) contains only one single layer of the material InP with permittivity (εr) equal to 13.

Figure4.6: cross sectional preview of asynchronous CPW with InP substrate

GND Signal

InP, t=250um, (σ=0, =13) 2S g W

27

Figure4.7 shows the graphs corresponding to its characteristic impedance and epsilon effective. These figures are for when the sizes are defined as 2s=120um, slots g=5um, ground strips w=400um and length is equal to 2000um.

(a) (b)

Figure4.7: (a) Characteristic impedance value for ACPW, (b) effective permittivity

It is seen in the figure4.7 that the achieved impedance is almost 50ohm. It can be enterpreted that having only one layer in substrate is the effective parameter . So it is obvious that unlike the previous sections where substrate incompases several layers, here using only one layer

substrate decreases the influence of surface waves in increasing the impedance. Although penetration of signal from metal strip into the Inp substrate with higher permitivity still causes spike in the result.

4.1.2 Symmetric CPW

A symmetric coplanar waveguide contains a signal strip aligned in between two ground planes. The uniform InP substrate is the only type of substrate in analyzing symmetric coplanar wave guide in this thesis. Its cross sectional preview is displayed in figure4.8.

Figure4.8: cross sectional preview of synchronous CPW with InP substrate

Parameters in simulation of this line are 2s=40um, slots g=15um, ground strips w=150um and length is equal to 2000um.

(a) (b)

Figure4.9: (a) characteristic impedance, (b) effective permitivity, L=2000um

5 10 15 20 25 30 35 40 45 0 50 20 30 40 50 60 70 10 80 freq, GHz Z _ 0 Readout m1 m1 freq= Z_0=52.31210.70GHz 5 10 15 20 25 30 35 40 45 0 50 1 2 3 4 5 6 7 0 8 freq, GHz E p si lo n _ e ff 5 10 15 20 25 30 35 40 45 0 50 46 48 50 52 54 44 56 freq, GHz Z _ 0 5 10 15 20 25 30 35 40 45 0 50 5 10 15 20 25 30 0 35 freq, GHz E p si lo n _ e ff GND Signal GND W g 2S InP, t=250um, (σ=0, =13)

28

Simulation results are available in figure4.9. A similar effect like in ACPW is observed in the case of symmetric CPWs when the length of line is almost long.

To investigate the effect for shorter lengths, new simulations are done for line with length 1000um.

(a) (b)

Figure4.10: (a) characteristic impedance, (b) effective permitivity, L=1000um

Depicted in figure4.10, there is not that sharp spikes which are seen in figure4.9 when the length of the line is 200um. So it is concluded that as it was explained previously for asymmetric

coplanar wave guides, here also using shorter length ends up in better results in a wider range of frequency.

4.2 Coupled coplanar wave guides:

Crosstalk in coupled CPW is investigated for various lengths between coupled lines and for asymmetric CPWs. Figure4.11 is momentum layout of two coupled ACPWs in ADS. The line length in this figure is 1000um and distance between them is 50um.

Figure4.11: Momentum layout of coupled ACPWs

Results of simulation at frequency 50GHz, for different length of coupled lines are shown in the following. 5 10 15 20 25 30 35 40 45 0 50 49 50 51 52 53 54 55 48 56 freq, GHz Z _ 0 Readout m1 m1 freq= Z_0=48.889 34.35GHz 5 10 15 20 25 30 35 40 45 0 50 6.2 6.4 6.6 6.8 7.0 7.2 7.4 6.0 7.6 freq, GHz E p si lo n _ e ff

29

Figure 4.12: Dependences of the near end, S31, and far end, S41, crosstalks on the length of the coupled line sections L. f=50GHz, distance D=50um.

Figure4.12 compares the near and far end crosstalk between coupled CPWs. The sudden huge increment in far end (S41) crosstalk around 700um length is a good clue proving this claim that these lines are suitable in shorter length usages to avoid large amounts of crosstalk.

4.3 Bends in coplanar wave guides:

Following discussions is a closed form analytic model for the bends in CPW based on InP substrates.

Validity analysis of the proposed model is carried out by comparing the results with the ADS Momentum simulations. For these two mentioned radiuses and cross sectional sizes (width of the signal strip, slots, ground planes) of the bends the difference between the reflection coefficient, S11, of the model and Momentum simulations is less than 10%.

4.3.1 Model:

Formally the CPW may be represented as two coupled asymmetric CPWs (two slot lines),

figure4.13 (b), and the equivalent circuit of its small ∆x segment may be represented as shown in figure4.13(c).

In a straight CPW, per unit capacitance, inductance and impedance equations for segment ∆x in any slot line are equal to:

C1’=C2’=C’/2, L1’=L2’=2L’ hence Z1’=Z2’= (2L’/ 0.5C’)0.5=2Z0,

where C’ and L’, figure4.13 (a), are per unit capacitance and inductance respectively for any transmission line in TEM mode.

Also the propagation constant in these slots are:

β1=β2= W*(2L’*0.5C’)0.5 _{=W*(L’*C’)}0.5_=β0.

As it is seen, the impedances of the slots are twice the impedance of the CPW, while the propagation constant of each slot is the same as the CPW.

-43 -38 -33 -28 -23 -18 0 300 600 900 1200 1500 1800 2100 2400 2700 3000 Sp ar ame te rs (d B) Length(um) CPW @ 50GHz S31 CPW @ 50GHz S41

30

(a)

(b) (c) Figure4.13: (a) Equivalent circuit of a general transmission line, (b) layout of a CPW, (C) equivalent circuit of two

segments of CPW

In the case of bend, shown in figure4.14 (a), equivalent circuit of small ∆φ segment also may be represented as two coupled lines, figure4.14 (b). However the propagation constants in the slots are not equal and the simple relationship for Ci and Li considered above is not working anymore.

The waves in the external slot (radius r2) travel longer way and experience larger phase shift

compared with the waves in the internal slot (radius r1). In the equivalent circuit this phase

shifts are represented as incremental inductors in series with the per unit length inductors. Similarly, the capacitors C1 and C2 apart from per unit length capacitances include incremental

capacitances representing the redistribution of charges in the bend due to fringing fields:

(4.4) (4.5) Where δCi and δLi are geometry dependent increments associated with bending.

(a) (b)

Figure4.14: (a) Layout of the 90o _{bend in a CPW, (b) equivalent circuit of segment ∆φ of bend}

dx C1’=C’/2 L1’=2L’ C2’=C’/2 L2’=2L ’ ∆l2 r1 r0 r2 ∆φ W 2S g ∆l1 ∆l0 C1 0.5L₂ dx L’ C₂ L’ 0.5L₂ C’ dx L’

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As a first approximation each segment is assumed to be a straight section of the CPW with the lengths of the slots ( ):

( ( )) ( ) (4.6) ( ( )) ( ) (4.7) Where r0 is the radius of the midpoint in the signal strip and for a 90o bend

, n 1 (4.8) And

(4.9) Then the parameters of the equivalent circuit are approximated by

[ ( )] ( ) (4.10) C1’ and L1’ are capacitance and inductance of a regular CPW per unit length. C1 is then per unit

length capacitance for the first slot of the bend and for the segment with length ∆l1 of it. The first

term in the right hand side of equation (4.10) is due to per unit length capacitance of a straight line with length L0, while the second term is the incremental capacitance associated with the

bend.

The other parameters also contain incremental contributions associated with the bend: So ( ), ( ), where i=1,2.

The approximations used in the above treatment are rather crude. They allow establishing qualitative dependences of the bend parameters given in (4.8)-(4.12). Comparison with the momentum simulations shows that a correction term

(4.12) should be used to match momentum simulations. S is a scaling parameter and w is the width of the ground plane, figure4.14 (a).This scale factor, S<1, takes into account the fact that with increasing radius ro the contributions of the incremental inductance and capacitance Li and Ci

become negligible since in the case of very large r0 the bend performance is very similar to the

performance of a regular CPW. Using (4.12) the parameters of the equivalent circuit in figure4.14 (b) may be given as:

( ) (4.13) ( ) (4.14) ( ) (4.15) ( ) (4.16) In capacitance the scale factor S is squared since the capacitance is proportional to the area while the inductance is proportional to the length of the strips.

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=

( )( ( _{( )} ))

(4.17)

In case that the line resistance is known at a reference frequency fo, the frequency dependence of

line resistance may be given in skin effect approximation:

( ) √ (4.18) In next section some limited examples for 900 _{bend are shown. For these examples both}

parameters which are calculated using equations (4.13)-(4.18) also generated by curve fitting are listed in Table I. For curve fitting the L and C parameters and the loss resistance are used as variables to fit the S-parameters of the bend to the S-parameters simulated in Momentum. 4.3.2 Results of 90o _bend:

Two different radiuses with 900 _{bend are analyzed as example. The simulation results from the}

layout Momentum for any of them is compared with the results approached from the analytic circuit and optimized values of LCR parameters to check the amount of error in each case. An ADS based optimization procedure is used to fit the approximations (4.13)-(4.18) in equivalent circuit to Momentum simulated S-parameters.

In all the figures below, S33 is the exact result from layout simulation in ADS Moment and S11 is the result from equivalent schematic circuit after optimization of LCR parameters. This is the same for S43 and S21 respectively.

ErrS11 or is the error calculated using equation (4.19) and related o S11 and S33. Similarly S33 ( ) belongs to S21 and S43. The related LCR parameters are summarized in Table1. Radius (r0) in any case is equal to: r0= rin+s+g+w. rin is constant and equal to 200um in both

examples.

The relative errors in S-parameters are defined as:

(4.19)  r0=260um

2s=10um, g=5um, w=100um