a master's thesis khalid aabouch azougarh master in
TRANSCRIPT
Strategies for Efficient Fibre Wireless Networks (FiWiN)
A Master's Thesis
Submitted to the Faculty of the
Escola Tècnica d'Enginyeria de Telecomunicació de
Barcelona
Universitat Politècnica de Catalunya
by
KHALID AABOUCH AZOUGARH
In partial fulfilment
of the requirements for the degree of
MASTER IN TELECOMMUNICATIONS ENGINEERING
Advisor: MarΓa ConcepciΓ³n Santos Blanco
Barcelona, January 2021
Abstract
In recent years a growing number of users require wireless communication of access network. This demand requires the incorporation of radio over fibre system, this allows the connection of many users with optical fibre link. Current systems have certain limitations due to fibre dispersion and low efficiency of optical power.
The aim of this thesis is a theoretical study to maximise the number of users from access network through a radio over fiber system. Different configurations of transmitting process using Mach-Zehnder Modulator (MZM) are presented to provide an efficient and configurable radio over fiber system.
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Acknowledgements
I would like to thank my supervisor Maria Concepcion Santos Blanco for giving me the opportunity of this thesis. for her confidence, great patience and helpful discussions. Thanks for the support during this time.
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Revision history and approval record
Revision Date Purpose
0 21/12/2020 Document creation
1 07/01/2021 Document revision
1 19/01/2021 Document revision
1 28/01/2021 Document revision
Written by: Reviewed and approved by:
Date 21/12/2021 Date 01/02/2021
Name Khalid Aabouch Azougarh Name MarΓa ConcepciΓ³n Santos Blanco
Position Project Author Position Project Supervisor
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Table of contents
Abstract ............................................................................................................................ 0
Acknowledgements .......................................................................................................... 1
Revision history and approval record ................................................................................ 2
Table of contents .............................................................................................................. 3
1. INTRODUCTION ....................................................................................................... 5
1.1. Access network .................................................................................................. 5
1.2. State of the art .................................................................................................... 6
1.3. Project objectives ............................................................................................... 7
1.4. Methodology. ...................................................................................................... 7
1.5. A thesis overviews .............................................................................................. 7
2. ROF FUNDAMENTALS ............................................................................................. 9
2.1. Chromatic dispersion .......................................................................................... 9
2.2. Output Optical Fiber signal ............................................................................... 10
2.3. RF Amplitude fading ......................................................................................... 10
2.4. Optical carrier to signal (OCSR) ....................................................................... 11
2.5. Direct-detection ................................................................................................ 12
2.5.1. NOISE ....................................................................................................... 12
2.5.2. Thermal Noise ........................................................................................... 12
2.5.3. RIN Noise .................................................................................................. 13
2.5.4. Shot Noise ................................................................................................. 13
3. BASICS OF ELECTRO-OPTICAL MODULATION AT OPTICAL FREQUENCIES ... 14
3.1. External modulation .......................................................................................... 14
3.1.1. Phase electrooptical modulators ................................................................ 14
3.2. Mach-Zehnder modulator (MZM) ...................................................................... 15
3.3. MZM-Push-Pull (MZM-PP) ............................................................................... 16
3.3.1. Compression at -1dB ................................................................................. 17
4. TRANSMITTER CONFIGURATION FOR RoF LINKS ............................................. 20
4.1. MZM-PP transmitter configuration for RoF ....................................................... 20
4.1.1. OCSR ........................................................................................................ 20
4.1.2. Dispersions effect ...................................................................................... 21
4.1.3. Electrical Signal detected .......................................................................... 21
4.2. MZM-SSB transmitter configuration for RoF ..................................................... 21
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4.3. MZM-Dual-Drive transmitter configuration for RoF ............................................ 23
4.3.1. OCSR ........................................................................................................ 24
4.3.2. Dispersions effect ...................................................................................... 24
4.3.3. Electrical Signal detected .......................................................................... 24
4.4. MZM-Dual-Parallel transmitter configuration for RoF ........................................ 24
4.4.1. OCSR ........................................................................................................ 25
4.4.2. Dispersions effect ...................................................................................... 26
4.4.3. Electrical Signal detected .......................................................................... 26
4.5. SUMMARY AND COMPARATIVE .................................................................... 27
5. SIMULATIONS AND RESULTS .............................................................................. 28
5.1. VPIphotinic ....................................................................................................... 28
5.1.1. Design features ......................................................................................... 29
5.2. Simulation of MZM-PP Configuration ................................................................ 30
5.3. Simulation of MZM-DD Configuration ............................................................... 31
5.4. Simulation of MZM-DP Configuration................................................................ 34
5.5. Sumary of the three MZMs configurations ........................................................ 37
6. SENSITIVITY STUDY.............................................................................................. 38
6.1. Design features ................................................................................................ 39
6.1.1. Simulation scenario ................................................................................... 40
6.2. System sensitivity Simulations Results ............................................................. 41
6.2.1. MZM-PP configuration ............................................................................... 41
6.2.2. MZM-DD configuration .............................................................................. 42
6.2.3. MZM-DP configuration ............................................................................... 43
7. Conclusions and future development ....................................................................... 44
8. Referencias ............................................................................................................. 45
9. Annex I .................................................................................................................... 46
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1. INTRODUCTION
1.1. Access network
The imminent advent of the next generation of wireless networks, 5G+, requires the
efficient tackling of several technological challenges to ensure the demand for high
transmission rates and high bandwidth in both fixed and wireless networks communications.
Over the past decade, the number of wireless users and devices has exponentially
increased resulting in the migration towards higher radio-frequency (RF) frequencies to
cover more bandwidth and then more capacity [1]. However, the higher wireless
attenuation produced by the higher frequencies demands the use of cellular architectures
relying on small cells. Figure 1.1 a) shows a cellular system where the base station (BS) of
each cell is connected to the wireless networkβs backhaul. A complete BS has several
components that increase the installation costs, especially when migrating to the higher
frequencies. Hence, the economics of setting up a cellular system in which each small cell
is served by a BS is challenging, because of the large number of BSs needed.
Figure 1.1: Comparing the current cellular system (a) to a cellular system employing ROF (b)
Radio over fibre (ROF) is a promising solution to the challenge of handling a large number
of small cells with high-RF frequencies [3]. Figure 1.1 b) shows a cellular architecture
relying on RoF, where multiple cells are served by a single BS through radio access points
(RAPs) that are connected to the BS using optical fibre. The RAP performs minimum signal
processing and is not expensive, while most of the signal processing hardware is retained
in the BS and is shared by multiple cells [4][5]. The advantages of the ROF-aided
architecture include ease of system upgrades, better resource allocation, better wireless
coverage, and higher power efficiency [2], and that allows access for more users. The aim
of this project is to explore how to transmit radio frequency (RF) signals from wireless
networks for serving as many users as possible on a single wavelength over a single fiber,
using minimum power to feed the RAPs while ensuring a minimum Bit Error Rate (BER)
transmission quality.
In looking at the future of optical networks the one obvious common trait is that of
continuous change. That makes the ability to adapt to change a most sought feature in a
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RoF system. In this work we will mainly focus on RoF solutions which may easily
reconfigured to work at different RF bands, taking advantage of the wide bandwidth
inherent to optical components
1.2. State of the art
Figure 2.1 shows the basic scheme of the RoF link that will be considered in this work. The
context is the downlink, from BS to RAP. At the BS we find laser providing the optical carrier.
The standard telecom infrastructure works at C-band or the third window, conventional
band (1530-1565) nm. This band is characterized by a high value of chromatic dispersion
(CD) with a typical CD coefficient D=17ps/nmKm [6], this effect is detrimental in a an typical
RoF system using double-side band modulation because it leads to interference in between
the RF modulation bands that may cause total cancellation the RF signal at the
photodetector for some frequencies [6]. Other optical transmission bands can be
considered such as O-band around 1.3 um with an almost null D value, and hence free of
CD effects. However, the drawbacks associated with the O-band are mainly the high
propagation loss and the lack of convenient solutions for optical amplification such as
Erbium-Doped Fiber Amplifiers (EDFA), whereby, in this work, we focus on RoF systems
in C-band.
Figure 2.1 a basic scheme of a radio over fiber system
The continuous wave emitted by the laser is modulated in an external element, which here
will be considered a kind of electro-optical Mach-Zehnder (MZM) modulator, in different
configurations, as explained in chapter 3. The use of MZM provides wide modulation
bandwidths but requires elements for the control of the input polarization, and is affected
by a voltage bias drift so that voltage control is usually convenient. That is why it is often a
good solution for the RoF link from BS to radio access point (RAP) (downlink). For the RAP-
BS direction (uplink) solutions based on Direct Modulated Lasers (DML) are more
appropriate [7]. The optical output signal travels through an optical fiber link where are
affected by the attenuation and dispersion of the fiber.
The optical signal before or after the optical fiber link can be amplified and the electrical
signal is directly detected by a photodetector. We focus on the downlink direction of the
RoF link, for that, the receiver will consist of a simple direct photodetector which just
provides at its output a photocurrent that is proportional to the intensity of the optical wave.
Coherent receivers could be employed in the uplink direction, or even also in the downlink
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in the more advanced proposals [6b], but these are outside of the scope of the present
work.
It is worth noting that the EDFA found at the photodiode input will not be necessarily present
in a real application, as it would increase the cost of the RAPs. The reason to keep it in our
basic RoF scheme is that since we will be interested in finding optimum configurations that
minimize the power required at the RAP for a given BER quality threshold, in our
simulations we will set the EDFA to maintain a constant optical power despite changes in
the TX configuration parameters. We may just think that the EDFA will actually be placed
at the TX side output to maintain a maximum optical power given by the optical fiber
maximum power threshold, and that this power needs to be distributed over as many users
as possible, thus providing a maximum optical power budget for the RoF network.
1.3. Project objectives
In view of the state of the art, in this section we describe the objectives of the present work
β’ Review of fundamentals of RoF Systems
Looking at the elements of an RoF system starting from the transmitter, to understand the
effects of fibre dispersion on the optical signal, find the optimum optical carrier to signal
(OCSR) that maximizes the optical power received and show the behaviour of RF signal
fading at the RF output of the photodetector.
β’ Review of fundamentals of RoF Systems
β’ Theoretical analysis of TX configurations and identification of optimum parameter
choices
β’ Build a simulation setup for confirming the theoretical findings and the optimum TX
parameter choices to provide best values of sensitivity for a threshold PRE-FEC
π΅πΈπ = 10β3.
1.4. Methodology.
This project makes use of a photonics software which is basically designed for the field of
photonics βVPIPhotonicsβ which can be referred as VPI. Matlab and python software can
be used to interlink with VPI to either provide or extract data. The entire optimization of the
fiber link such as optical to carrier ratio (OCSR), error probability, power penalty is being
performed using VPI software. This software contains all the necessary tools to a design a
perfect optical communication system, transmission system, optical link configuration and
photonics circuits.
1.5. A thesis overviews
The thesis is organized in the following manner:
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β’ Chapter 2 gives the theoretical bases of the RoF system, it is shown how the fading
produced by the chromatic dispersion affects the DSB signals.
β’ Chapter 3 gives the theory about the electro-optical external modulator. the
optimum OCSR value for a basic RoF signal with fixed total optical power, and the
sources and characterization of noise.
β’ Chapter 4 presents the mathematical development of transmitters configurations, a
brief mention is made to the modulation in SSB [8] using the MZM, the optimal value
of the OCSR is found analytically for each modulation method and compares the
advantages and drawbacks for each configuration.
β’ Chapter 5 shows the simulations and characterizes the results by giving input
values and analysing the graphs obtained
β’ Chapter 6 shows the study of the system sensitivity when data are introduced, and
compares the results whit the values found in the previous chapter.
β’ Chapter 7 closes the thesis with the conclusions obtained and comments on future
research lines.
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2. ROF FUNDAMENTALS
In a conventional RoF System, at the output of the Base Station (BS), the optical
signal consists of an optical carrier and a double sideband (DSB) RF signal, each of these
sidebands travels through the fiber link with a time delay, the double-sideband transmission
of an RF subcarrier will suffer from frequency-dependent fading caused by fiber dispersion,
its effect modifies the behaviour of the signal at the output of the fiber.
2.1. Chromatic dispersion
Chromatic dispersion (CD) is caused by the fact that single mode glass fibres transmit light
of different wavelengths at different speeds. this effect causes signal widening along with
the fiber and is characterized by the CD coefficient D[ππ /ππΒ·ππ], which gives the delay
between two spectral components separated 1nm when going through 1 km of fiber. A
standard single-mode FO has D=17 ππ /ππΒ·ππ at the C-band.
In the mathematical modelling of chromatic dispersion, the propagation constant is the term
that indicates how the phase travels as a function of space, depends on the frequency and
is expressed with π½[10]. considering the carrier frequency π0 much bigger than the RF
frequency ππ πΉ , one can develop the propagation constant with the following Taylor
expansion:
π½(π + π0) = π½0 + π½1 + π½2 + β― EQ (2.1)
π½0
= π½(π0); π½1
=ππ½
ππ(π0)(π β π0)
π½2
=π2π½
ππ2(π0)
(π β π0)2
2
π½0 is the term that gives the phase velocity, understood as the speed with which the phase
of a wave propagates in space [6], The second term π½1is the group delay at a frequency π
defined as the delay per unit length of the envelope, its expression is derived from [6] π½(π )
π£π =π½2πΏ
π0 EQ (2.2)
The higher order terms refer to signal dispersion with π½2 as the most relevant, where Vg is
the group velocity and it is defined as:
ππ = (ππ½
ππ)
β1 EQ (2.3)
Thereby, the frequency dependence of the group velocity causes a widening of the pulse
due to the fact that the different spectral components of the pulse are dispersed during
propagation and do not reach simultaneously the end of the fiber [10]. If Ξπ is the spectral
width of the pulse, the degree of widening after propagating through a fibre of length L is
given by:
Ξπ =ππ
ππΞπ =
π
ππ(
πΏ
ππ) Ξπ = πΏ
π2π½
ππ2 Ξπ = πΏπ½2Ξπ EQ (2.4)
In terms of wavelength, where π =2ππ
π is and Ξπ = (β2ππ
π2 ) Ξπ, the degree of widening can
be written as:
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Ξπ = π
ππ(
πΏ
ππ) Ξπ = π·πΏΞπ EQ (2.5)
π· =π
ππ(
1
ππ) = (β
2ππ
π2 ) π½2 EQ (2.6)
Where D is the CD coefficient expressed in ππ /ππΒ·ππ [6].
2.2. Output Optical Fiber signal
All frequency components are delayed when they propagate through a medium such as
fiber optics. In our RoF system, there is a modulated RF signal on a carrier so there are
two types of delay, the phase delay, which affects the carrier, and the group delay, which
affects the envelope of the transmitted signal, i.e. the modulated signal.
The low-pass equivalent referred to the optical carrier frequency π0, with an envelope
modulation at a frequency ππ πΉ is defined at the output of the modulator with the following
expression:
πΈππ’π‘ = 1 + π0
2(ππππ πΉπ‘ + πβπππ πΉπ‘) EQ (2.7)
Note that in the above expression, the field amplitude is normalized to unity optical carrier
amplitude, as it is common practice in optical propagation analysis. The effect of the
different optical elements in the field amplitude can be considered in a separate analysis.
At the output of the optical fibre of length L, our signal will be affected by the propagation
constant π½.Using the Taylor expansion EQ (2.1), the field after a propagates fiber length L
can be written
πΈππ’π‘ = 1 + π0
2[ππππ πΉπ‘π
βπ(π½0π0π‘+π½1ππ πΉ+π½22
ππ πΉ2)πΏ
+ πβπππ πΉπ‘πβπ(π½0π0π‘βπ½1ππ πΉ+
π½22
ππ πΉ2)πΏ
]Q (2.8)
The carrier is affected by phase delay ππ =π½0πΏ
π0, which can be ignored since the receiver
relies on amplitude detection. We may then write the field as
πΈππ’π‘ = 1 + π0
2[ππππ πΉπ‘π
βπ(π½1ππ πΉ+π½22
ππ πΉ2)πΏ
+ πβπππ πΉπ‘π+π(βπ½1ππ πΉ+
π½22
ππ πΉ2)πΏ
]
πΈππ’π‘ = 1 + π0πβππ½22
ππ πΉ2πΏcos (ππ πΉ(π‘ β π½1πΏ)) EQ (2.9)
π = βπ½2
2ππ πΉ
2 πΏ =ππ·π0
2ππ πΉ2 πΏ
π EQ (2.10)
πΈππ’π‘ = 1 + π0πππcos (ππ πΉ(π‘ β π½1πΏ)) EQ (2.11)
In the result of the signal at the fiber output, the parameter π is introduced, as can be seen
from equation (2.10) it is directly proportional to the length of the fiber and the square of
the RF frequency.
2.3. RF Amplitude fading
The detection of signal is done in terms of intensity, that is proportional to the square of the
modulus of the optical field, the intensity detected is
πΌππ· = |πΈππ’π‘|2 = 1 +π0
2
2+ 2π0 cos(π) cos (ππ πΉ(π‘ β π½1πΏ)) EQ (2.12)
From here, the transmission S21 parameter can be obtained as:
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|π21| = 2π0 cos(π) = 2π0 cos (ππ·π0
2ππ πΉ2 πΏ
π ) EQ (2.13)
The term |π21| in EQ (2.13) is graphically represented by Matlab to see the amplitude
response. In a frequency sweep of this parameter, nulls appear at specific frequencies, as
shown in Figure 2.3. This phenomenon is called "RF amplitude fading" and is given by
destructive sideband interference.
Figure 2.3 Representation of the theoretical S21 parameter of a SMF fibre at two different distances, in red at
L=20km and in blue at L=40km.
In this representation, the higher the dispersion, the nulls will appear at a lower frequency.
For a fixed dispersion, the other parameter that will affect the fading is the length of the
fibre. in the figure 2.3, it is represented for two different lengths, L=20km (red) and L=40
km (blue). we see that the length of the fibre is proportional to the frequency as doubling
the fiber length causes a reduction of the fading frequency in a factor β2
2.4. Optical carrier to signal (OCSR)
The total optical power from the modulator is distributed between the optical carrier frequency and the laterals mathematically:
ππ = ππ + 2πππ΅ EQ (2.14)
Here the ratio of optical carrier to sideband (OCSR) is defined as the ratio of the optical power in the power in the two first-order sidebands:
ππΆππ =ππ
2πππ΅ EQ (2.15)
Recalculating the optical power using the OCSR expression in rewritten as:
ππ = 2πππ΅(1 + ππΆππ ) EQ (2.16)
And then power the power corresponding to the RF signal is detected is:
ππ πΉ = 2πππππ΅ EQ (2.17)
In this mode, we can look for the value that maximises the RF power as a function of the OCSR. The result is:
ππ πΉ = 2πππππ΅ = 4ππΆππ β πππ΅2 = ππΆππ
ππ2
(1+ππΆππ )2 EQ (2.18)
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Whereby, the value of the OCSR that maximizes the RF power EQ (2.18) is when OCSR=1,
i.e., when the carrier power contained in the two first-order sidebands ππ = 2πππ΅ [8][9].
2.5. Direct-detection
The photodetector is an optical receiver that converts optical signals into electrical signals.
The PIN photodiode is one of the most common photodetectors, has a three-layer structure,
the middle layer being an intrinsic semiconductor, and the outer layers being P-type and
N-type [13]. The intrinsic zone allows the carriers to accelerate under the influence of the
strong field due to the ionized carriers at the edge of the P and N zones.
The process that takes place inside the device is optical absorption, a phenomenon by
which the energy of the photon generates an electron-hole pair in the active zone. The
generated electrons and holes are accelerated in opposite directions due to the electric
field through which the diode is polarized, creating a current flow, which is proportional to
the incident optical power. The output of the photodetector is a photocurrent and is
expressed by the following equation:
πΌππ· = π πππ β |πΈππ|2 EQ (2.19)
When R in [π΄/π€] is the Responsibility and πππ the input power to the photodetector.
2.5.1. NOISE
For efficient reception, the useful signal level should be at a certain distance from the noise
level, then, it is necessary to know and compensate the noise power produced in the
system due to various effects.
2.5.2. Thermal Noise
This is the noise generated by electron agitation. Resistive elements correspond to thermal
noise sources of this type, which introduce a root mean square (rms) voltage β¨ π£π‘β2 β© = 4πΎππ
level or intensity β¨πΌπ‘β2 β© =
4πΎπ
π into the system, as shown in Figure 2.4. In our simulations,
the thermal noise is characterized by 10ππ΄
βπ»π§β
Figure 2.4 equivalent model of thermal noise sources
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2.5.3. RIN Noise
Relative intensity noise is the result of random intensity fluctuations. The root mean square
intensity is obtained as:
β¨πΌπ πΌπ2 β© = π πΌπ πΌπ·
2
Where the noise factor RIN is given by the laser used and πΌπ· is the DC current level in the
photodetector. In our simulations this kind of noise is neglected as it is usual in external
modulation systems.
2.5.4. Shot Noise
This noise is the result of fluctuations in the electric current due to the quantized nature of
the process of electron generation through absorption of photons. The root mean square
(rms) intensity in this case turns out to be:
β¨πΌππ»2 β© = 2ππΌπ·
Where π is the value of the electron charge q = 1.6 β 10 β 19 C . and πΌπ· is the discrete
current value of the detected current. It is important to bear in mind, that contrary to the
thermal noise term which only depends on temperature and therefore remains constant at
the ambient temperature value, shot noise increases with the optical power present at the
input of the photodiode.
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3. BASICS OF ELECTRO-OPTICAL MODULATION AT OPTICAL
FREQUENCIES
This chapter shows the theory about the Electro-optical external modulator and the
Mach-Zehnder modulator (MZM) is introduced, and its linear behaviour showed.
3.1. External modulation
In an external modulation the laser generates an optical intensity constant in time
(continuous wave laser) that later passes through an external optical device to which the
modulating signal is sent. At the output, the radiation is modulated to the desired shape
and coupled to the fibre.
All the modulators used are based on the variation that the properties of a material undergo
with the application of certain signals of different nature. The most popular modulators, in
terms of both performance and design economy, are the electro-optical type, where an
electrical signal causes a change in the refractive index of the material, and thus, it can
modulate the phase of the optical signal with a voltage applied in the right direction [10].
Through the use of interferometry, the phase modulation may be translated into an
amplitude modulation. The most common kind of interferometer is the Mach-Zehnder.
It is within this group that the Mach-Zehnder modulators are found, however, to better
understand the operation of Mach-Zehnder amplitude modulators, electro-optical phase
modulators are introduced.
3.1.1. Phase electrooptical modulators
Figure 3.1: Basic structure of the operation of an optical phase modulator [10]. The design corresponds to the
commonly known structure of a capacitor: an embedded dielectric between two conductive surfaces on which
an external electrical voltage is applied.
A properly oriented electro-optical crystal can modulate the phase and intensity of the
optical signal with a voltage applied in the correct direction. Lithium Niobate (πΏππππ3) is
the most common electro-optic crystal used to manufacture electro-optic type external
modulators. There is an optimal direction of the electro-optical waves for which it is most
efficient. In a LiNbO3 crystal, if we apply an electric field along the x-axis of the waveguide,
as shown in figure 3.1, the refractive index of the material changes by a value given by the
expression:
βπ =1
2π0
3π33πΈπ₯ EQ (3.1)
15
Where π33 es the EOM coefficient with a value of 328 β 10β6 πππβ for LiNbO3, π0 is the
material refractive index of the waveguide with zero voltage and πΈπ₯ is the electric field
applied to the width of the guide (x-axis), as shown in figure 3.1. The phase shift of the
optical input signal, after travelling a length πΏπ is [8]:
ββ 0 =2πβππΏπ
π0= πππ
3π33ππΏπ
ππ0 EQ (3.2)
Where π0 is the wavelength of the optical signal in vacuum, πΏπ and π are the geometric
dimensions of capacitor (see figure 3.1) the voltage required to cause a 180Β° phase shift is
defined as:
ππ =ππ0
ππ3π33πΏπ
EQ (3.3)
It will be a fundamental design parameter in the phase modulator.
In the design of a phase modulator, one of the main objectives is to reduce the value of the
voltage ππ in order to consume as little electrical power as possible during modulation. This
would be achieved by increasing the coefficient πΏπ/π which would in turn increase the
internal capacity of the modulator causing a slower temporary response to its input. This is
known as the Bandwidth-sensitivity trade off [11].
3.2. Mach-Zehnder Modulator (MZM)
Mach-Zehnder is an external amplitude modulator that generally provides better quality
than DML, provides high modulation bandwidths to the generated signal, and reaches high
transmission speeds, making these devices fundamental elements in high-capacity optical
networks.
Electrode
Wave guide
Figure 3.2 Diagram of an amplitude modulator based on the Mach-Zehnder interferometer
Figure 3.2 illustrates an amplitude modulator based on a Mach-Zehnder interferometer
(MZI) structure. The optical input signal is divided into two paths by a Y junction. A signal
is obtained whose amplitude and phase will depend on the phase shift introduced between
both branches of the interferometer, i.e. the result is a signal that is modulated both in
phase and amplitude. The output of the MZM can be written as:
πΈππ’π‘(π‘) = πΈππ(π‘)β(π‘) EQ (3.4)
Where h(t) represents the MZM transfer function given by
β(π‘) =1
β2
ππ ππππ‘π’ππππππ(
ππ1(π‘)π£π
)+ππ ππππ‘πΏππ€πππ
π(Β±ππ2(π‘)
π£π)
π΄π‘π‘πππ’ππ‘πππ EQ (3.5)
The parameters that characterize this transfer function are V1(t) and V2(t) as a voltage
applied to the microwave contacts. The junction has excess extinction ratio (ER) losses,
the power ratio between the maximum and minimum transmission:
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ππ ππππ‘π’ππππ = π = β0.5 + π
ππ ππππ‘πΏππ€ππ = β1 β π2
πΈπ =ππππ₯
ππππ= (
π+β1βπ2
πββ1βπ2)
2
= (1
π2) EQ (3.6)
The term Ξ΅ represents the difference in the upper and lower power split ratios. For a perfect
50/50 split in between the MZM branches Ξ΅ = 0 This allows the MZ structure to have an
infinite ER. However, in real Mach-Zehnder devices, a perfect split cannot be obtained, due
to fabrication tolerances. This means that the device will have a finite ER. This is known as
the intrinsic extinction ratio of the device, and is normally measured at very low speeds.
For typical off-the-shelf high-speed Lithium Niobate Mach-Zehnder modulators, the intrinsic
extinction ratio is usually in the 35 to 55 dB range. This effectively unbalances an ideal MZ
device introducing some chirp.
There are mainly two different structures for coupling the electrical modulating signal to the
optical guide, single-drive and dual-drive. In a single drive modulator, the two paths of the
MZI are phase modulated with antipodal phase shifts Β±ππ(π‘)/2ππ, which guarantees that
for ideal infinite ER the modulator has a null chirp factor. Dual-drive structure a different
voltage is applied to each branch.
3.3. MZM-Push-Pull (MZM-PP)
Push-Pull, is the conventional MZM configuration where the two paths of the MZI are phase
modulated with antipodal phase shifts Β±ππ(π‘)/2ππ, that can be achieved with the single-
drive structure or with the dual-drive structure feeding the lower arm with the opposite sign
than the upper arm.
MZM
-
Figure 3.2 Conventional MZM-Push-Pull (MZM-PP)
In this project The MZM structures are assumed ideal with 0dB insertion loss and very high
Extinction Ratio (ER). The equation field at the output of the modulator has the following
expression:
πΈππ’π‘ =πΈππ
2βπΏπππ(π
πππ (π‘)
2ππ + πβπππ (π‘)
2ππ ) = πΈππ cos (π
2πππ(π‘)) EQ (3.7)
Where πΈππ is the optical carrier wave and the π(π‘) voltage at the port of the MZM (see
Figure 3.2) is composed of a bias voltage ππ΅ and the RF signal of amplitude ππ πΉ and
frequency ππ πΉ. Mathematically it is written as:
π(π‘) = ππ΅ + ππ πΉ cos(ππ πΉπ‘)
17
QP
Figure 3.3 MZM transfer function (blue), the small RF signal (red) has as an ππ πΉ index modulation m and is biased at the quadrature point.
By applying the transfer function of the MZM it is the optical power at the output yields
πππ’π‘ = | πΈππ’π‘|2 = πππ cos (π
2πππ(π‘))
2
=πππ
2[1 + cos(ππ΅ + π cos(ππ πΉπ‘))]
Using the basic trigonometric identity, the previous equation can rewritten as:
πππ’π‘ =πππ
2[1 + cos(ππ΅) cos(π cos(ππ πΉπ‘)) β sin(ππ΅) sin(π cos(ππ πΉπ‘))] EQ (3.8)
Where ππ΅ = ππ΅π
ππ and π =
ππ πΉπ
ππ are the expressions of the phase of the bias and the
modulation index respectively. The operating point is determined by the bias phase shift of the modulator ππ΅. The difference between the voltage for which the first maximum and the first zero of the function is ππ΅ = π, i.e when ππ΅ = ππ. Figure 3.3 shows the transfer function where the bias voltage is applied at the quadrature point, whereby, the transfer function has a linear behaviour.
One of the disadvantages of the external modulation as compared to DML is its intrinsic nonlinear character. It is necessary to know these limits to avoid distortion of the RF signal.
3.3.1. Compression at -1dB
Modulators are mainly used within the linear range, i. e. small modulation index, m, so that
the small signal approximation may be applied. Beyond this range, nonlinear effects begin
to appear. In this section we will be looking for these limits, usually quantified as the 1 dB
gain compression point, which is the input RF voltage for which the slope of the transfer
function is reduced by 1 dB. To find this limit it is necessary to know the real behaviour of
the optical power, whereby, Equation EQ (3.9) is rewritten taking into account the terms of
the Jacobi-anger expansion (table 3.1) [12] as:
cos(π cos(πΌ)) = π½0(π) + 2 β (β1)ππ½2π(π) cos(2ππΌ)π=β
π=1
18
Sin(π cos(πΌ)) = β2 β (β1)ππ½(2πβ1)(π)π=βπ=1 cos((2π β 1)πΌ)
πππ§ cos π = β πππ½π(π§)ππππ
π=β
π=ββ
πππ§ sin π = β π½π(π§)ππππ
π=β
π=ββ
Table 3.1 Jacobi-anger Expansion
πππ’π‘ =πππ
2[1 + cos(ππ΅)(π½0(π) + 2 β (β1)ππ½2π(π)π=β
π=1 cos(2πππ πΉπ‘))β¦
β¦ β π ππ(ππ΅)(β2 β (β1)ππ½(2πβ1)(π)π=βπ=1 cos((2π β 1)ππ πΉπ‘))]
πππ’π‘ βπππ
2πΏπππ
[cos(ππ΅)π½0(π) β 2π ππ(ππ΅)π½1(π) cos(ππ πΉπ‘) EQ (3.9)
The π½π refers to terms related to the amplitude of the Bessel function for each harmonic
[15]. In EQ (3.9) only terms up to the first order are considered relevant, in figure 3.4 it can
be seen that for small input values π½0(π) can be approximated as a constant and π½1(π) as
a linear function.
Figure 3.4 harmonic content riven by Bessel function
Table 3.2 Bessel approximations
Table 3.2 shows the approximations for small values of the modulation index. The objective
is to find the limit value of the modulation index m where the difference between the real
value and the approximate value is 1dB. The following figure shows the compression at -
1dB.
π½0(π) β 1
π½1(π) βπ
2
19
Figure 3.5 Theoretical representation of the compression point at -1dB
In figure 3.5 all the values are expressed in dB, we see that the term affects the RF signal
has the compression at -1dB in m=0dB, therefore m=1. Therefor the maximum voltage
amplitude of the modulation index that guarantees to work in the linear zone is when
ππ πΉ =ππ
π.
20
4. TRANSMITTER CONFIGURATION FOR RoF LINKS
Once the theory about the behaviour of an optical field signal in an RoF system has
been consolidated and we know how the external modulator MZM works and shown
analytically is mathematical expressions it is time to talk about the different transmitter
configurations for an RoF system.
4.1. MZM-Push-Pull transmitter configuration for RoF
The first transmitter configuration considered is MZM-PP, taking the conventional MZM into
an RoF system, where continuous wave (CW) optical source produces an optical signal
that is inserted into the MZM, is phase and amplitude modulated with an RF signal. The
optical output field travels over a fibre link to the RAP as seen in figure 4.1
MZM
LD
SMF
- -
Figure 4.1: Radio over Fiber system with MZM-PP configuration
The result at the output of the modulator has been introduced in the previous chapter, here
it is rewritten whit the corresponding small-signal approximations:
πΈππ’π‘ βπΈππ
βπΏπππ[cos (
ππ΅
2) β sin (
ππ΅
2)
π
2cos(ππ πΉπ‘)] EQ (4.1)
4.1.1. OCSR
The Optical carrier to signal ratio can be calculated extracting from the optical field of the
modulator the component of power corresponding to the optical carrier and the RF signal.
In the DSB system, half of the optical field amplitude has to be taken into account when
calculating the RF signal power.
ππ = ππ + 2πππ΅ EQ (4.2)
For a conventional MZM-PP, the optical carrier and sidebands power levels are given
respectively by:
ππΆ = cos (ππ΅
2)
2 EQ (4.3)
πππ΅ = |β1
2sin (
ππ΅
2)
π
2|
2 EQ (4.4)
Which takes to the following OCSR expression
ππΆππ =ππΆ
2πππ΅
21
ππΆππ = 8
π2 tan(ππ΅
2)
2 EQ (4.5)
From here, the RF power detected is maximum when OCSR = 1, whereby the optimum
bias voltage will be:
ππ΅_πππ‘ =2ππ
πtanβ1 β8
π EQ (4.6)
4.1.2. Dispersion effect
The optical field πΈππ’π‘ is transmitted through the optical fiber cable where it is affected by
the attenuation and dispersion. For a standard SMF the attenuation is 0.2dB/km in C-band,
although, it is not taken into account for the study since can be included into the power
budget that we focus on chromatic dispersion, the optical field at the output of the fiber is:
πΈπΏ =πΈππ
βπΏπππ(cos (
ππ΅
2) β
m
2sin (
ππ΅
2) πβπβ cos(ππ πΉ(π‘ β π½1πΏ))) EQ (4.7)
The result adds to the signal the propagation constant π½1 and the phase dispersion
β which is directly proportional to the RF frequency and the optical fiber cable length
4.1.3. Electrical Signal detected
The signal at the output of the optical fibre is amplified with an optical amplifier EDFA to
obtain the power ππ. At the photo detector output, the πΌππ· current in the electrical domain
is obtained as
πΌππ· =βπΈππ
2
ππ[cos2 (
ππ΅
2) +
π2
4sin2 (
ππ΅
2) cos2(ππ πΉ(π‘ β π½1πΏ)) β ππππ (
ππ΅
2) sin (
ππ΅
2) cos(π)πππ (ππ πΉ(π‘ β π½1πΏ))]
EQ (4.8)
For small RF amplitude value of the modulation index m higher order than one can be
neglected. In addition, fading only affects the RF signal, hence at the output of the
photodetector, πΌπ πΉ has the following expression:
πΌπ πΉ =βπΈππ
2
ππππππ (
ππ΅
2) sin (
ππ΅
2) cos(π)πππ (ππ πΉ(π‘ β π½1πΏ)) EQ (4.9)
Equation (4.9) shows the amplitude of the RF signal is affected by the phase bias (ππ΅), as
well as by the dispersion parameter π may be maximized by tuning the voltage bias, as it
will be seen later, but the dispersion at the frequency of work is independent of the bias,
whereby with the configuration of the MZM-PP it is not possible to compensate the
amplitude loss due to fading.
4.2. MZM-SSB transmitter configuration for RoF
Theoretically, we study a configuration of the MZM-SSB, intending to analytically see how
this configuration avoids the CD effect in an RoF system.
22
MZM
90ΒΊHybrid
Coupler
Figure 4.5 RoF System with SSB configuration
The chromatic dispersion can be avoided using a single-sideband (SSB) modulation.
Taken the dual-drive structure of the MZM, seen in Figure 4.5, the RF signal is applied to
both electrodes with 90ΒΊ phase shift. A DC bias voltage is also applied to one arm at the
quadrature point, while the other DC terminal is grounded [7]. The optical field πΈππ’π‘(π‘) from
the MZM has the following expression:
πΈππ’π‘ =πΈππ
2 βπΏπππ
(πππ1π
ππ + πππ2π
ππ )
π1 = ππ΅ + ππ πΉ cos(ππ πΉπ‘)
π2 = ππ πΉ cos (ππ πΉπ‘ β π
2) = ππ πΉ sin(ππ πΉπ‘)
ππ΅ = (2π β 1)π
2 ; π =
πππ πΉ
ππ
πΈππ’π‘ =πΈππ
2 βπΏπππ[β2ππ
π
4 β πππππ πΉπ‘] EQ (4.10)
The result of the optical field at the output of the modulator is shown in EQ (4.10), (see
development in (Annex I) It can be seen that there is only one phasor component
corresponding to the RF signal. The power spectral density stands for the optical carrier
while the second term represents one of the sidebands at the frequency of work, as can be
seen in the figure 4.6:
Figure 4.6 Power spectral density for the optical carrier and the sidebands at the RF signal
23
keeping up with the mathematical development, the electrical current of the RF signal component is obtained as:
πΌπ πΉ =βπΈππ
2
2βπΏπππβ2π πππ (ππ πΉ(π‘ β π½1πΏ) β β β
π
4) EQ (4.11)
Where it is seen that the dispersion parameter β does not affect the amplitude, which remains constant regardless of the working frequency.
However, electrical phase shifters or hybrid couplers were required to achieve a 90ΒΊ phase shift in the SSB modulation, which only works at a fixed frequency band and so it lacks flexibility because it makes the frequency of work as a hardware characteristic and this limits the RoF system [13].
4.3. MZM-Dual-Drive transmitter configuration for RoF
The second transmitter configuration considered is MZM-DD. Using the dual-drive structure
of the MZI. the upper branch is fed by the amplitude RF signal and the lower branch by the
bias voltage, while the other terminals are grounded, as seen in figure 4.7
MZM
LD
SMF
Figure 4.7 Radio over Fiber system with MZM-DD configuration
The optical field at the output of the MZM-DD is given by:
πΈππ’π‘ =πΈππ
2 (π
ππ1π
ππ + πππ2π
ππ ) ; π1 = ππ πΉ cos(ππ πΉπ‘) ; π2 = ππ΅
V1 and V2 corresponds to the RF signal and VB is the bias voltage respectively. The optical
field output can rewritten as:
πΈππ’π‘ =πΈππ
2 (πππ cos(ππ πΉπ‘) + ππππ΅) EQ (4.12)
By means of the Bessel functions approach we may arrive to:
πΈππ’π‘ βπΈππ
2 βπΏπππ(π½0(π) + 2π½1(π) cos(ππ πΉπ‘) + ππππ΅) EQ (4.13)
Same as the MZM-PP the index modulation is small enough to apply a small signal
approximation, whereby Jacobi-Anger is applied to consider the first harmonic and the
Bessel function for small argument is approximated, the equation result is:
πΈππ’π‘ = πΈππππππ΅
2 (cos (ππ΅
2) + π
βπ(ππ΅
2β
π
2) π
2cos(ππ πΉπ‘)) EQ (4.14)
24
4.3.1. OCSR
The optical carrier and sidebands power levels are given respectively by:
ππΆ = cos (ππ΅
2)
2 EQ (4.15)
πππ΅ = |β1
2π
βπ(ππ΅
2β
π
2) π
2|
2
=π2
16 EQ (4.16)
The OCSR in this configuration, has the following expression:
ππΆππ = 8 cos(
ππ΅2
)2
π2 EQ (4.17)
The optimal voltage maximize the RF power detected is.
ππ΅βπππ‘ =2ππ
πcosβ1 π
β8 EQ (4.18)
4.3.2. Dispersions effect
The result of the optical field after travelling over the fibre link is:
πΈπΏ β πΈππππππ΅
2 (cos (ππ΅
2) +
π
2π
βπ(ππ΅
2βπβ
π
2)
cos(ππ πΉ(π‘ β π½1πΏ))) EQ (4.19)
4.3.3. Electrical Signal detected
The electrical current at the output of the photodetector shows the result of the setting
parameters. The amplitude of the RF signal is affected by the phase bias (ππ΅), as well as
by the dispersive parameter π.
πΌπ πΉ = βπΈππ2
ππππ (ππ΅
2)
ππ
sin (ππ΅
2β π) πππ (ππ πΉ(π‘ β π½1πΏ)) EQ (4.20)
In this case, if the RF frequency is greatly affected by the dispersion of the fibre, is
compensated with the voltage bias. The condition is:
sin (ππ΅
2β π) = Β±1 ;
ππ΅
2β π = Β±(2π β 1)
π
2β ππ΅ = Β±(2π β 1)π + 2π = Β±(2π β 1)π + 2
π·π02ππ πΉ
2 ππΏ
π
ππ΅_πππβ = ππ [Β±(2π β 1) +2π·π0
2ππ πΉ2 πΏ
π] EQ (4.21)
Where ππ΅_πππβ is the value of the bias voltage that increases the frequency response of the
πΌπ πΉ current and keeps it constant in a certain bandwidth around the frequency of work. This
modification also alters the power level and the power is no longer maximum as compared
to the MZM-PP, however, makes it possible to transmit the signal at frequencies wherein
the MZM-PP configuration is completely cancelled.
4.4. MZM-Dual-Parallel transmitter configuration for RoF
The last optical transmitter scheme introduced in this project is the Mach-Zehnder
Modulator Dual-Parallel (MZM-DP), this method adds more complexity than the previous
configurations, the structure is a MZM with two small nested MZM-PP configurations in
25
each of its branches, Figure (3.9) The RF signal and the first bias voltage (ππ΅1) are applied
to the upper MZM-PP. An optical phase shift may be applied between the two MZMs
outputs through the third bias voltage (ππ΅3) while the second bias voltage (ππ΅2) is applied
in the lower MZM.
Figure 4.8 Radio over Fiber system with MZM-DP configuration
The optical field at the output of the MZM πΈππ’π‘, shows πΈ1 and πΈ2 as an expression similar
to the MZM-PP:
πΈππ’π‘ =1
2[πΈ1 + π
ππ3π
ππ πΈ2] EQ (4.22)
πΈ1 =πΈππ
2 [π
ππ
2πππ1 + π
β ππ
2πππ1] = πΈππ cos (
π
2ππ( ππ΅1 + ππ πΉ cos(ππ πΉπ‘)))
πΈ2 =πΈππ
2 [π
ππ2ππ
π2 + πβ
ππ2ππ
π2] = πΈππ cos (π
2ππ ππ΅3 )
Using the basic trigonometric identity, the previous equation can rewritten as:
πΈππ’π‘ βπΈππ
2 [cos (
ππ΅1
2) cos (
π
2cos(ππ πΉπ‘)) β π ππ (
ππ΅1
2) π ππ (
π
2cos(ππ πΉπ‘)) + ππππ΅3 cos (
ππ΅2
2)] EQ (4.23)
Applying the respective approximations for small amplitude signals, the output optical field
expression of the MZM-DP looks like:
πΈππ’π‘ βπΈππ
2 [cos (
ππ΅1
2) β π ππ (
ππ΅1
2)
π
2cos(ππ πΉπ‘) + ππππ΅3 cos (
ππ΅2
2)] EQ (4.24)
The amplitude of the RF signal can be maximized, taking advantage of the appearance of
the new adjustment parameters, the first bias voltage is set at a null-point, i.e., equalling
the value of ππ΅1 =π
2. In this way, it is possible to eliminate the contribution of the optical
carrier it whose amplitude will be controlled through the bias applied to the other nested
MZM. As a result, the optical field πΈππ’π‘(π‘) has the following expression:
πΈππ’π‘ βπΈππ
2 [ππππ΅3 cos (
ππ΅2
2) β
π
2cos(ππ πΉπ‘)] EQ (4.25)
4.4.1. OCSR
Optical Carrier-to-Signal in this configuration, has the following expression:
ππΆππ =8 cos(
ππ΅22
)2
π2 EQ (4.26)
26
In this configuration the voltage Bias ππ΅2 is used to maximize the RF power detected, it
may be written as:
ππ΅2βπππ‘ =2ππ
πcosβ1 π
β8 EQ (4.27)
4.4.2. Dispersions effect
The result of the optical field after travelling over the fibre link is:
πΈπΏ =πΈππ
2 π
πππ΅32 [π
πππ΅32
cos (ππ΅2
2) β
π
2πβπ(
ππ΅32
βπ) cos(ππ πΉ(π‘ β π½1πΏ))] EQ (4.28)
4.4.3. Electrical Signal detected
The electrical current is detected at the output of the photodetector. As it can be seen the
πΌπ πΉ current is affected by two different bias voltages:
πΌπ πΉ ββπΈππ
2
4
ππππ (ππ΅2
2)
ππcos (
ππ΅3
2β π) cos (ππ πΉ(π‘ β π½
1πΏ)) EQ (4.29)
The phase bias ππ΅2 is used to maximise the amplitude leaving the ππ΅3 free to eliminate the
CD effects at the frequency of work, as follows:
cos (ππ΅3
2β π) = Β±1
ππ΅3
2β π = Β±ππ β ππ΅3 = Β±2ππ + 2π = Β±2ππ + 2
π·π02ππ πΉ
2 ππΏ
π
ππ΅3 = 2ππ [Β±π +π·π0
2ππ πΉ2 πΏ
π] EQ (4.30)
The MZM-DP transmitter is the most complete of the three and offers full reconfigurability in an RoF system, it can transmit at the maximum RF signal independently of the frequency of work with the most efficient power.
27
4.5. SUMMARY AND COMPARATIVE
Regarding the three transmitter configurations for RoF we are now in a position to make a
comparative analysis where the advantages and disadvantages of each method are
highlighted. The relevant equations of each configuration have been gathered in table 4.1
MZM-PP MZM-DD MZM-DP
πΈπππ cos (
ππ΅
2) β sin (
ππ΅
2)
π
2cos(ππ πΉπ‘) cos (
ππ΅
2) + π
βπ(ππ΅2
βπ2
) π
2cos(ππ πΉπ‘) ππππ΅3 cos (
ππ΅2
2) β
π
2cos(ππ πΉπ‘)
|πΌπ πΉ| π
πππ‘π (ππ΅2
)
+π2
8tg (
ππ΅2
) cos(π) ππππ (
ππ΅2
)
cos (ππ΅2
)2
+π2
8
sin (ππ΅
2β π)
ππππ (ππ΅2
2)
cos (ππ΅2
2)
2
+π2
8
cos (ππ΅3
2β π)
OCSR 8
π2 tan (ππ΅2
)2 8 cos (
ππ΅2
)2
π2 8 cos (
ππ΅22
)2
π2
ππ΅βπππ‘ 2ππ
πtanβ1 β8
π 2ππ
πcosβ1
π
β8
2ππ
πcosβ1
π
β8
ππ΅βπππβ ---------- ππ[Β±(2π β 1) + 2π] 2ππ[Β±π + π]
Table 4.1 the relevant equation in the modulations MZM-PP, MZM-DD and MZM-DP
π =π·π0
2ππ πΉ2 πΏ
π ; ππ΅π =
πππ΅π
ππ ; m=
πππ πΉ
ππ
The first column shows the equations corresponding to the configuration in MZM-PP. The
value of ππ΅βπππ‘ makes the electrical current response to πΌπ πΉ to reach its maximum value,
however, the bias does not have an effect on the frequency at which CD nulls occur for a
certain fiber length and therefore we will be limited to work at frequencies where we may
have a flat response, with no control of the RF operative band
In the central column, there is the equation of the MZM-DD configuration, like the previous
one, we put the bias value in ππ΅βπππ‘ to maximize the πΌπ πΉ signal, on the other hand, we can
adjust the bias voltage to ππ΅βπππβ to avoid the dispersion produced by the fading, as this
change modifies the amplitude of the signal. This will allow to work at the notch frequencies
at which the PP cannot possibly work but at the price of a lower gain than the maximum
possible because the bias to avoid the notch does not allow to reach the optimum OCSR
condition.
The third column shows the MZM-DP configuration, in which more variables are added for
the control of the bias, ππ΅3βπππβ is used to move the notch and ensure a flattened response
the ππ΅2βπππ‘ may achieve the maximum OCSR Making this option the most recommended
configuration to offer a fully reconfigurable RoF system.
28
5. SIMULATIONS AND RESULTS
Now that the mathematical feasibility of the proposed transmitters configurations for
RoF system has been analysed from a theoretical point of view is time to move on to
present the results that were obtained using a simulation-based study employing realistic
systems parameters.
5.1. VPIphotinic
In this chapter the different functions and blocks of the software VPIphotinic are presented,
where the characteristics of the design are chosen and the previous three configurations
of the RoF system are simulated taking the values according to the mathematical
development.
The simulation scenario built in VPI photonics resembles very closely the basic scheme of
an RoF system. Figure 5.1 shows the different parts of the system into relevant stages.
1.CW
5.OCSR
2.TX
3.SMF4. RAP
5.1 VPIphotonic diagram of MZM-DP transmitter for RoF
CW is the continuous wave laser, generates an optical carrier in C-Band and has as input
parameter the optical power level. In Figure 5.1 The TX stage represents the most complex
of the structures studied, the two nested MZM-PP configuration and a phase stage in
between the two arms of the big MZM-DP structure. From there, the others transmitters
configuration may be straight forwardly derived by eliminating some elements and
rearranging their parameters.
SMF is a single mode fiber whose relevant parameters are length and dispersion parameter.
The RAP stage is where the amplifier EDFA raises the signal to the desired power and the
electrical RF signal is detected by a photodetector PIN, who introduce both shot and
thermal noise. The last block is an analyser that represents graphically the amplitude of
|πΌπ πΉ| as a function of a frequency sweep.
OCSR is calculated by VPI photonics, takes the optical signal at the Tx stage, and
separates the optical and RF power using bandpass filters and then a mathematical
operator calculates the OCSR.
29
5.1.1. Design features
In table 5.1 some parameters of design are presented. The selection criterion has been in
accordance with the constraints proposed in the theoretical analysis and to comply with the
small-signal approximations, a small value of the modulation index has been chosen.
The input power level to the optical source and the EDFA amplifier is kept fixed at the same
value for all simulations, thus making it easy to compare them with each other.
In the MZM, a high value for ER (ER=65dB) and 0 dB for insertion loss has been selected
to simulate ideal behaviour, the design value of ππ has been normalised to unity.
For a realistic RoF system, the CD parameter is the standard for C-band SMF and the
length of the fibre cable (L=25Km) remain fixed for all simulations, keeping the frequency
of work as a variable parameter.
The rest of the parameters such as thermal noise are kept by default, as VPI is a very good
program for simulating optical circuits and its default parameters match the standards of
optical systems. A summary of all relevant parameters is presented in table 5.1
Parameter Definition Value
Optical Source Pin Optical power input 1 [ππ] (0 ππ΅π)
π0 Wavelength carrier 1.55 [ππ]
π0 Optical frequency carrier 193.1 [ππ»π§]
MZM ππ For each voltage port 1 [π£]
ER Extinction ratio 55 dB
IL Insertion Loss 0 dB
m Index modulation 0.15
ππ πΉ RF Amplitude voltage ππ πΉ =π
πππ [π£]
VB Bias voltage βDesignβ
ππ πΉ RF carrier [0 to 30 ]GHz
SMF L Fiber Length πΏ = 25 [ππ]
D Fiber Dispersion parameter 17 [ππ
ππ β ππβ ]
Amplifier EDFA Power controlled 1 [ππ](10 ππ΅π)
Photodetector Shot Shot Noise On
Th Thermal noise 10 ππ΄
βπ»π§β
Table 5.1 relevant parameters selected for RoF simulations
30
To illustrate the theoretical results, all simulations will be done in a frequency sweep
between 0 and 30GHz and with the bias voltage around its optimum value, as given by
equations EQ (4.6), EQ (4.18) and EQ (4.27) for each configuration.
5.2. Simulation of MZM-PP Configuration
The first simulation run is the conventional configuration of the MZM-PP, where the bias
voltage is set at quadrature point. To comply with the formulas of the MZM-PP structure,
ππ must be a half-wave, so the null value point is 0.5 v. Therefore, for the quadrature bias:
ππ΅ =ππ
2= 0.25π£
Figure 5.2 MZM-PP frecuency respons of |I-RF| signal at Quadrature Point
Figure 5.2 shows the signal at the I-RF output. The bias voltage at the quadrature point
VB=0.25v. As shown, it reaches a maximum amplitude of -10dBm, and at 12.12 GHz, the
signal is completely cancelled out by the fading produced by the dispersion of the fibre.
The simulator is used to find graphically the optimal bias value that is maximizes the RF
power detected, in figure 4.4 a scan is made with the bias voltage parameter and the OCSR
graph is represented.
31
Figure 5.3 MZM-PP Represent The OCSR in funtion of bias voltage.
This graph shows that for VB=0.5v, i.e. ππ΅ = ππ it is OCSR=0 since this cancels out the
optical power of the carrier This confirms that for MZM-PP the null point is achieved with a
push-pull voltage of 0.5 V. The optimal bias value is when OCSR=1 is when VB=0.483 v
thus confirming the calculated theoretical value.
ππ΅βπππ‘ =2ππ
πtanβ1 β8
π = 483.13ππ
The simulation is run again with VB-opt, figure 5.3 (red) shows that the I-RF achieves the
maximum amplitude.
Figure 5.3 Comparative between |I-RF| VB=0.25v at QP (blue) and VB=0.483v (red)
Figure 5.3 shows the results of the I-RF current, adjusting the bias voltage to the
Quadrature point (blue) compared with its optimum value (red), we can conclude that we
have a gain of 10dB with its optimum value, but the signal nulls are produced at the same
frequencies independently of the bias value.
In an RoF system, the MZM-PP configuration is easy to implement and presents low
complexity but it is limited, as it can be seen in figure 4.5, it only can guarantee the
maximum capacity if our frequency of work is below 9GHz or in a range from 15GHz to
20GHz for example. If the frequency of work is 12.12GHz, the MZM-PP configuration is
completely useless.
5.3. Simulation of MZM-DD Configuration
As well as the MZM-PP simulation the optimal value of the bias voltage is sought with the
OCSR representation, in this case, in the dual-drive configuration, the null carrier point is
found at a bias voltage ππ΅ = ππ = 1 π.
32
Figure 5.4 MZM-DD Represent The OCSR in funtion of bias voltage
Similar to the previous case the bias voltage optimum is when OCSR=1. In figure 5.4 this
value is found in VB = 0.965 V. It is verified that it coincides with its theoretical value:
ππ΅βπππ‘ =2ππ
πcosβ1 π
β8 =
2
πcosβ1 0.15
β8 = 966.2 ππ
Now, the frequency response of the I-RF current with ππ΅βπππ‘ is simulated
Figure 5.5 MZM-DD frecuency respons of |I-RF| signal with optimal bias voltage
Figure 5.5 shows that the I-RF current achieves the maximum amplitude, but it presents
attenuations at the same frequencies as in the case of the MZM-PP. however, with the
MZM-DD configuration, these attenuations can be avoided by adjusting the bias voltage.
To study how the signal is modified with these settings, the bias voltage ππ΅ β πππβ is
adjusted using the theoretical equation:
ππ΅2 β πππβ = ππ [(2π + 1) +2π·π0
2ππ πΉ2 πΏ
π]
33
The frequencies selected are one with a certain amplitude and another with a null signal,
Table 5.2 shown the result of the ππ΅2 β πππβ calculated at these frequencies.
D=17ps/km*nm ; π0 = 1.55ππ; L=23km ; 3 β 108π/π and ππ = 1π£; n=0
ππ πΉ = 9πΊπ»π§ ππ πΉ = 12.12πΊπ»π§
ππ΅βπππβ 1.5514 v 1.999 v
Table 5.2 numerical values of ππ΅βπππβ calculated at ππ πΉ = 9πΊπ»π§ and ππ πΉ = 9πΊπ»π§
Figure 5.6 MZM-DD compares VB-optima (Red) with VB-noch at 12.12GHz (Black) and with VB-noch at 9
GHz (Green)
Analyzing the comparisons in figure 5.6 shows that by modifying the bias value to avoid
attenuation at a selected frequency, the behavior of the signal amplitude is affected, and
therefore it is no longer maximum.
In Figure 5.6 (red) we see that at the frequency where there was a null, now the amplitude
has been improved to reach the value around -10dBm figure 5.6 (Black), however, in
Figure 5.6 (Green), it can be observed that the change is not more favorable than the
original signal.
In conclusion, the MZM-DD configuration may avoid the cancellation of the signal at our
frequency of work, but if the frequency shows a small attenuation, it is more efficient the
MZM-PP configuration. However, the advantage of the MZM-DD configuration is a flat
response around the operating frequency, making it possible to transmit the signal over a
wider bandwidth.
34
5.4. Simulation of MZM-DP Configuration
The third RoF system simulated is the MZM-DP configuration, which consists of nesting
two small MZMs with the same structure as the MZM-PP each.
the upper drives the RF signal with the first bias voltage ππ΅1, the second bias voltage ππ΅2 is
connected to the DC voltage of the lower MZM, at the output from this the third bias voltage
ππ΅3 is connected.
This design is more complex than the others, adds more bias voltage variables giving more
freedom of configuration to obtain a better frequency response at the output of the
photodetector.
The first design criterion is to eliminate the carrier frequency coming from the upper MZM,
for this purpose, the first bias voltage is fixed at a null point, i.e, ππ΅1 = ππ. Figure 5.6 shows
the spectral density showing only the two sidebands are presented at the output of the
upper MZM.
Figure 5.6 MZM-DP shows the spectral density at the output of the first MZM whit ππ πΉ = 10πΊπ»π§ and ππ΅1 = ππ
Same as the previous configurations, the optimal bias voltage which meets OCSR=1 is
calculated.
ππ΅2βπππ‘ =2ππ
πcosβ1
π
β8 =
2 β 0.5
πcosβ1
0.15
β8 = 483.11ππ
Now with ππ΅1 at a null point and ππ΅2 at the optimal value, the firs simulation is run with
ππ΅3 = 0π . The resulting frecuency response of the electrical current |I-RF| is represented
as.
35
Figure 5.7 MZM-DP result of frecuency response of |I-RF| signal with optimal bias voltage and ππ΅3 = 0π
Figure 5.7 shows the same optimal frequency response as the previous methods. In this
case, the third bias voltage is released for avoid attenuation at the selected frequency whith
its corresponding theoretical equation
ππ΅3βπππβ = 2ππ [Β±π +π·π0
2ππ πΉ2 πΏ
π]
D=17ps/km*nm ; π0 = 1.55ππ; L=25 km ; c= 3 β 108π/π and ππ = 1π£; n=0
ππ πΉ 9 πΊπ»π§ 12.12πΊπ»π§
ππ΅3βπππβ 1.2757 V 1.5 V
Table 5.3 MZM-DP numerical values of ππ΅βπππβ calculated at ππ πΉ = 9πΊπ»π§ and ππ πΉ = 12.12πΊπ»π§
36
Figure 5.8 MZM-PD whit VB-opt (red) , VB3-noch=1.27V at ππ πΉ = 9πΊπ»π§ (Green) and VB3-noch=1.5V at
ππ πΉ = 12.12πΊπ»π§ (Black)
Figure 5.8 (red) shows the original frequency response. The bias voltage ππ΅3βπππβ is used
to avoid attenuation of signal at two selected frequencies ππ πΉ = 9 πΊπ»π§ and ππ πΉ =
12.12 πΊπ»π§ respectively. It is seen that all of them achieve the maximum amplitude.
37
5.5. Sumary of the three MZMs configurations
Finally, as a summary and for comparison, the frequency response of the |I-RF| signal of
the three MZM configurations is shown in figure 5.9. In blue, the MZM-PP configuration is
shown, with the bias voltage it can be optimized to reach its maximum amplitude but it
shows attenuations and nulls of the signal always at the same frequencies. In red we
feature the MZM-DD configuration whereby adjusting the bias voltage, the nullity of the
signal at the frequency of work can be avoided, but this modification affects the amplitude
of the signal and it no longer reaches its maximum value. Finally, we have in green the
MZM-DP configuration where more bias control variables are added to avoid the null to any
frequency of work keeping the amplitude at its maximum value.
Figure 5.9 Comparison between MZM-PP, MZM-DD and MZM-DP configurations
38
6. SENSITIVITY STUDY
The results obtained in the previous chapter are highly encouraging, especially for
the RoF system with the MZM-DP configuration. In this chapter we will confirm those
expectations in a digital transmission, through measures of BER. The RF signal comes
whit a QAM modulation. The goal will be to find the minimum optical power that guarantees
the correct operation of the different RoF systems proposed. This value will provide the
PONs power budget and hence the number of users that may share a common passive
optical Network (PON).
Figure 6.1 VPIphotonic diagram of RoF whit QAM signal
Figure 6.1 shows a diagram of one of the RoF configuration when the QAM modulation
signal is introduced, in this case the main difference from the previous configuration is the
presence of the new digital block that add the data to the RF configuration.
Simulations are performed over a range of values of optical power at the input of the optical
source and at the EDFA output. The received signal is considered valid for a threshold
π΅πΈπ = 10β3 adds because with this threshold there are Soft FEC methods able to reduce
the system BER beyond 10β12 [15]
39
6.1. Design features
Before explaining how these simulations are performed, let us have a look at the design
parameters in table 6.1.
Parameter Value
Bitrate 1Gbps
Sample Rate 64*BitRate
Number of Bits (Nbis) 217
Bits per second (Bps) 2
Bandwibth Bitrate/ Bps = 500MHz
Roll-Off factor 0.18
Up/Down Sample factor π
πππππππ ππ‘πβπ΅πππ΅ππ‘π ππ‘π
Input code [I,Q,BitSeq]=IQ_TX(Nbits,BpS,a)
Output code p=IQ_RX(I,Q,BitSeq,BpS)
Optical power Range [-40 to 0] dBm
Table 6.1 properly value of QAM signal
In Figure 6.2 Matlab code takes from table 6.1 as input parameter Bps and Nbits and
generates the sequence of bits corresponding to the IQ components of the QAM
modulation, this sequence is Up sampled to achieve the required sample rate, then
connected to a square root raised cosine pulse with a roll-off factor and fed into the system
with the RF carrier, phase-shifted by 90Β° for the quadrature component.
Figure 6.2 input data for QAM modulation
40
Figure 6.3 shows the process of IQ component recovery. At the output of the receiver, the
electrical carrier from each component after being mixed with the RF tone at phase and
quadrature is low-pass filtered, goes through square root raised cosine pulse shaping, and
the symbol sequences are down Sampled, the separate bit sequences enter another
Matlab code together with the original BitSeq, the code obtains the received bit sequence,
compares it with the sent data sequence and the probability P is returned.
RoF
Figure 6.3 output data for QAM Modulation
6.1.1. Simulation scenario
As shown in figure 6.4, the simulation is run with a two-level sweep, the first iteration with
the bias voltage. In the second iteration, it searches the power level and displays those
which have a BER less than 10β3 . A matrix of these values is exported from the
VPIphotonic and a short code of Matlab is run to choose the value of optical power that is
closer to ππ = 10β3. Finally, the optical power level is plotted as a function of bias voltage.
Figure 6.4 Screenshot of simulation sweeps
41
6.2. System sensitivity Simulations Results
The systems are reconfigured with the new parameters for data input, and we have run
different simulations setting the working frequency for each of them.
Figure 6.5 frequency response of |I-RF| for all configurations (a) and for MZM-DD and MZM-DP configuration
(b)
Figure 6.5 shows the selected frequencies, for all simulations the frequencies ππ πΉ = 4πΊπ»π§
and ππ πΉ = 10πΊπ»π§ have been chosen. Already known from the previous study is a fact that
they presents a different power level for the optimum bias voltages shown in figure (a). For
the MZM-DD and MZM-DP configurations figure 6.5 (b), simulations have also been made
at ππ πΉ = 12.12πΊπ»π§ with corresponding VB-noch tuning. Now we are going to display the
results of power sensitivity for each configuration.
6.2.1. MZM-PP configuration
Figure 6.6 shows the bias sweep as a function of power in the MZM-PP configuration, it is
seen that ππ πΉ = 4πΊπ»π§ (Blue) is more efficient than ππ πΉ = 10πΊπ»π§ (Orange) but both have
the minimum power around at VB=0.47v. As expected, the simulations at the exact
frequency of the notch did not yield any valid result for sensitivity.
This confirms that with this bias value, the RoF System with the MZM-PP configuration
achieves its maximum efficiency but with restrictions on the operating frequency.
Figure 6.6 Sensitivity response of MZM PP at ππ πΉ = 4πΊπ»π§ (Blue) and ππ πΉ = 10πΊπ»π§ (Orange)
42
6.2.2. MZM-DD configuration
In the MZM-DD configuration, first, the simulations are performed at the same
frequencies selected in the previous case. Figure 6.7 shows the simulation results
confirming once again that the minimum power is at the optimum bias value, taking
into account that for the dual-drive structure the ππ is doubled as compared to the
Push-Pull, the optimum bias is at VB=0.96v.
Figure 6.7 Sensitivity response of MZM DD at ππ πΉ = 4πΊπ»π§ (Blue) and ππ πΉ = 10πΊπ»π§ (Orange)
The second simulation is run setting the bias sweep around the theoretical value that avoid
null at ππ πΉ = 12.12πΊπ»π§. Figure 6.8 shows the result of the power sensitivity,
Figure 6.8 Sensitivity response of MZM DD at ππ πΉ = 12.12πΊπ»π§
Figure 6.8 shows that the minimum value is around -21dBm. This power level is too high,
because at this bias value the frequency response of |I-RF| shown in figure 6.5 (b) the signal
remains flat at a higher bandwidth compared to the level of ππ πΉ = 12.12πΊπ»π§ in figure 6.5 (a).
This may be due to the fact that little bandwidth has been considered for a significant
change to be appreciated, or it may also be because in a simulation scenario the EDFA is
ideal and for a study in the laboratory the results may be different.
43
6.2.3. MZM-DP configuration
Finally, in MZM-DP configuration the simulations are run at ππ πΉ = 4πΊπ»π§ and ππ πΉ =
12.12πΊπ»π§ the latter with its corresponding bias parameters ππ΅3βπππβ = 1.27π£ . Show the
power level depending on the bias voltage (see figure 5.1). We appreciate that the power
level is minimum at VB=0.47v in both cases as shown in figure 6.9.
Figure 6.9 Sensitivity response of MZM DP at ππ πΉ = 4πΊπ»π§ (Blue) and ππ πΉ = 12.12πΊπ»π§ (Orange)
This corroborates that the RoF system with the MZM-DP configuration achieves its
maximum efficiency without restrictions on operating frequency.
44
7. Conclusions and future development
As a summary of this work, we have carried out a review of radio over fibre (RoF) systems intending to propose a system that allows reconfigurability and with the lowest possible sensitivity.
We have started with research on the main elements building into an RoF system, the RF signal fading and the dispersive fiber link, and focusing on the transmission process where three transmission configurations have been proposed and mathematically characterised MZM-PP, MZM-DD, and MZM-DP.
A key parameter in order to achieve low values of sensitivity that may allow to extend the power budget of RoF access networks, is the OCSR. We have shown that the optimum value is OCSR=1, and have provided expressions for OCSR for the three transmission configurations studied. Also, expressions for the optical field and Rx photocurrent have been derived and for the fading frequencies and the voltage condition that avoids it.
At the simulation level, the study has comprised setting up and optimizing two simulation scenarios with VPI, one with pure RF signals to compare and confirm the main conclusions steaming from the analytical study and a second one including digital data in QAM format in order to explore the sensitivity values that may be obtained with each Tx. As a main conclusion, we have demonstrated with calculations and simulations that, the optical power can be optimised at a certain frequency for all transmission configurations proposed. MZM-DD configuration can avoid the RF fading for a specific frequency of work, but at the expense of a very poor sensitivity. Also, it has been demonstrated that the MZM-DP configuration can optimise the optical power without frequency restrictions.
Second conclusion, with the sensitivity study we have verified the minimum power that guarantees the correct operation of the three systems. But for the case of the MZM-DD, configured to avoid RF fading, we expected a better response than what we have obtained since it offers higher bandwidth compared to another frequency at a linear level of the signal, however, the power obtained is much higher. This may be due to the fact that little bandwidth has been considered for a significant change to be appreciated, or it may also be because in a simulation scenario the EDFA is ideal and for a study in the laboratory the results may be different.
Here a reduced number of simulations could be presented, but the designed setup could be exploited for obtaining more results with higher data bandwidth, more realistic ER, or higher modulation indices, in order to explore the limits and effects of nonlinearities. Also of interest is the study of coherent receivers and the demonstration of the results of this study in a laboratory setup.
45
8. Referencias
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communications for 5G cellular: it will work!β, IEEE Access, 2013, 1, pp. 335β349
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reduction techniques for radio over fiber communicationsβ, IEEE Commun. Surv.
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[3] Thomas, V., El-Hajjar, M., Hanzo, L.: βMillimeter-wave radio over fiber optical
upconversion techniques relying on link non-linearityβ, IEEE Commun. Surv.
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[4] Beas, J., Castanon, G., Aldaya, I., et al.: βMillimeter-wave frequency radio over
fiber systems: a surveyβ, IEEE Commun. Surv. Tutor., 2013, 15, pp. 1593β1619
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[6] S. Mas Gomez, J. Caraquitena Sale y P. Sanchis Kilders, βControl de la dispersiΓ³n cromΓ‘tica en guΓas
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Valencia, 2009.
[7] B. G. Kim, S. H. Bae, H. Kim and Y. C. Chung, "RoF-Based Mobile Fronthaul Networks Implemented by
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[8] I. N. Cano, M. C. Santos, and J. Prat, βOptimum carrier to signal power ratio for remote heterodyne DD-OFDM in PONs,β IEEE Photon. Technol. Lett., vol. 25, no. 13, pp. 1242β1245, Jul. 2013.
[9] C. Lim, M. Attygalle.A. Nirmalathas, D. Novak and R. Waterhouse, βAnalysis of Optical Carrier-to-Sideband Ratio for Improving Transmission Performance in Fiber-Radio Linksβ, IEEE Trans. Microwave Th. And Techniques, Vol. 54, No 5, May 2006.
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[11] Fuste, J. A. I., & Blanco, M. C. S. (2013). Bandwidthβlength trade-off figures of merit for electro-optic traveling wave modulators. Optics letters, 38(9), 1548-1550.
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[15] A. Leven, F. Vacondio, L. Schmalen, S. ten Brink and W. Idler, "Estimation of Soft FEC Performance in Optical Transmission Experiments," in IEEE Photonics Technology Letters, vol. 23, no. 20, pp. 1547-1549,
Oct.15, 2011, doi: 10.1109/LPT.2011.2162725.
46
9. Annex I
Single-side Band Configuration
MZM
90ΒΊHybrid
Coupler
π1 = ππ΅ + ππ πΉ cos(ππ πΉπ‘)
π2 = ππ πΉ cos (ππ πΉπ‘ β π
2) = ππ πΉ sin(ππ πΉπ‘)
ππ΅ = (2π β 1)π
2 ; π =
πππ πΉ
ππ
πΈππ’π‘ =πΈππ
2 βπΏπππ
(πππ cos(ππ πΉπ‘)ππππ΅ + πππ sin(ππ πΉπ‘))
Jacobi-Anger expansion
πππ ππ¨π¬ π½ = β πππ±π(π)ππππ½
π=β
π=ββ
n=0, +1
πππ ππ¨π¬ π½ β π±π(π) + πππ±π(π) ππ¨π¬ π½
πππ π¬π’π§ π½ = β π±π(π)ππππ½
π=β
π=ββ
n=0, +1
Bessel-function
π±π(π) = (βπ)ππ±π(π)
π±π(π) β π
π±π(π) βπ
π
47
πππ π¬π’π§ π½ β π±π(π) + πππ±π(π) π¬π’π§ π½
πΈππ’π‘ =πΈππ
2 βπΏπππ
[(π½0(π) + 2ππ½1 (π)cos(ππ πΉπ‘))ππππ΅ + π½0(π) + 2ππ½1 (π)sin(ππ πΉπ‘)]
πΈππ’π‘ =πΈππ
2 βπΏπππ
[(1 + ππ cos(ππ πΉπ‘))ππππ΅ + 1 + ππ sin(ππ πΉπ‘)]
ππ΅ =π
2
πΈππ’π‘ =πΈππ
2 βπΏπππ
[cos (π
4) π
π4 + βπ(cos(ππ πΉπ‘) + π sin(ππ πΉπ‘))]
πΈππ’π‘ =πΈππ
2 βπΏπππ
[β2πππ4 β πππππ πΉπ‘]
πΈπΏ =πΈππ
2 βπΏπππ
[β2πππ4 β πππ(ππ πΉ(π‘βπ½1πΏ)ββ )]
πΌππ· =βπππ
2
ππ[2 + π2 β β2π (ππ(ππ πΉ(π‘βπ½1πΏ)ββ βπ
4) + πβπ(ππ πΉ(π‘βπ½1πΏ)ββ βπ
4))]
πΌπ πΉ =βπΈππ
2
2βπΏπππ
β2π πππ (ππ πΉ(π‘ β π½1πΏ) β β βπ
4)