calculation of capacitance of the rectangular coaxial...
TRANSCRIPT
Calculation of Capacitance of the Rectangular Coaxial
Lines with Offset Inner Conductor by Strong FEM Vladimir V. Petrovic
1 and Žaklina J. Mančić
2
Abstract – In this paper, capacitance per unit length of
rectangular coaxial transmission lines with offset nonzero-
thickness inner conductor, having an isotropic and anisotropic
dielectric, using strong FEM formulation is calculated. The
results were compared with the results obtained by the weak
FEM and commercial software FEMM, which uses node-based
first-order basis function. Based on that, appropriate conclusions
are made.
Keywords – Quasi-static analysis, Finite element method,
Strong FEM formulation, lines with rectangular cross section,
offset inner conductor, isotropic and anisotropic dielectric,
capacitance per unit length.
I. INTRODUCTION
Problem of capacitance per unit length of square or
rectangular lines calculation, especially lines with offset inner
conductor is topical in theory and practice. The paper [1]
gives a review of the literature, dealing with this task and it
performs the calculation of capacitance of the rectangular
coax line with offset inner conductor by using the weak FEM
formulation [2]. This paper deals with calculation of
capacitance per unit length of square and rectangular coaxial
lines filled with isotropic and anisotropic dielectric by using
strong FEM formulation [3-6]. The results are compared with
those obtained by weak FEM [1] and by commercial software
FEMM [6]. FEM is a very suitable method for the analysis of
closed polygonal structures and it can be simply used for
analysis of geometries with anisotropic dielectrics, unlike the
methods that use Green’s function (e.g., MoM or EEM) for
which an additional complicated step of anisotropic Green’s
function determination is needed [7]. Besides classifying FEM
into strong and weak formulation, this method can be
classified as a node-based [1,6,8,9] and non node-based (with
hierarchical basis functions) [2-5, 10-12]. Node-based FEM
can be found much more often than non node-based FEM.
However, weak FEM formulation is usually presented in the
literature, while strong formulation can rarely be found. In
weak FEM formulation, only function’s continuity condition
is exactly satisfied, whereas in strong FEM formulation,
boundary conditions for the both function and its first
derivative are satisfied exactly [2-5,10-12]. In this paper are
obtained for the third order basis functions ( 3n ).
II. BRIEF DESCRIPTION OF THE STRONG FEM
FORMULATION
FEM approach in this paper is based on hierarchical strong
basis functions of higher (arbitrary) order that are constructed
by using mutual multiplication of 1D strong basis functions
[13]. Consider a two-dimensional domain, uniform with
respect to z-axis, Fig. 1, filled with linear inhomogeneous
dielectric without free charges, in which the distribution of
electrostatic potential, ( , )V x y , is the unknown function. Let
the problem be of the closed type: on one part of the domain
boundary ( 1C ), boundary conditions of the first kind (given
V ), and on the rest of the boundary ( 2C ), boundary
conditions of the second kind (given /V n ), are imposed
(Fig.1). (Boundary condition of the second kind here is
equivalent to given /nD V n .) Differential equation
for ( , )V x y can be defined with:
div ( grad ) 0S S V , (1)
In previous equation divS and gradS denote surface
divergence and gradient, respectively. Calculation domain is
divided into M sub-domains (elements) in FEM solution of
Eq. (1).
Exact solution ( , )V x y is expressed as a linear combination
of basis functions with unknown coefficients,
1
N
j jj
V f a f
.
Fig. 1. Two-dimensional calculation domain divided into elements.
The system of linear algebraic equations for unknown
coefficients is obtained by applying the weak Galerkin
formulation [14, 15], and it is defined with:
[ ][ ] [ ]ij j iK a G , , 1, ,i j N= , (2)
where
ε grad grad dij i jS
K f f S ,
2
0 di i nC
G f D l . (3)
1Vladimir V. Petrovic is with the Robert Bosch, GmbH,
Reutlingen, Germany , e-mail [email protected] 2Žaklina J. Mančić is with the Faculty of Electronic Engineering,
University of Niš, Aleksandra Medvedeva 14, 18000 Niš, Serbia, e-
mail [email protected].
In previous equation with 0nD is denoted a normal
component of vector D on the contour 2C , whereas i and j
represent global serial numbers of basis functions.
Furthermore, S represents the union of all the element’s
surfaces, defined with 1
Me
e
S S=
= . Next, rectangular elements
of arbitrary order are utilized for strong formulation. Strong
basis functions automatically satisfy continuity of potential V
( 0C continuity) and continuity of nD (generalized 1C
continuity) on interelement boundaries ( intC in Fig..1).
Complete set of strong basis functions for 2-D problems in
homogeneous (isotropic or anisotropic) media is presented in
[13]. Instead of for anisotropic dielectrics it should be used
ε x y in equation (3) .
III. NUMERICAL EXAMPLES
I. Square coaxial line with offset inner conductor
For a square coaxial line with offset inner conductor, Fig. 2,
for 4/ ab , results for normalized capacitance per unit
length, '/εC , are presented in Fig. 3. When the inner
conductor is moved from the center and positioned closer to
the outer conductor, the normalized capacitance increases.
The results of '/εC in the case when 4/ ab are compared
with the corresponding results obtained by FEMM [6] and
results obtained by weak FEM [1]. The results are shown in
Fig. 3 and an excellent agreement can be observed. In this
case, it is not possible to exploit symmetry for the problem
solution. In all the cases the mesh that consists of 288
rectangular elements is used for strong and weak FEM. This
resulted in 1152 unknowns for strong FEM and 2448
unknowns for weak FEM formulation. In order to obtain
results of the similar accuracy by using FEMM software, the
number of nodes (which is equal to the number of unknowns)
was between 3980 and 4130 while the number of triangular
mesh elements was between 7592 and 7830.
Fig. 2. Square coaxial line with offset inner conductor.
Coordinate origin is in the center of the outer conductor.
Fig. 3. Ratio /'C depending on ax /0 , where ay /0 is
parameter, 4/ ab and dielectric is isotropic.
II. Rectangular coaxial line with offset inner conductor
For rectangular coaxial line, Fig. 4, '/εC dependance of
ax /0 is shown in Fig. 5.
Fig. 4. Rectangular coaxial line with offset inner conductor
Fig. 5. Ratio /'C depending on ax /0 , where by /0 is a
parameter, 2/ ba and dielectric is isotropic, Fig. 4.
III. Rectangular coaxial line with offset inner conductor
and multilayered dielectric
Fig. 6 shows the structure with layered isotropic dielectric
in which the inner conductor was moved in direction t.
Fig. 6. Rectangular coaxial line with offset inner conductor and
multilayer isotropic dielectric
In Fig. 7 dependence of the normalized effective permittivity
1/ e on 21 for two different values of bt for a square
coaxial line from Fig.1 is shown, where 2/111 babaaa .
Fig. 7. Normalized effective permittivity 1/ e of a
rectangular coaxial line with offset inner conductor and
multilayered isotropic dielectric, Fig.6, for two different values
of ratio bt / .
IV. Square coaxial line with offset inner conductor and
anisotropic dielectric
For a square coaxial line with offset inner conductor, Fig.
1, for 4/ ab , filled with anisotropic dielectric Sapphire,
where yx , results for relative permittivity re , are
presented in Fig. 8, for the following cases: a) ,4.9x
6.11y and b) 4.9y 6.11, x . The required number
of unknowns for strong FEM formulation is 1152 and for
weak FEM formulation is 2448, whereas the number of
rectangular elements is 288. On the other hand, FEMM
requires the number of unknowns between 3964 and 4088,
whereas the number of triangular elements is between 7559
and 7804. From Fig. 8 both effects of the proximity and
anisotropy can be noticed, as described in detail in [2, 4, 5].
Moreover, an excellent agreement with FEMM results can be
noticed, which proves that the strong FEM can be
successfully applied for an accurate and efficient calculation
of rectangular coaxial line with offset anisotropic dielectric.
Fig. 8. Effective relative permittivity re , of a rectangular coaxial
line with offset inner conductor and anisotropic dielectric Sapphire,
Fig. 2, for different ratios ay /0 .
CONCLUSION
Based on numerical examples shown in section III it can
be concluded that the strong FEM formulation of the higher
order and hierarchical basis functions can successfully be
applied for accurate and efficient analysis of transmission
lines with offset inner conductor of finite thickness in the case
of isotropic and anisotropic dielectrics. Excellent agreement
of obtained results and those obtained by weak FEM and
commercial software FEMM has been observed. The
advantage of strong FEM formulation compared to weak FEM
is approximately one half of the number of unknowns. The
advantage of both strong and weak FEM, is more than 25
times smaller number of required finite elements with respect
to FEMM.
ACKNOWLEDGEMENT
This research is supported by Serbian Ministry of Education,
Science and Technological Development (Project TR-32052
MNTR)
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Design and Analysis of Realistic Vehicle Traces Model
based on the Evolutionary Algorithms Danijel Čabarkapa1 and Petar Pavlović2
Abstract – Vehicular ad-hoc networks (VANETs) are subclass
of mobile ad-hoc networks (MANETs). VANETs use vehicles as
mobile nodes to provide communication among nearby vehicles
and between vehicles and nearby roadside equipment. Due to
several constraints such as reproducibility, logistic and
considerably economic cost of implementing, most research in
VANETs relies on simulations. A key component for VANETs
simulations is a vehicular mobility model. The quality of these
simulations strongly depends on the degree of reality of the
vehicular mobility model. The current trend in vehicular
mobility modeling is the generation of vehicular traces at a
citywide area or region scale. The main part of the paper focuses
on the realistic simulation of vehicular traces generated by
population-based metaheuristics Evolutionary Algorithms (EAs).
In addition, featured solutions in EAs domain for generating
realistic vehicular traces are briefly introduced and their pros
and cons are analyzed.
Keywords – VANETs, vehicular traces, traffic simulation
model, evolutionary algorithms, traffic network simulator
I. INTRODUCTION
VANETs are advanced dedicated wireless networks that
support cooperative driving among a large number of
dynamically moving communicating vehicles on the road.
Vehicles perform as communication nodes or relays, forming
highly dynamic vehicular networks together with other nearby
vehicles or with nearby roadside equipment. VANETs provide
both Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure
(V2I) dedicated communication [1]. VANETs have specific
characteristics that distinguish them from typical mobile ad
hoc networks. Vehicles do not move at random and they are
limited to known paths road topology while moving, often in a
predictable manner. Additionally, a specific vehicle might
have only predictable routes. If the road information is
available, it is possible to predict the future position of a
vehicle or get information about various risk traffic events and
accidents. Generally, variable network traffic density mostly
depends on the time and the area, and usually at rush hours the
traffic is high and it is low in rural or suburb areas [2].
The majority of applications, protocols and communication
algorithms proposed in VANETs are designed to improve
active safety in driving, efficiency and travel convenience.
Developing vehicular applications and protocols usually
requires experimental expensive testbeds and real simulation
tools. Real-world simulations for VANETs require realistic
network and mobility models. Due to several constrains such
as reproducibility, economic costs and lack of scalability,
simulation is one of the most often used methods for
performance evaluation. The recent challenge in mobility
modeling process is the synthetic generation of realistic
vehicular traces (at geographical and temporal domain) as an
input to a network simulator [3]. The current research trend in
realistic vehicular traces modeling is based on evolutionary
algorithms (EAs). The EA model uses freely available source
data - geographical from online digital maps, and set of traffic
volume counts corresponding to the region covered by the
digital map. The automatic counting of the vehicle traffic
comprises a set of counting roadside devices (induction loops,
radars) installed on main roads and highways. Collected data
describes the cumulated volume of the traffic flow over a
particular spot and can be distinguished regarding time,
direction or type of a vehicle.
The rest of the paper organized as follows. Section II
describes the basic concepts of realistic VANET simulation,
while Section III focuses on EAs approach used for
optimizing vehicular mobility models. Section IV presents
some of the related solutions in the field of EAs vehicular
traces optimization, and we finally conclude in Section V.
II. REALISTIC VANET SIMULATIONS
Vehicular traffic simulators generally can be classified
into macroscopic, microscopic and mesoscopic. Macroscopic
models consider traffic flow, density and velocity of vehicles.
Microscopic approach considers the movement of each
individual vehicle (acceleration-deceleration, line change…)
and mesoscopic models consider some interactions among
vehicles at an individual level.
There are three classes of VANET mobility models: trace-
based, survey-based and traffic simulator-based [4]. In the
first class, mobility patterns are extracted directly from real-
world mobility movement traces. A collections of datasets can
be generated from traces obtained by GPS tracking of vehicles
or by commercial vehicles (public busses, taxis). Such traces
have a limited availability and are limited to the type of
tracked vehicles. In the survey-based models mobility patterns
are derived from traffic statistics (arrival times at work,
breaks, pedestrian and vehicular dynamics etc.) at the
macroscopic level. Traffic simulator-based mobility models
based on microscopic traffic simulators. It determines the
movement of each vehicle at the microscopic level (breaking,
acceleration, energy consumption, noise level monitoring
etc.). This class of mobility models can realistically simulate
road infrastructure and interactions between vehicles.
1Danijel Čabarkapa is with the Higher School of Professional
Technological Studies Šabac, H. Veljkova 10, Šabac 15000, Serbia,
E-mail: [email protected] 2Petar Pavlović is with the Higher School of Professional
Technological Studies Šabac, H. Veljkova 10, Šabac 15000, Serbia,
E-mail: [email protected]
A recent research trend in mobility modelling is to
combine real-world information such as digital maps, traffic
counters and statistical data together with microscopic
simulation. In order to obtain realistic vehicular mobility at
macroscopic and microscopic levels, trace information needs
to be used in relationship with microscopic traffic simulation.
According to the concept picture in Figure 1, the EA model
uses two sources of real-world data inputs (geographical map
and traffic volume counts). As outputs, microscopic model
generates three elements for each time slot: a prediction of the
origin/destination (O/D) pairs for vehicles, a set of a routes for
all generated O/D pairs and the estimation of the departure
time for vehicles moving in the area covered by the digital
map. The output data is then processed by a traffic generator
that models traffic demand and generates synthetic traces as
an input to a traffic simulator [5].
A microscopic traffic simulator moves vehicles in
accordance to requested routes and physical rules. A network
simulator based on new vehicles position update its own
nodes positions and communications links in every time step.
Interactions between particular elements present reciprocal
impact and further increase the realism of a simulation.
Traffic simulator can change vehicle routes as a result of
VANET applications. Traffic generator fuses all real-world
data that can be useful to determine the traffic demand and
can uses a feedback from traffic microsimulator. Information
about current traffic situation can influence the traffic demand
by changing traveler decisions and adjusting activity
schedules. The separation of particular steps ensures
modularity what makes easier the replacement of each module
and testing of different scenarios. Although many microscopic
simulators enable to specify traffic demand integrally,
researchers tend to implement a separated module to gain the
flexibility and modularity of the platform [6].
III. EA ALGORITHM - OPTIMIZATION BASICS
Evolutionary algorithms (EAs) are a family of nature-
inspired computational techniques and interactive heuristics
that evolve a set of candidate solutions, represented as
individuals that are grouped in a population. That candidate
solutions are able to reproduce themselves to an additional
selection procedure. Implementation of an EA begins with a
definition of the search space as a finite bounded domain.
Parameters are the population size (α) as well as the number
of offspring (β) that have to be created each generation (see
Algorithm 1). Additionally, a genotypic search space G must
be determined together with a decoding function dec: GΩ
that determines to which phenotypic candidate solution a
genotype is mapped. Ideally, a mapping from genotype to
phenotype is bijective [7].
The crucial step is determining a fitness function. The value
of the fitness function indicates the amount of closeness to the
optimal solution. Using EA implementation is as good as the
fitness or evaluation function. Generally, the fitness of an
individual determines the probability of its survival to the next
generation. The next step is the initialization or selection of
the initial population PPL(t). Through the next generations of
the population, the existing solution is iteratively improved.
This iterative process is called generation and stops after some
termination condition is met (e.g. predefined number of
iterations). Two basic operators are crossover and mutation.
Crossover operator takes two individuals (parents), which are
combined to form new chromosomes or offspring (PPL',
PPL''). Iteratively applying the crossover operator, genes of
good chromosomes appear more frequently in the population,
leading to convergence to the optimal solution. The mutation
operator alters one individual to produce a single new solution
and introduces random changes into the characteristics of
chromosomes. Reproduction involves the selection of
chromosomes for the next generation [7]. The processing
scheme of the general EA is shown in Algorithm 1 in
pseudocode.
ALGORITHM 1 GENERAL EVOLUTIONARY ALGORITHM EA (PSEUDOCODE)
1: INPUTS: parameters α, β … quality function f : ΩR
2: PARAMETERS: population size α, number of offspring β, genotype G, decoding function decod
3: t 0
4: PPL(t) //create a population of size α 5: evaluate individuals in PPL(t) using decod and f
6: while termination criteria not fulfilled do
7: E //select parents for β offspring from PPL(t) 8: PPL' //create offspring by recombination of individuals in E
9: PPL'' //mutate individuals in PPL'
10: evaluate individuals in PPL'' using dec and f
11: t t + 1
12: PPL(t) //select α individuals from PPL'' (and P(t -1))
13: end while 14: OUTPUT: best individual in PPL(t)
Fig. 1. Generation of vehicular traces and bidirectional coupling between microscopic traffic and network simulators
Figure 1 shows the evolutionary cycle of EA algorithm. In
this section we review standard algorithms and paradigms that
are relevant in the remainder of this paper, namely genetic
algorithms (GAs), developed by Holland [8] and evolution
programming (EP) [9].
IV. EVOLUTIONARY ALGORITHMS FOR VANETS
Evolutionary algorithms have been applied to vehicular
networks for the last decade. There are still many optimization
problems in these complex networks that can be solved using
a suitable EA. New architecture of EAs are continuously
proposed such as coevolutionary and parallel evolutionary
algorithms. During this section, we followed the optimization
solution proposed in [10, 11, 12] which defines a EAs generic
framework for generating realistic mobility vehicular traces
using real-world input traffic data.
The current trend in vehicular traces generation is to
combine many approaches into a single process in order to
obtain the required level of realism. EA model proposed in
[10] generates a set of vehicular traces that consider temporal
and spatial aspects of traffic distribution. Mobility model uses
freely available source data - from digital OSM (Open Street
Maps) maps [13], and set of traffic volume counts obtained
from roadside control points. This model relies on
probabilistic geographical zone surface and attraction points
used to select the destination of each vehicle. The residential,
commercial and industrial zone types are defined and
extracted from OSM maps. Each of them is assigned with a
probability of being selected as a destination type. EA model
requires the following parameters: zone type, location of
zones belonging to each type and location of attractivity areas.
The probability for choosing a zone is influenced by the
weight of its zone type or the weight of its attractivity area. In
the first step EA selects probability of a zone type and then in
second step selects the probability of an attractivity area for
the selected zone. The third step is applied if within the
selected attractivity area more than one zone of selected type
exists. This EA model uses simple weighted Dijkstra shortest
path algorithm for the route generation between origin-
destination vehicle pair. EAs are iterative heuristics that
evolve a set of candidate solutions. Two individuals (parents)
are chosen in the population using a given criteria. In the
evolutionary cycle they are then recombined with fitness
dependent probability to produce an offsprings. The obtained
offsprings are mutated and they are evaluated and inserted
back into the population following a given criteria [14]. As
presented in Fig. 3, after procedure for selection of a
destination zone, next step is optimization of EA parameters
(fitness function, encoding and genetic operators).
The fitness of the individuals is the basis for the
environmental selection, where for each individual a decision
is met whether it will survive and be a potential parent in the
next iteration (see Fig. 2). In this EA model fitness is a quality
metric and indicates how the generated traces are consistent
with real traffic volume counts. We can conclude that the best
fitness is able to reproduce such a realistic traffic vehicle
behaviour. The EA fitness function F is computed according
to the following equation:
C
c
T
t
cc tctrF1 1
)()(
Here, C is the number of control points and T is the number
of time slots. Parameter rc(t) is the real traffic volume count at
control point c in time slot t, and cc(t) is the number vehicles
at control point c derived from the generated traffic flows in
time slot t. Generally, the objective is to minimize this sum F
of absolute differences between the real traffic volume counts
and the estimated ones for all the control points for the
simulated period [11, 12].
Fig. 4 shows how the basic parameters of the model are
encoded. This model uses integer gene representation where
each gene represents one parameter. Zone probabilities are
noted as PT where T {R, C, I} denotes the zone type. The
length of the chromosome depends on the numbers of zone
types and attractivity areas. The sum of probabilities of each
group must be 100 and it is basic constraint. For the fitness
evaluation F (see equation) all of the values for each gene are
scaled and must be in the range from 0 to 1. This model uses a
Fig. 2. Schematic description of the fitness evaluation in EAs
Fig. 3. Schematic EA model of the vehicle trace generation
modified uniform mutation operator which replaces the value
of the chosen gene with a random value selected between 0
and 100. As Fig. 4 shows, the gene with value 88 is mutated
and replaced by 42. Therefore, gene with value 12 is also
changed to 58. [10]
In order to obtain more realistic traffic distribution,
Cooperative Coevolutionary GA (CCGA) gives more efficient
optimization. CCGA proposed and discussed in [15] uses
Gawron’s algorithm [16]. Model modifications include time-
frame reduction, geographical model decomposition and
additional attractivity areas. CCGA consists of splitting the
whole population into several subpopulations. Instead of
evolving a population of similar individuals representing in
classical EAs, CCGAs consider the coevolution of
subpopulations of individuals representing different species.
Each subpopulation runs a genetic algorithm.
The output of the proposed EA and CCGA mobility models
is a set of vehicles with their route and ready to be used as an
input for SUMO [17] traffic simulator. Finally, the newly
generated traces will be compared to the original model
accuracy.
V. TRENDS AND CONCLUSION
This paper presented that realistic vehicular simulation is
one of the biggest promising challenges in a VANETs
research. We have acknowledged the need of realism in every
aspect of simulation in order to obtain reliable results. The
paper indicated that the future direction in research of inter-
vehicle communication and applications is based on mobility
traces. We have presented the main features and restrictions
that should be taken into consideration for the use of
evolutionary algorithms in generating traces for citywide area
for which traffic volume counts exist. Additionally, we have
reviewed the main works found in the research literature and
we believe that the use of EAs in generating of realistic traces
for vehicular mobility simulations is in a very dynamically
stage of research.
The major concern of generating realistic vehicular traces is
how to select the values of the probabilities associated with
attraction points. A genetics operators and fitness function are
proposed to model the problem, but in some cases the results
notably deviate from real traffic count data. This is due to the
route generation process of the EA model. The future research
can be EAs expanding with the more tunable and time-variant
probabilistic model of areas and zones.
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Fig. 4. EA encoding scheme and uniform mutation operator
Transmitting coherent carrier frequencies in modern
CATV/HFC systems Oleg Borisov Panagiev
1
Abstract – In this paper are presented the researches made on
the effort to improve the parameters of modern CATV/HFC
systems for Downstream. Mathematical equations are drawn and
an algorithm for calculation of the digital carrier in HRC/IRC
systems for the standards B/G and D/K is proposed. In a table
matter are also presented the values of the digital carrier for
standard and coherent distribution, as well as the values of BER,
MER and SNR.
Keywords – CATV/ HFC, HRC, IRC, DVB-C.
I. INTRODUCTION
This paper is a scientific development for allocation of
television channels for the standards B/G and D/K by using
DVB-C in modern CATV/HFC systems. The digital carriers
are coherent synchronized, which improves the BER, MER,
SNR and other parameters. The transmission of coherent
digital carrier is realized with the methods of harmonically
related carrier/coherent (HRC) and incrementally related
carrier/coherent (IRC). Those methods ensure improvement of
Fig.1. Menu tuning channels
the parameters of 20% to 80% depending on the number of
channels, the modulation, the frequency spectrum and the
frequency allocation of the channels [1], [2], [3], [4]. In North
America those methods have already found an application in a
number of cable operators. Some of the main manufacturers
have designed and are manufacturing television sets [5], [6],
[7], [8] which can receive channels from both the standard
distribution (STD), and the HRC and IRC distribution (Fig.1).
The modulation of the analog carriers is AM-VSB and
8VSB/16VSB/m-QAM of the digital carriers [9], [10], [11].
These channel allocations are made for the FCC: standards
ITU-T/J.83B/J.112, CEA-542-B, meanwhile for B/G and D/K
there are none. Because in [3] are considered and presented
the relations for HRC and IRC transmitting of analogue
carriers, in this publication will be presented the mathematical
relations and the results for digital carries for the standards
B/G and D/K by DVB-C.
II. STRUCTURAL SCHEMATICS OF A HEAD END
WITH COHERENT CARRIERS
The method of transmittion with coherent carriers consists
of the usage of modified schemas for allocation of the carrier
frequencies, which leads to the elimination of some
components of the composite three-component beat.
In the Head End the oscillators in the modulators, the
converters and the transmodulators are synchronised by a
separate circuit from a Main oscillator, where by the
synchronizing signal is feed by a shirmed/coaxial cable, and
it's frequency fR is in the range of megahertz, mostly 1MHz.
The unstability of the generated signals must not be worst
then 10-6
.
Structural schematic of a Head End with coherent carriers is
presented on Fig.2, where the generator for synchronisation is
a quartz generator and the step f0 is defined by the type of the
synchronization (HRC or IRC), whereby fo≤ fR.
Fig.2. Structural schematic of Head End with coherent carriers
1Oleg B. Panagiev is with the Technical University of Sofia,
Bulgaria, E-mail: [email protected].
The influence of coherent synchronisation on the
CATV/HFC system's spectrum when transmitting "channel to
channel" is shown on Fig.3a, for decrease (Fig.3b) of the
Main oscillator's frequency, as well as for its increase
(Fig.3c). In this case the overlaping of the neighbouring
channels with eachother (which is possible for noncoherent
carriers) is lacking, because by frequency alternation (increase
or decrease), the whole spectrum is being shifted to the
left/right with the value of unstability of the Main oscillator.
This way the neighbouring channels cannot overlap with
eachother and respectively cannot get a throbbing between
them, and hence also nonlinear distortions.
a) fosc=const.
47 MHz 862 MHz
b) fosc - Δf
c) fosc + Δf
- Δf +Δf
Fig.3. CATV/HFC system's spectrum
III. TRANSMISSION OF HARMONICALLY RELATED
CARRIERS
By this method the carring frequencies synchronise with the
phase of the harmonics of the generator with comb-spectrum,
whose main frequency is chosen with value equal to the
bandwidth of the channel for the relevant standard.
Since for the standard B/G in VHF range the bandwidth of
every channel is 7MHz, and for UHF range 8MHz, the
application of the HRC method is impossible. By D/K
standard the bandwidth of every channel is 8MHz for both
ranges. Because of those reasons are presented below the
mathematical expressions for the standard D/K by DVB-C.
The carrier frequency of each channel is described by the
following formula:
0, )( fkf nc , where (1)
n=RI, RII,…, SR1,…, RVI,…, SR11,…, SR21,…, 21,…, 69;
k=1, 2, 3,…, 102 is channel destination (Ch. Des.);
=5; fo=8MHz.
The advantages of this method are:
coherence of emerging beats of second and third order
with fc,n, in which no essential distortions and worsening of
BER, MER, and C/N happen;
Decrease of the transitional (interchannel) distortions;
Use of one Main oscillator and others.
Disadvantages
Low flexibility;
Difference in the values of digital carrier to the standard
distribution (STD) - central frequency of the channel;
The signals of NMS, pilot signals and other do not
synchronize by phase.
IV. TRANSMISSION OF INCREMENTALLY RELATED
CARRIERS
By the IRC method most of the disadvantages of the HRC
method are prevented. The principle of obtaining the digital
carrier is the same as with the HRC method, but the step is
different.
Here the step of synchronization is part/increment of the
frequency of the synchronization signal, respectively of the
width of the channel, as the value of fo is an integer much
smaller than them. Frequently fo=100kHz, 125kHz, 250kHz.
As a disadvantage can be considered the uncoherence of the
products of second order with digital carriers, respectively
with picture carriers.
By the derivation of the mathematical dependencies will be
considered the value of the synchronization step of the carrier
frequencies and the parameters of the channels: width,
quantity, order number and etc., which determine the number
of the harmonic according to fo.
For standards B/G and D/K formula (1) becomes [3]:
0, . fkf nc , (2)
where k takes into account the values of k and for every
carrier frequency in the range 47862MHz.
Every digital carrier is made by multiplying a fold integer
k by the step.
In such case, the value of every digital carrier is an even
number and simultaneously it represents the number of the
harmonic according to the step.
Main oscillator can work on another frequency, different
from the step and few times larger than it, and the value of the
step is produced by division of the oscillation frequency (more
often by 4, 8 and 10 by fosc=1MHz).
A) Mathematical relations for the standard D/K
The channel distribution for DVB-C refers to the whole
frequency spectrum from 47862MHz, where equation (2)
changes as follows:
0, )...( fBkCAf nc , where (3)
A=42.C; C=fR/fo; k=1…102; B=8MHz;
n=RI, RII,…, SR1,…, RVI,…, SR11,…, SR21,…, 21,…, 69.
B) Mathematical relations for the standard B/G
Because the channels’ bandwidth in the frequency bands
VHF and UHF is different (BVHF=7MHz; BUHF=8MHz)
equation (3) changes as follows:
0, )..)42.[( fBksCf nc , where (4)
s=0; k=1…36; B=7MHz;
s=32; k=37…106; B=8MHz;
n=2,…, S1,…, 5,…, S11,…, S21,…, 21,…, 69.
By comparing equations (3) and (4) we can deduce an
aggregate equation for both standards, where when calculating
the values for a digital carrier we need to take in a
consideration the above mentioned conditions and
dependencies for n, k, B and f0.
0, )...[ fBkCf nc , or (5)
0, )..).[( fBksBfCf bnc , where (6)
A=.C; =(fb-B-s) and fb=fc,RI or fb=fc,2.
Based on the deduced mathematical relationships is
composed algorithm (Fig.4) for calculating the digital carrier.
The numerical results are presented in Table 1 and Table 2.
Start
Introduce
n, fo, k, fR, B/G, D/K, B, μ, fb, s
Choice the standard for DVB-C
B/G or D/K
Calculation of C
Yes
No
Choice the synchronization method
HRC or IRC
Calculation of A
fc,n ≤ 858MHz
Calculation of kμ
Calculation of fc,n
k+1
createTables
Results print
End
Fig.4. Algorithm for calculating the digital carrier
TABLE I
CHANNEL DISTRIBUTION FOR D/K (STD, HRC, IRC)
Band Channel
Channel
BW
MHz
fc,n
MHz
STD
DVB-C
HRC
DVB-C
all
position
Ch.
Des.
HRC
DVB-C IRC
DVB-C
1 2 3 4 5 6 7
Standard D
VHF I
R I 48,5-56,5 52,5 48
56
64
72
80
88
48 50
R II 58-66 62 56 58
R III 76-84 80 80 82
VHF II R IV 84-92 88 88 90
R V 92-100 96 96 98
S
Low
SR1 110-118 114 112 114 SR2 118-126 122 96 120 122
SR3 126-134 130 104 128 130
.…. ….. ….. ….. ….. ….. SR8* 166-174 170 144
152
…..
200
208
…..
272
168 170
VHF III
R VI 174-182 178 176 178
….. …… …… ….. ….. R XII 222-230 226 224 226
S
High
SR11 230-238 234 232 234 ….. ….. ….. ….. …..
SR19 294-302 298 296 298
Standard K
S Extended
(hyper)
SR21 302-310 306 280 304 306 ….. ….. ….. ….. ….. …..
SR30 374-382 378 352 376 378
….. ….. ….. ….. ….. ….. SR41 462-470 466 440 464 466
UHF
IV/V
21 470-478 474 448 472 474 ….. ….. ….. ….. ….. …..
29 534-542 538 512 536 538
30 542-550 546 520 544 546 ….. ….. ….. ….. ….. …..
39 614-622 618 592 616 618
40 622-630 626 600 624 626 ….. ….. ….. ….. ….. ….. 49 694-702 698 672 696 698
50 702-710 706 680 704 706 ….. ….. ….. ….. ….. ….. 59 774-782 778 752 776 778
60 782-790 786 760 784 786 ….. ….. ….. ….. ….. …..
69 854-862 858 832 856 858
840
856
In Table 3 are presented the data for improving the quality
of transmitted signals in a IRC system in accordance to a
system for cable television with noncoherent distribution of
the channels.
TABLE II
CHANNEL DISTRIBUTION FOR B/G (STD, HRC, IRC)
Band Channel
Channel
BW
MHz
fc,n
MHz
STD
DVB-T/C
IRC
DVB-C
1 2 3 4 5
Standard B
VHF I
2
3
4
47-54
54-61
61-68
50,5
57,5
64,5
49
56
63
S
Low
S2
…..
S10*
111-118
…..
167-174
114,5
…..
170,5
112
…..
168
VHF III
5
…..
12
174-181
…..
223-230
177,5
…..
226,5
175
…..
224
S
High
S11
…..
S20
230-237
…..
293-300
233,5
…..
296,5
231
…..
294
Standard G
S
Extended
(hyper)
S21
…..
S30
…..
S41
302-310
…..
374-382
…..
462-470
306
…..
378
…..
466
306
…..
378
…..
466
UHF
IV/V
21
…..
29
470-478
…..
534-542
474
…..
538
474
…..
538
30
…..
39
542-550
…..
614-622
546
…..
618
546
…..
618
40
…..
49
622-630
…..
694-702
626
…..
698
626
…..
698
50
…..
59
702-710
…..
774-782
706
…..
778
706
…..
778
60
…..
69
782-790
…..
854-862
786
…..
858
786
…..
858
TABLE III
BER, MER AND SNR
CATV/HFC
system Parameters
862 MHz
51 channels
DVB-C
BER
(RS,Viterbi)
MER
dB
SNR
dB
noncoherent 10-8
36 32
coherent 10-12
44 37
V. CONCLUSION
The results allow concluding that transmitting with HRC
synchronization is possible only for the D/K standard, because
the bandwidth of each television channels is identical, for both
the VHF and UHF bands. The difference in bandwidth of the
channels for the B/G standard in VHF and UHF bands do not
allow HRC synchronization.
It is possible to use IRC synchronization for both standards
by using steps with values divisible by 7MHz, respectively by
8MHz.
The distribution of the channels, the synchronization
frequency, the step and the standard are not influenced by the
signals’ type (SD; HD) and the compression (MPEG-2;
MPEG-4).
The coherent methods for synchronizations prevent
interference in the channel (n) when a change of the digital
carrier in the channel (n-1) and (n+1) occurs - an overlap is
absent.
REFERENCES
[1] Ciciora, W., J. Farmer, D. Large and M. Adams, Modern Cable
Television Technology, 2nd ed., Morgan Kaufmann, Elsevier
Inc., 2004.
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HFC plant, 3th ed. Burlington, MA: Morgan
Kaufmann/Elsevier, 2009. ISBN 9780123744012.
[3] Panagiev, O. Analysis and reduction on nonlinear distortions
for signals in the broadband cable communication systems,
Dissertation, Technical university of Sofia, 2006.
[4] Panagiev, O. B. Intermodulation composite distortions
theoretically research in HFC networks. ICEST, Proc. of Papers,
vol.1, Ohrid, 24-27 June 2007, pp. 325-328
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http://www.eiae.org, http://www.jvc.com.
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438-7000 USA & Canada (800) 421-1587, Toll Free FAX (800)
468-1340, Nov. 2011, www.linearcorp.com.
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http://www.startrac.com.
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Radio with dock for iPod, http://www.philips.com/usasupport.
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II-150, ISSN 1313-230X.
Control of Photon Energy Sharing for Photovoltaic Power Charge in Power Grid of Optic Fiber With Enhanced
Effectiveness Jovan Shikoski1, Juli Zlatev2, Tinko Eftimov3, Georgi Stanchev4
Abstract – In the following article have been reviewed two
methods of photon energy charge with: Optical splitter and Optical switch, with purpose of smart Sensors charging. Energy efficiency was analysed and compared.
Keywords – Smart sensor, Optical splitter, Optical switch,
Optical power, Optical fibre, Power IR laser, Photovoltaic power converter PPC-4E.
I. INTRODUCTION
At a high level of electric and high-frequency interferences and extreme meteorological conditions, explosive surrounding and more it is not appropriate for the sensors to get charged with copper conductors or standard photovoltaics [1,2]. Lately there is a trend optic fiber to be used for photon energy conduction in the range of 100mW~2W, generated by a laser diode for the charge of remote smart sensors [3,4]. For that purpose there are specialized photovoltaic power converters being offered with a convertor for coupling to optical fiber [5,6] (PPC-E – for 12.6 and 4V).
The article reviews the possibility of optical power sharing on two photovoltaic convertors PPC-4E with the purpose of autonomous charging of two separated smart sensors, positioned at a distance from each other.
The sharing of optic power, coming from the IR laser, to the relevant photovoltaic inputs have been made by passive optical splitter [7]. The main task of the following release is to present alternative mesh for sharing of optic power, which must have better energy characteristics by specific consumption in the grid circle and conditions of exploitation. There is also algorithms for controlling of the both types of grid charging.
In addition in the following article both circles of optic power sharing have been analyzed. The main purpose is to compare their energy efficiency as well the conditions in which the suitable method could be used. .
II. PRINCIPLE OF OPERATION
А. Optical system for distribution of photon power with an optical splitter
A splitter with two outputs has been chosen with the purpose of receiving more energy at the outputs, which has to be delivered to the corresponding photovoltaic by a multi- mode optic fiber 62.5 μm. The sharing energy at the splitter 1x2 is equal at every output (each 50%) with a loss of 3.83dB.
In the Figure 1 was represented a block diagram of an optical system for optical energy sharing with optical splitter. Microcontroller in the smart sensor SS, parallel with his main functions, observes the condition of the Li- ion battery. When the electric tension of the battery reduces to a level of 3V, there is a request for recharging to the central controller transmitted through the optical transmitter on the channel for data CF (optical communication fiber). The central controller switches on and manages the powerful IR laser diode PLD through PLDD driver. The photon energy from the laser, occurred on the entry of the optical splitter OSP, splits equal on both exits. The light energy, through optical fibers PF (electric cable), distributes simultaneously to both photovoltaic converter PPC-4E, then transforms in electric energy and both charger devices BBC in the sensors start charging the batteries. Until the charging process lasts, DC- DC converters supply the sensors with electrical energy, that comes from the entry 1 (the voltage of photovoltaic). DC- DC converters have been designed to automatically switch and use the voltage of entries 2 (voltage of the batteries), when the voltage of entries 1 are zero (voltage of photovoltaic). That happens, when the charging of the batteries is over. As opposition of the sensor, which requests starting of charging process, the battery of the other sensor is not empty, but after the powerful laser switches on, the photon energy, delivered to the optical splitter, enters equally to the both photovoltaic cells and the both batteries are starting to recharge simultaneously. The battery with the higher voltage at the beginning of the process will charge to 4,2 V earlier and the sensor SS2 indicates to the central, that the battery is fully charged. The central controller CC checks the ID address of the relevant sensor and confirms, that this sensor has not gave request for charging and continues with the charging. When the battery is charged to the level of active mode of sensor SS2, he receives an energy trough DC- DC converter of the photovoltaic, but if the sensor is in sleep mode, then the delivered energy of the photovoltaic would be spend inefficient. In the moment when the central controller receives
1Jovan Shikoski is with the Faculty of Telecommunications atTechnical University of Sofia, 8 Kl. Ohridski Blvd, Sofia 1000,Bulgaria.
2Juli Zlatev is with the Faculty of Telecommunications atTechnical University of Sofia, 8 Kl. Ohridski Blvd, Sofia 1000,Bulgaria.
3Tinko Eftimov is with University of Telecommunications andPost, 1 Stefan Mladenov sreet, Sofia 1700, Bulgaria.
4Georgi Stanchev is with the Faculty of Mechanical Engineeringat Technical University of Sofia, 8 Kl. Ohridski Blvd, Sofia 1000,
output signal from the relevant sensor, that the battery is fully charged, the charging process disconnects.
In Figure 2 has been described the specified algorithm of operating of the grid.
B. Optical system for distribution of photon power with optical switch
The difference between optical splitter compared with optical switches is, that the photon energy is sharing simultaneously and equal to all of the exits by the splitters and the full energy is distributed only in one output channel, which is the focus of the mirror, by the switches.
The experiments in the article are made for optical switch with 1 input and 2 outputs with 62,5 μm multi-mode optical fiber. The losses on the first exit are 0,58 dB and for the second 0,35 dB. The maximal optic power, which is the
limit of working conditions for the switch is 500mW with light length of 850nm. The switch time from one to another position is 8 ms. The control system of the switch is digital through l2C or TTL interface. The block diagram of distribution of photon energy with optic switch is described in Figure 3. When the smart sensor SS1 sends request for charging to the base station, the main controller CC manages the optical switch through I2C interface and aims the mirror to the outputs of the optic fibre to the direction of the relevant sensor. With the help of the driver PLDD the main controller switches on and manages the powerful IR laser diode PLD with maximal power of 500mW. Compared to the splitter, the optic switch delivers the whole photon energy through the optic fibre to the photovoltaic of the relevant smart sensor. When the battery is charged to 4,2 V, the smart sensor sends a signal to the main station thorough the optic fibre for communication CF, the central controller stops the power laser and the process of charging interrupts. The same process replays by the charging of the other sensor. The frequency of charging of the smart sensor in the grid depends on the time of charging of the batteries. Because the charging of the sensors is successive, it is necessary the sensors to be chosen with different by discharging of the
batteries or with phase displacement by the charge process, in order for the system to charge them just in them with energy. The main target is to avoid the situation of charging both of them simultaneously. For the optimisation of the charging time the battery must start to be charging from the moment of voltage under 3,5 V (0,2 V under the nominal value). From big importance by the design of this type of sensor system is
Fig. 2. Algorithm for optical grid with splitter
Fig. 1. Optical grid with splitter
the consumption and the time of active regime of the sensors to be distributed without critical situations, where the both sensors must be charged simultaneously.
The block algorithm which describes the work principles of the optic system for sharing of photon power with optical switch is shown in the Figure 4.
III. DESIGN INSTRUCTION
At the beginning of the design of the optic sensor grid must be evaluated the main energy losses as a sum of the losses of every single component from the pick tail of the powerful laser to the photovoltaic device [8]:
Sfsplicespliceconnectorconnector BbzBnBnB +++= . [dB] (1)
as they follow: nconnector =2 is the number of connectors from the sensor to the base station, Bconnector=0,5dBare the losses in the connectors, nsplice = 2- number of the weld seams in the optic fiber Bsplice= 0,1 dB- those are the losses in the welds of the optic fiber, bf = 2,7 dB/km are the losses for a kilometer through multimode 62,5 μm optic fiber with light with length of the wave of 808nm [9]. The length of the optic fiber in
centimeters in “z”, measured in kilometers. BS are the losses in the optic distributor as it follows: optic splitter -BS=3,83dB and optic switch BS=0,58dB for the first one and BS= 0,35 dB for the second output. From the equation (1) the main energy loss for the optic system with splitter is B=6,38 dB, for optic system with optic switch is BS=3,13dB for the first and BS=2,9dB for the second output.
The energy design of the optic system is a response of the following equation:
PVS PBP += [dBm] (2)
here PS is the optical power of the source of light, in our experiment IR laser, B- the main energy losses in the optic system and PPV -The optic power on the input of the devices of photovoltaic converter. From equation (2) for the calculation of the provided optic power in the system we receive the following condition:
Fig. 3. Optical grid with a switch
Fig. 4. Algorithm for optical grid with a switch
BPP SPV −= [dBm] (3)
The IR laser with optic power of 1W (30 dBm) has been
chosen for the optic system of sharing of photon energy with passive splitter, where every photovoltaic have inputs power of PPV= 23,6 [dBm]. In the optic system with optic switch, the power of the IR laser has been reduced to 500mW (27dBm). When we add the losses in (3), we receive the optic power PPV= 23,9 [dBm] in the first output of the photovoltaic and PPV= 24,1 [dBm] on the input of the second.
We convert the power from dBm to W with the following equation:
10)(
10.1)(
mWP
mWP mW = (4) After the convert from (4), by the system with splitter with
input optic power of 1W, every photovoltaic of the equipment receives P(mW)= 229 mW. For a system with switch and adjusted power of 500mW input optic power, the hardware of the first photovoltaic receives P(mW)=251mW and at the input of the second P(mW)= 257 mW optic power.
In the Table 1we can see the dependency between the maximum output electric power with adjusted different levels of experimental power on the input of the photovoltaic [6].
TABLE I Electrical power by different levels of optic power for photovoltaic
PPC-4E
Optical Power (mW)
50
100
250
500
750
1000
1500
Pmax (mW)
17.6
34.8
86
168
240
304
432
Vmp (V)
4.4
4.4
4.3
4.2
4
3.8
3.6
Imp (A)
4
8
20
40
60
80
120
IV. CONCLUSION
When the time of voltage release by the batteries are almost the same, the usage of optic splitter as a sharing of photon energy is the better solution, because it gives the opportunity for simultaneously recharging of all batteries in the optic grid. The bigger amount of the sensors will need a splitter with bigger number of outputs, which comes with higher optic power of the supply laser. The usage of more powerful laser is considered as a disadvantage, because they are more expensive and the increase of the optic power leads to the destruction of the structure of the optic fiber [10]. That’s why there is a limit of the optic power through the fibers and it will limit the number of the sensors. A disadvantage of this method of sharing of energy could be the ineffective usage of the energy from the sensors, which need to charge their battery, but they are in sleep mode.
The usage of optic switch as sharing of optic power is the better decision, when the times of discharge are different and
it is possible every single battery to be charged separately. Compared to the splitters, the optic switch sharing the optic power discrete to every fiber, which allows the usage of laser lower power supply. This makes this type of system more energy effective. Because of the limitation of the power to 500mW, the working power of the switch, the usage of microcontroller and sensors is necessary. The biggest effort comes with the management of the time for charging of the separate sensors and the avoidance of the situation, when two or more sensors must be charged simultaneously. With bigger number of sensor this issue grows definitive. The possible solution could be made with the software with the building of command structure between the sensors in the optic system. That means, that the sensors which have more time in active mode must be with higher priority for recharging in compare with others, which are higher time in sleep mode.
From the analysis and the comparison of the both models for sharing of photon energy can be noted, that the system with optical splitter is technically easier for construction and maintenance and also cheaper.
The method of sharing of optic power with optic switch has better energy effectiveness in the following aspect: the whole optic energy is used for charge, the supply laser is two times less powerful, the effective moment power by the separate sensors is a little bit higher, because of the lower losses in the switch.
V. REFERENCES
[1] JDSU, Photonic power solutions for sensor applications, December, 2006.
[2] J.G. Werthen, M.J. Cohen, T.C. Wu, and S. Widjaja, ELECTRICALLY ISOLATED POWER DELIVERY FOR MRI APPLICATIONS, Photonic Power Business Unit, JDSU, Milpitas, CA, United States, Proc. Intl. Soc. Mag.
[3] Furey J., Anaheim, CA (US), Power over optical fiber systems, Ulllted States Patent Application Publication, No.: US 2009/0016715 A1, Jan. 15, 2009.
[4] Wilson C., Kawasaki (JP); Chee S.S., Kokubunji (JP); Nutt L., Houston, TX (US); Yamate T.,Yokohama (JP); Kamata M., Kawasaki (JP); Methods and apparatus for photonic power conversion downhole, Ulllted States Patent, No.: US 7,696,901 B2, Apr. 13, 2010.
[5] JDSU, Photovoltaic power converter, 12 V (PPC-12E), datasheet, December 2006.
[6] JDSU, Power Over Fiber Kit PPM-500-K, April 2014. [7] JDSU, Power Over Fiber, March 2014. [8] Mitzev C., Dimitrov K., Optical Communications seminar
exercises guide, Technical University, Sofia, ISBN:978-954-438-77-8, p.p. 10-27, 2013.
[9] Corning Incorporated, Corning Clear Curve Multimode Optical Fiber Product Information, , p.p.2-4, 2011.
[10] Seo K., Nishimura N., Shiino M., Yuguchi R. and Sasaki H., Evaluation of High-power Endurance in Optical Fiber Links, Furukawa Review, No. 24, 2003.
Polynomial-Based Extraction Procedure for
Determination of HEMT Noise Wave Temperatures Vladica Đorđević
1, Zlatica Marinković
2, Olivera Pronić-Rančić
2 and Vera Marković
2
Abstract – The noise wave model defines relationships between
the noise wave parameters and the noise parameters. As the
noise wave model is related to device intrinsic circuit and
available measured transistor noise parameters are related to the
whole device, the noise wave parameters are usually extracted
using time-consuming optimization procedures in circuit
simulators. In this paper, a new, faster and more efficient
extraction procedure based on using polynomial functions is
presented. The detailed validation of the proposed procedure is
done by comparison of the transistor noise parameters of the
entire circuit, obtained by using the noise wave parameters
extracted by the proposed approach, with the measured
transistor noise parameters.
Keywords –HEMT, noise parameters, noise wave model, noise
wave parameters, polynomials.
I. INTRODUCTION
The need for precise noise modeling of microwave
transistors (MESFETs/HEMTs) that are used in modern
microwave communication systems, has led to development
of different transistor noise models [1-10]. These models
enable implementation of transistors within microwave circuit
simulators, which results in the efficient noise analysis. The
main classification of transistor noise models is into physical
and empirical noise models. Most microwave circuit designers
use the empirical noise models since the parameters related to
device physical characteristics are often unavailable. The
parameters of the empirical noise models are usually extracted
from the measured transistor noise parameters
(Fmin – minimum noise figure, Γopt – optimum source
reflection coefficient and rn – normalized noise resistance).
In recent years, the noise wave model treating the noise in
terms of waves has appeared as a very appropriate noise
model at the microwave frequencies [2], [7-9], [11-19]. The
wave representation of noise provides a suitable alternative to
the most commonly used representations of noise generated in
two-port network based on the equivalent voltage and/or
current sources [6]. The noise wave parameters are the noise
wave temperatures and it is shown that these temperatures are
frequency dependent [14]. The extraction of the frequency
dependent noise wave temperatures is usually done using the
optimization procedures in circuit simulators. However, the
fact that the optimization procedures are time-consuming
makes them relatively inefficient extraction tool.
In this paper, a new, faster and more efficient extraction
procedure based on using polynomial functions is proposed.
In addition to saving time, the proposed extraction procedure
also enables a very accurate transistor noise modeling using
the noise wave model.
The paper is organized as follows: after Introduction,
Section II contains a short description of the noise wave
model. Polynomial-based extraction procedure is presented in
Section III. Section IV contains the most illustrative numerical
results and obtained observations. Concluding remarks are
given in Section V.
II. NOISE WAVE MODEL OF MICROWAVE FETS
Noise in linear two-port networks can be characterized in
many different ways. In the noise wave representation, a noisy
two-port network is described by using a noiseless linear
equivalent circuit and the waves that emanate from its
ports [2].
It is very convenient to use the noise wave temperatures as
empirical model parameters, as in that way the noise
performance of any two-port network can be completely
characterized by the two real temperatures, Ta and Tb, and the
complex correlation temperature, cj
c cT T e
. These
temperatures can be expressed in terms of the noise
parameters of transistor intrinsic circuit - minimum noise
figure, Fmini, optimum source reflection coefficient,
optij
opti opti e
, and noise resistance, Rni, as [2]:
20
0 20
4( 1)
1
ni optia mini
opti
R TT T F
Z
, (1)
002
0
4( 1)
1
nib mini
opti
R TT T F
Z
, (2)
0
20
4
1
ni optic
opti
R TT
Z
, (3)
where Z0 ˗ the normalization impedance (50) and T0 ˗ the
standard reference temperature (290K).
1Vladica Đorđević is with the Innovation Center of Advanced
Technologies, Bulevar Nikole Tesle 61, lokal 5, 18000 Niš, Serbia,
E-mail: [email protected]. 2Zlatica Marinković, Olivera Pronić-Rančić and Vera Marković
are with the Faculty of Electronic Engineering, University of
Niš, Aleksandra Medvedeva 14, 18000 Niš, Serbia, E-mail:
III. PROPOSED POLYNOMIAL-BASED EXTRACTION
PROCEDURE
As already mentioned, the optimization procedures in
circuit simulators that are usually used for extraction of the
noise wave temperatures are time-consuming. Instead, the
extraction of the noise wave temperatures can be done by
using efficient polynomial-based procedure illustrated in
Fig. 1, which is detailed as follows:
1. Design the small-signal equivalent circuit schematic of
the considered transistor within the standard circuit
simulator and implement the noise wave model
expressions,
2. Generate n random samples of the noise parameters of
transistor intrinsic circuit (Fmini, Rni, |Γopti|, and φopti),
3. For each of n samples of the noise parameters generated
in a previous step, calculate the noise wave
temperatures (Ta, Tb, |Tc|, and τc) using Eqs. (1-3),
4. Assign the calculated noise wave temperatures to the
noise wave model implemented within the standard
circuit simulator in step 1,
5. Simulate the noise parameters of entire transistor (Fmin,
Rn, |Γopt|, and φopt) at the considered frequency range,
ambient temperature and operating conditions,
6. Apply the Eqs. (1-3) to the noise parameters of entire
circuit obtained by simulations, and calculate the fictive
noise wave temperatures (Taf, Tbf, |Tcf|, and τcf)
referring to the whole circuit,
7. Express the correlations between the noise wave
temperatures and the fictive noise wave temperatures
for the considered frequency range by using first degree
(m = 1) polynomials,
8. Based on the measured noise parameters of the
considered transistor, calculate the fictive noise wave
temperatures (Taf, Tbf, |Tcf|, and τcf) using Eqs. (1-3),
9. Use the calculated fictive noise wave temperatures and
obtained correlations expressed by polynomials to
determine the noise wave temperatures (Ta, Tb, |Tc|,
and τc),
10. In order to validate the proposed extraction procedure,
assign the extracted noise wave temperatures to the
noise wave model implemented within the standard
circuit simulator in step 1,
11. Simulate the noise parameters of entire transistor (Fmin,
Rn, |Γopt|, and φopt) at the same frequency range,
ambient temperature and operating conditions as in
step 5,
12. Compare the obtained noise parameters with the
measured ones,
13. If the obtained results do not have satisfactory accuracy,
increase a polynomial degree (m) by 1, and repeat steps
from 7-12. Otherwise, use the noise wave temperatures
extracted in step 9.
Fig. 1. Proposed polynomial-based extraction procedure
flowchart.
IV. NUMERICAL RESULTS
The proposed polynomial-based extraction procedure was
applied to a packaged HEMT, type NE20283A by NEC, and
some of the obtained results are presented in this paper. All
simulations were performed using microwave circuit
simulator ADS (Advanced Design System) [20]. Measured S
and noise parameters have been available in the frequency
range 6-18 GHz over the temperature range 233-333 K, step
20 K [21].
The equivalent circuit of a packaged HEMT used in this
research is shown in Fig. 2 [21]. The intrinsic circuit is
denoted by the dashed line, and it is common to the most of
microwave FET models. The remaining elements embedded
in the extrinsic circuit represent parasitic effects and the
package.
Fig. 2. Equivalent circuit of HEMT in packaged form.
As can be seen in Fig. 2, there are 19 equivalent circuit
elements (ECPs). The values of small-signal ECPs of the
considered transistor were taken from [21].
First, the values of the noise parameters of transistor
intrinsic circuit were generated randomly. Then, the noise
wave temperatures determined from these random generated
intrinsic noise parameters were used to obtain the fictive noise
wave temperatures within ADS [20] circuit simulator. In this
case, for the considered frequency range, the correlations
between the noise wave temperatures and the fictive noise
wave temperatures were expressed with high accuracy by the
first degree polynomials:
[K] [ ] [GHz]a a a af aT x y T K z f , (4)
[K] [ ] [GHz]b b b bf bT x y T K z f , (5)
| | [K] | | [ ] [GHz]c c c cf cT x y T K z f , (6)
[ps] [ps] [GHz]c d d cf dx y z f , (7)
where xa-d, ya-d and za-d, are the polynomial coefficients
given in Table I for different ambient temperatures, and f is
the frequency. The frequency is included in Eqs. (4-7) because
the noise parameters of transistor extrinsic circuit are
frequency dependent. Also, all the units of variables in
Eqs. (4-7) were marked within square brackets.
TABLE I
POLYNOMIAL COEFFICIENTS FOR DIFFERENT AMBIENT
TEMPERATURES
233 K 253 K 273 K 293K 313 K 333 K
Ta
xa -82.09 -99.12 -109.3 -82.07 -48.95 -54.6
ya 1.507 1.584 1.567 1.257 0.97 0.976
za 4.92 4.973 4.836 5.9 7.662 8.364
Tb
xb -98.4 -77.26 -149.1 -164.2 -100.1 -110.7
yb 1.54 1.218 1.702 1.72 1.233 1.244
zb 7.226 8.385 9.251 9.852 10.48 11.63
|Tc|
xc -70.38 -67.85 -107.3 -171.4 -102 -105.1
yc 1.178 1.055 1.248 1.618 1.136 1.096
zc 8.696 9.901 11.7 13.62 13.47 14.85
τ c
xd 25.3 24.23 23.49 23.37 24.24 24.75
yd -0.098 -0.065 -0.046 -0.044 -0.046 -0.058
zd -0.332 -0.345 -0.348 -0.346 -0.372 -0.372
The polynomial coefficients from Table I and the fictive
noise wave temperatures calculated from the measured
transistor noise parameters were used for determination of the
noise wave temperatures. In order to validate the proposed
polynomial-based extraction procedure, the determined noise
wave temperatures were assigned to the noise wave model
implemented within ADS [20], and the noise parameters of
entire transistor circuit were simulated. The simulated noise
parameters were then compared with the corresponding
measured data.
As an illustration, Fig. 3 presents the simulated Fmin, rn,
and Γopt and the corresponding measured data. The results
shown in Fig. 3 were obtained for the ambient temperature of
313 K in the frequency range from 6 to 18 GHz. It can be seen
that the simulated values of noise parameters are very close to
the measured ones, confirming the accuracy of the proposed
extraction procedure. The results for the other available
temperatures show the same level of the noise modeling
accuracy.
V. CONCLUSION
Because the noise wave temperatures are frequency
dependent, the optimization procedures in circuit simulators
usually used for their extraction become time-consuming. For
this reason, a new efficient extraction procedure was proposed
in this paper. The presented procedure is based on the
polynomial correlations between the noise wave temperatures
and the fictive noise wave temperatures of entire transistor.
The proposed procedure was applied to a specific HEMT
device in a packaged form. Extraction of the noise wave
temperatures was carried out based on the polynomial
expressed correlations between them and the fictive noise
wave temperatures calculated from the available measured
transistor noise parameters. Based on the obtained noise wave
temperatures, the corresponding noise parameters of entire
transistor circuit were calculated in the circuit simulator. A
good agreement between simulated and measured transistor
noise parameters in a wide range of ambient temperatures
proves validity of the proposed procedure.
(a)
(b)
Fig. 3. Measured (symbols) and simulated (lines) values of: (a) minF
and nr , (b) Γopt ,depending on the frequency at 313K.
ACKNOWLEDGEMENT
The work was supported by the TR-32052 project of the
Serbian Ministry of Education, Science and Technological
Development. The authors would like to thank prof. Alina
Caddemi, University of Messina, Italy, for providing the
measured data.
REFERENCES
[1] R. A. Pucel, H. A. Haus, H. Statz, “Signal and Noise Properties
of Gallium Arsenide Microwave Field-Effect Transistors”,
Advances in Electronics and Electron Physics, vol. 38,
pp. 195-265, 1975.
[2] R. P. Meys, “A Wave Approach to the Noise Properties of
Linear Microwave Devices”, IEEE Trans Microw Theory Tech,
vol. 26, no. 1, pp. 34-37, 1978.
[3] H. Fukui, “Design of Microwave GaAs MESFET's for Broad-
Band Low-Noise Amplifiers”, IEEE Trans Microw Theory
Tech, vol. 27, no. 7, pp. 643-650, 1979.
[4] A. Cappy, A. Vanoverschelde, A. Schortgen, C. Versnaeyen,
G. Salmer, “Noise Modeling in Submicrometer-Gate Two-
Dimensional Electron-Gas Field-Effect Transistors”, IEEE
Trans Electron Dev, vol. 32, no. 12, pp. 2787-2795, 1985.
[5] M. S. Gupta, O. Pitzalis, S. E. Rosenbaum, P. T. Greiling,
“Microwave Noise Characterization of GaAs MESFETs:
Evaluation by On-Wafer Low-Frequency Output Noise Current
Measurement”, IEEE Trans. Microwave Theory Tech, vol. 35,
no. 12, pp. 1208-1218, 1987.
[6] M. W. Pospieszalski, “Modeling of Noise Parameters of
MESFET's and MODFET's and Their Frequency and
Temperature Dependence”, IEEE Trans Microw Theory Tech,
vol. 37, no. 9, pp. 1340-1350, 1989.
[7] S. W. Wedge, D. B. Rutledge, “Wave Techniques for Noise
Modeling and Measurement”, IEEE Trans Microw Theory
Tech, vol. 40, no. 11, pp. 2004-2012, 1992.
[8] O. Pronić, V. Marković, N. Maleš-Ilić, “The Wave Approach to
Noise Modeling of Microwave Transistors by Including the
Correlation Effect”, Microw Opt Technol Lett, vol. 28, no. 6,
pp. 426-430, 2001.
[9] O. Pronić, V. Marković, “A Wave Approach to Signal and
Noise Modeling of Dual-Gate MESFET”, AEU-Int J Electron
C, vol. 56, no. 1, pp. 61-64, 2002.
[10] G. Crupi, A. Caddemi, A. Raffo, G. Salvo, A. Nalli, G. Vannini,
“GaN HEMT Noise Modeling Based on 50-ohm Noise Factor”,
Microw Opt Technol Lett, vol. 57, no. 4, pp. 937-942, 2015.
[11] R. P. Hecken, “Analysis of Liner Noisy Two-Ports Using
Scattering Waves”, IEEE Trans Microw Theory Tech, vol. 29,
no. 10, pp. 997-1004, 1981.
[12] J. A. Dobrowolski, Computer-Aided Analysis, Modeling and
Design of Microwave Networks-The Wave Approach, Norwood,
Artech House, 1996.
[13] O. Pronić, V. Marković, N. Maleš-Ilić, “MESFET Noise
Modeling Based on Noise Wave Temperatures”, TELSIKS'99,
Conference Proceedings, pp. 407-410, Niš, Yugoslavia, 1999.
[14] O. Pronić-Rančić, V. Marković, “Microwave Transistors Noise
Modeling by Using Variable Noise Wave Temperatures”,
TELSIKS'01, Conference Proceedings, pp. 313-316, Niš,
Yugoslavia, 2001.
[15] V. Marković, O. Pronić-Rančić, Z. Marinković, “Noise Wave
Modeling of Microwave Transistors Based on Neural
Networks”, Microw Opt Technol Lett, vol. 41, no. 4,
pp. 294-297, 2004.
[16] D. Pasquet, E. Bourdel, S. Quintanel, T. Ravalet, P. Houssin,
“New Method for Noise-Parameter Measurement of a
Mismatched Linear Two-Port Using Noise Power Wave
Formalism”, IEEE Trans Microw Theory Techn, vol. 56, no. 9,
pp. 2136-2142, 2008.
[17] A. Colliander, T. Narhi, P. de Maagt, “Modeling and Analysis
of Polarimetric Synthetic Aperture Interferometric Radiometers
Using Noise Waves”, IEEE Trans Geosci Remote Sens, vol. 48,
no. 9, pp. 3560-3570, 2010.
[18] J. A. Dobrowolski, “Noise Characterization of Differential
Multi-Element Multiport Networks - the Wave Approach”, Int J
Electron Telecommun, vol. 61, no. 4, pp. 395-401, 2015.
[19] V. Đorđević, Z. Marinković, G. Crupi, O. Pronić-Rančić,
V. Marković, A. Caddemi, “Wave Approach for Noise
Modeling of Gallium Nitride High Electron-Mobility
Transistors”, Int J Numer Model Electron Network Dev Field,
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[20] Advanced Desing System, Agilent Eesof EDA, 2009.
[21] A. Caddemi, A. Di Paola, M. Sannino, “Microwave Noise
Parameters of HEMTs vs. Temperature by a Simplified
Measurement Procedure”, EDMO'96, Conference Proceedings,
pp. 153-157, Leeds, UK, 1996.
Study the impact of the instability of oscillators in the
Head End modules
Oleg Borisov Panagiev1
Abstract – Here are presented the results of the researches
about the influence of changes in the oscillation frequencies in
the modulators and channel converters in a Head End for cable
TV. The test channel (n) is the standard channel 46 from the
UHF range of B/G standard.
The studies of this article are made for modules forming both
analog and digital signals with a one-circular chain PLL.
Keywords – CATV/HFC, BER, PLL, transmodulator,
upconverter.
I. INTRODUCTION
The forming of the group signal in the Head End is done in
few ways – in serial, parallel and mixed connection of the
channel converters’ outputs (UpC – in the common case for
Downstream) by using splitters and taps. The necessary level
of group signal in the whole operating frequency range of the
CATV/HFC systems is achieved by:
Connecting of an electronic amplifier between the output
of the last summator and the coaxial (trunk) cable in the
CATV system;
Connecting an optical transmitter (with built in amplifier)
between the output of the last summator and the optical
fiber/splitter in dependence of the architecture of the
cable distribution system.
Regardless which of the two methods is used (CATV or
CATV/HFC) the stability of the carrier frequencies (fpc, fsc for
analogue AM-VSB signals and fc for the digital M-QAM
signals), as well as of the intermediate frequencies (IFpc, IFsc
and IFc), is from an essential importance for a reliable,
qualitatively and seamlessly transmission of information to
the subscribers.
There are several methods for supporting the stability of the
carrier (channel and intermediate) frequencies of the analogue
and digital signals (PLL, DLL, DCM, HRC/IRC), but in the
basis of most of them is the PLL (Fig.1), where the stability of
the output frequencies is defined mainly by the stability of the
reference oscillator (RO). The signals from RO and VCO
(voltage controlled oscillator) are feed to a phase detector
(PD), who is determining the phase relationships between
them. If the signals are in phase, the variation of the output
voltage is equal to zero. If there is a phase difference between
the two signals, alterations in the output voltage (±ΔU) occur,
whereat the variations are proportional to the phase difference
(±Δφ).
With the most complicated phase detectors can be also
determined the sign of mismatch of the phases. By a low pass
filter (LPF) that eliminates the high frequency composites of
the voltage from the PD, (±ΔU) go on the VCO. If the LPF is
missing, we observe the “Jitter” effect – a sharp variation of
the output voltage’s fronts. The VCO produces phase
corrected sync signals, one of which is used as an input signal
for the PD. Because the frequency values of the VCO and RO
are different (fVCO >> fRO), it is necessary to include frequency
dividers (integer and fractional), by which fR and fVCO become
comparable, which itself allows their comparison in the PD.
The change of the output frequency of the VCO is performed
step-by step programmatically, controlled via microprocessor
μP, as a being set different values of the dividers by I2C bus or
SPI bus [1], [2], [3].
The control can be accomplished in any module or for
many modules from an outside/standalone block, in which the
μP [4], [5], [6].is situated. In the first case the μP needs to be
built in every module [4], [7], [8].
Fig.1. PLL block diagram
II. PROBLEMS LEADING TO INSTABILITY OF THE
OSCILLATOR FREQUENCIES
As it is of significant importance to maintain the carrier
frequencies constant in time (lack of detuning until the
operator decided to change them), it is required to show,
analyze and research the problems, which can lead to their
instability.
The causes, which can lead to detuning of the carrier
frequency/-ies and are not dependent on the kind of the
signals (analogue or digital), which a certain module
processes, modulates and converts by frequency. They can be
connected with different factors, but their influence is only in
the frequency determining, and converting elements: integral
circuits, capacitors, diodes, inductances, resistors, quartz
resonators and etc., which build VCO; Mixer; divider; PD;
RO, and even μP/μC as well as SMPS. 1Oleg B. Panagiev is with the Technical University of Sofia,
Bulgaria, E-mail: [email protected].
One of the main reasons, which can cause the unwanted
alternation of the carrier frequencies is the so called “cold
solder”, since all elements are being soldered to a printed
circuit board (PCB). Furthermore, in the multilayer PCD with
bad metallization of the openings or breaking of a track on the
PCB again some frequency determining circuits will not work
at all or partially. Other reasons are the manufacturing
tolerances of the parameters of the elements, which appear
after a certain period of operation of the modules, temperature
dependencies, and damage in the very frequency determining
elements, change of power voltages and etc.
The above mentioned reasons affect, however, differently
the modules for analog and digital signals. In the present
paper are researched the influences of the adjacent lower (n-1)
and upper (n+1) channels in the testing channel (n). In the
most channel converters (UpC) the receipt of the channel
frequency is done by the upper setting of the oscillation
frequency:
][, MHzIFfff oscchout . (1)
This way, for example, for AM-VSB modulator (Fig.2) a
synchronization with PLL occurs only with the second sound
intermediate frequency (IFsc,2) , which for B/G standard is
5,5MHz, while for D/K it is 6,5MHz. However, the oscillator
frequency IFpc = 38,9MHz, through which is obtained the first
sound intermediate frequency IFsc (B/G33,4MHz and
D/K32,4MHz), does not synchronize. By change of the
oscillator frequency with ±ΔIFpc, also IFsc changes and after a
frequency convertion can be caused an unfavorable influence
(disturbance) in the adjacent upper channel (n), (Fig.3).
Fig.2. Simplified AM-VSB modulator block diagram
][,2, MHzIFfIF scoscsc (2)
][),()( 2,2, MHzIFIFffIF scscoscoscsc (3)
Fig.3. Unfavorable influence in the adjacent upper channel (n)
The synchronization of IFpc, respectively fpc, is performed
with bi-circular chain PLL in UpC (Fig.4), as through first
circle of the PLL, IFpc and the programmable synthesizer
stabilize the frequency of VCO. Through the second circle,
the programmable synthesizer, the VCO, Mixer 1 and BPF
form fpc for the corresponding channel, but for fsc its stability
is not support in UpC. In a given moment fsc increases (i.e.
fsc>5,5MHz or fsc>6,5MHz) or decreases (i.e. fsc<5,5MHz or
fsc<6,5MHz). In the first case, the distortion influences
negatively the upper (n) channel (Fig.3) and in the second
case – the effect is reflected in the channel itself (n-1), as the
sound does not reproduce itself or reproduces with distortions.
Fig.4. Up converter block diagram
][),( MHzIFIFff VCOch (4)
][),()( MHzIFIFfff VCOVCOch (5)
By stable IFpc and IFsc in the modulator, but unstable fpc
(i.e. decrease fpc of with -∆fpc or increase of fpc with +∆fpc) is
negatively influenced over the lower (Fig.5) or upper (Fig.3)
channel (n).
The synchronization of IFc=36MHz in QAM modulators
(Fig. 6) and fc in the channel convertors (UpC), respectively –
transmodulators, is being performed mainly with the one-
circular chain PLL. Some manufacturers [8] use infradyne
conversion (with two frequency converters), as the second
intermediate frequency is out (upper) of the operating
frequency range (Fig.7). In such case are used two of each:
VCO, Mixer, converter (UpC, DwC), PLL (not tuning,
tuning). VCO1 works with one frequency >>862MHz (in this
Fig.5. Unfavorable influence in the adjacent lower channel (n)
case fVCO1=1244MHz). The management and the settings are
performed by μC (MICOM). The stability of the frequencies
depends on the foregoing factors, while the influence of the
detuning ±ΔIFc and ±∆fc is illustrated on Fig.8 and Fig.9 with
adjacent to the testing channel (n) disturbing channels (n-1)
and (n+1), which are also digital with QAM modulation.
Fig.6. Simplified QAM modulator block diagram
][, MHzffIF ooc (6)
Fig.7. QPSK/8PSK-QAM transmodulator block diagram
Fig.8. Unfavorable influence in the adjacent upper channel (n)
Fig.9. Unfavorable influence in the adjacent lower channel (n)
By all detuning ±∆f (±ΔIF) no matter if the signals are
analog or digital is produced an overlap of the channels,
which leads to worsening of signal parameters and channels.
For the analog, CSO, CTB, C/N, respectively S/N worsens,
while for the digital: BER, MER, C/N and etc.
III. EXPERIMENTAL RESULTS
Here are presented the results of the researches about the
influence of changes in the oscillation frequencies in the
modulators and channel converters in a Head End for cable
TV. The test channel (n) is the standard channel 46 from the
UHF range of B/G standard. The signals, which are
transmitted in it are digital with 64-QAM, symbol rate
6900ks/s, fch=fc=674MHz, channel level U46=80dBV. Lower
disturbing channel (n-1) is the standard channel 45: analog
with AM-VSB modulation; fpc=663,25MHz; fsc=668,75MHz;
level of the channel with sound carrier fsc is U45,sc=60dBV.
The upper disturbing channel (n+1) is the standard channel
47: analog with AM-VSB modulation; fpc=679,25MHz,
fsc=684,75MHz; channel level with picture carrier fpc is
U47,pc=70dBV.
The change of the corresponding carrier frequency is with a
step f=250kHz, as for channel (n-1) sound carrier increases
(fsc+k.f) and for channel (n+1) picture carrier decreases (fpc-
k.f). Here k is the serial number of the step, such as its
maximal value in the researches is determined by the value of
postBER. When postBER reaches values 10-4
, the research is
terminated.
The results presented, in Table 1, are for the influence of
channel (n-1), and in Table 2, are for the influence of channel
(n+1). Fig.10 is constellation diagram of the signal with
absence of disturbance, and Fig.11a and Fig.11b are
constellation diagrams of the signal with existence of
disturbance (with maximal number of the step, respectively
k=8 and k=7). The levels of the signals are in accordance to
the nominal output levels of the modulators, channel
converters and transmodulators, as for the disturbing channels
are also accounted the influences of varicaps tunable bandpass
(BPF) filters over the levels of the signals, whose frequency is
outside of passband B0,7.
TABLE 1
VALUES OF BER, MER, C/N AT THE INFLUENCE OF
THE CHANNEL (n-1)
TABLE 2
VALUES OF BER, MER, C/N AT THE INFLUENCE OF THE CHANNEL (n+1)
Fig.10. Constellation diagram for ch.46 with absence of disturbance
a) from ch.45
b) from ch.47
Fig.11. Constellation diagram for ch.46 with disturbance
IV. CONCLUSION
The results for the standart B/G can successfully refer also
to the 46th channel of the D/K standard [9]. The picture
carrier for both standards is the same, so the influence of the
(n+1) channel on the channel (n) by decrease of its value
(respectively the oscillator frequency) is the same as the
present case. Differently stays the case of the influence of the
(n-1) channel onto the (n) channel, because the sound carrier
at the D/K is closer with 1MHz to the next upper channel. In
this case, smaller alterations in the sound carrier lead to
overlapping with the (n) channel and deterioration of BER,
MER and C/N. The applied approach for channel 46 can be
applied for every digital (QAM) DVB-C channel, which is
adjacent to an analogue (AM-VSB) channel, where the
Fig.12. Non standard (mixed) frequency plan
of CATV/HFC system
number of the channel depends on the frequency plan [10],
[11] of the corresponding cable provider. By a standard
(classical) frequency plan an overlaping of the examined type:
channel (n-1) with the channel (n) is possible only between
the last analogue channel and the first digital channel, whereas
when other conditions are equal, the non standard (mixed)
frequency plan (Fig.12) ensures lower level of nonlinear
products from the crossmodulation.
REFERENCES
[1] MT-086 Tutorial, Fundamentals of Phase Locked Loops
(PLLs), Analog Devices, Inc., 2009.
[2] W. Kester, "Converting Oscillator Phase Noise to Time Jitter,"
Tutorial MT-008, Analog Devices, Inc., 2009.
[3] E. P. Ugryumov, Cifrovaya shemotehnika, 3th ed., BHV-
Peterburg, ISBN 978-5-9775-0162-0, 2010.
[4] http://wisi.de/en/wisi-group
[5] https://www.kathrein.com/
[6] http://www.televes.com/en/eng/home
[7] http://www.blankom.de/
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distortions Influence in the CATV/HFC networks. ICEST, Proc.
of Papers, vol.1, Ohrid, 26-29 June 2013, pp. 33-36
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cable television networks, Ex-Press, Gabrovo, 2010.
Mixer Linearization in Direct Conversion Receiver Aleksandar Atanasković1, Aleksandra Đorić2 and Nataša Maleš-Ilić1
Abstract – In this paper, the linearization of the mixer in direct conversion receiver is performed by the technique that exploits the baseband signals. The signals for linearization are formed and processed in digital domain, set on the appropriate amplitude and polarity and inserted at the mixer. The linearization effects of the applied linearization method on the third- and fifth-order nonlinearities are observed for the case when the signals for linearization are driven at the transistors' drain of the RF stage differential pair in the Gilbert mixer cell. Additionally, the effects of I/Q signal imbalances on the linearization of the mixer are examined. Analysis are performed for two types of the signal – ideal I/Q signal without imbalances and I/Q signal with imbalance effect (up to 30% amplitude imbalance and 50 degrees phase imbalance). Tests were performed for two different input signal power levels and for two cases of frequency spacing between signals.
Keywords – Direct Conversion, Mixer, Linearization method, I/Q imbalances.
I. INTRODUCTION
The direct-conversion receivers (DCRs), also known as zero-IF receivers, over the last decade have become popular alternative approach to the classical heterodyne architecture in the development of RF integrated circuits (ICs) in modern wireless communication systems. The DCR architecture has become an attractive solution for the commercial applications due to its exquisite characteristics, such as low-cost, low-power, wide bandwidth, and highly integration with RF circuitry. On the other hand, linearity of the receiver become necessary feature and mixer is one of the influential components which can determine system performances. The mixers have frequency-conversion/demodulation function in RF and microwave receivers. The major goals of the mixer design are to minimize conversion loss, noise figure and intermodulation distortion.
Different techniques for the mixer linearization have been deployed, such as predistortion, feedforward, a technique based on transconductance cancelation of the third-order, techniques based on the insertion of the second harmonic and/or the difference frequency signal in the analogue domain [1-5].
The technique applied in this paper for the mixer linearization uses the modified signal in the baseband which is a low-frequency product of the second-order nonlinearity
of a nonlinear system induced by the useful baseband signal, [6], [7]. The in-phase I and quadrature-phase Q components of the signal are digitally processed in order to create adequate signals for linearization, which are tuned in amplitude and polarity and injected at the mixer cell.
The effects of the proposed linearization method are examined through the simulation process for QAM signal at two input power levels , where I and Q components are single tones with frequency interval between spectral components of 0.2 MHz and 2 MHz. Additionally, the impact of the imbalances of the I and Q signals on the intermodulation products is investigated. Output power levels of the fundamental signal, as well as levels of the third- and fifth-order intermodulation products, are observed in terms of the amplitude and phase mismatch of the I and Q signals.
II. THEORETICAL APPROACH
The direct-conversion receivers translate the desired RF spectrum directly to DC using a local oscillator (LO) which frequency is equal to the RF-carrier frequency of the desired signal. The mixed output is the signal that is downconverted directly to the baseband, so that the IF stage is not required. Figure 1 shows the schematic diagram of the direct-conversion receiver including the mixer linearization circuit.
The theoretical approach of the proposed linearization technique is based on the nonlinearity of the transistor output current [7-9]. The in-phase, I and quadrature phase, Q components are extracted at the demodulator output in the receiver to be adequately processed in the baseband to create signals for linearization:
2 2mod ( , )BB f I Q I Q= = + (1)
The formed linearization signals are separately adjusted in amplitude and polarity { }e oa across two branches, as
indicated in Figure 1. Indexes, e and o in subscript are related to the signals prepared for the insertion in the mixer cell through the serial LC circuit. According to the analysis performed in [6-9], the second order nonlinearity of the transistor in the mixer cell leads to the interference of the injected baseband signal for linearization and fundamental signal, which generates additional third-order nonlinear products that may suppress the original intermodulation products distorted by the transistor nonlinear characteristic.
1Aleksandar Atanasković and Nataša Maleš-Ilić are with theFaculty of Electronic Engineering, University of Niš, Serbia,Aleksandra Medvedeva 14, 18000 Niš, Serbia, E-mail: [aleksandar.atanaskovic, natasa.males.ilic]@elfak.ni.ac.rs
2Aleksandra Đorić is with the Innovation Centre of AdvancedTechnology, Niš, Serbia, Bulevar Nikole Tesle 61, 18000 Niš,Serbia, E-mail: [email protected]
Fig.1. Schematic diagram of the DCR with the mixer linearization circuit
III. LINEARIZATION RESULTS
The linearization was applied to the Gilbert mixer that is used in the direct conversion receiver (Figure 1). The impact of the performed linearization method on the intermodulation products reduction was analysed through the simulation process in ADS for the mixer cell that uses transistor MOSFET model. The linearization was carried out for the ideal case where I and Q components have equal amplitudes and phase difference of 90 degrees.
The mixer cell was tested for QAM modulated signals that comprise the I and Q single tone baseband components. The frequency spectrum of such a signal contains two spectral components and we considered two cases, when the spectral components are separated by 0.2 MHz and 2 MHz.
The carrier frequency of the input signal is 1 GHz as well as the frequency of the local oscillator. Linearization of the mixer was performed for the cases when the input power of the RF carrier is PinRF = -20 dBm and -30 dBm, while the power of the signal from the local oscillator is PinLO = -3 dBm.
The optimization process of the adjustable parameters of the linearization signals was performed to reduce the third-order intermodulation products, IM3 and to restrain the fifth-order intermodulation products, IM5 at the levels below the suppressed IM3 products.
Figures 2 and 3 show the intermodulation products, IM3 and IM5, before and after the applied linearization method. After applied linearization, suppression of the IM3 products is around 12 dB for higher power level and both frequency spacing. For lower power, the IM3 products are improved about 22 dB for 0.2 MHz frequency spacing and 8 dB for 2 MHz signal separation. On the other hand, the IM5 products are aggravated, but they are still below linearized IM3 products.
a) b)
Fig 2. Intermodulation products before and after the linearization forPinRF = -20 dBm, PinLO = -3 dBm: a) IM3 i b) IM5
a) b)
Fig 3. Intermodulation products before and after the linearization forPinRF = -30 dBm, PinLO = -3 dBm: a) IM3 i b) IM5
IV. EFFECTS OF I/Q IMBALANCES
In ideal case, the signal from the local oscillators in the I and Q channels have equal amplitude and phase difference of -90 degrees, as depicted in Figure 1. When the asymmetry occurs, the amplitudes and phases of the LO signals in the channels deviate from the values in the ideal case. In practice, I channel is defined as a reference (0 degrees phase, amplitude value 1).
The signal at the mixer input is in the form:
( ) ( ) ( ) ( ) ( )ttQttItX ccRF ω−ω= sincos (2) where cω is the carrier frequency. Imbalance is characterized by amplitude (α) and phase shift ( θ ) of the signal from the local oscillator XLO in Q branch as:
( )θ+ωα−= tX LOLO sin (3)
Then, the IQ imbalanced signal at the mixer output can be written as follows:
( ) ( )tItI BB =
( ) ( ) ( ) ( ) ( )[ ]θ−θα= sincos tItQtQBB (4)
In 3D figures, 4 and 5, the output power of the fundamental signal for both, input power levels and signal spacing, in terms of amplitudes and phases misalignment of the I and Q components is presented. Figures clearly indicate that output power levels stay almost unchanged with the increase of the parameters α and θ for the considered signal separation and input signal levels.
Figures 6 to 9, represent the IM3 and IM5 products after the linearization when IQ imbalances are considered. For low level of IQ imbalances ( 5%α < , deg3<θ ) the IM3 products after the linearization retain almost unaltered in case of 0.2 MHz signal spacing. When signal spacing is 2 MHz, the IM3 products are less susceptible to the amplitude and phase changing, especially for lower considered power. In the cases of greater IQ imbalances, values of the IM3 products after the linearization are approaching the levels of the IM3 products before the linearization. As far as the IM5 products are concerned they slightly increase with the rise of the IQ imbalances, but they still stay below the linearized IM3 products considered under the same imbalance conditions.
a) b)
Fig. 4. Output power of the fundamental signal for signal spacing 0.2 MHz in terms of I/Q imbalances : a) PinRF = -20 dBm,
PinLO = -3 dBm; b) PinRF = -30 dBm, PinLO = -3 dBm
a)
b)
Fig. 5. Output power of the fundamental signal for signal spacing 2 MHz in terms of I/Q imbalances: a) PinRF = -20 dBm, PinLO = -3 dBm; b) PinRF = -30 dBm, PinLO = -3 dBm
a) b)
Fig. 6. Intermodulation products of the direct converted mixer for signal spacing 0.2 MHz, PinRF = -20 dBm, PinLO = -3 dBm: a) IM3;
b) IM5
a) b)
Fig. 7. Intermodulation products of the direct converted mixer for signal spacing 0.2 MHz, PinRF = -30 dBm, PinLO = -3 dBm: a) IM3;
b) IM5
a) b)
Fig. 8. Intermodulation products of the direct converted mixer for signal spacing 2 MHz, PinRF = -20 dBm, PinLO = -3 dBm: a) IM3;
b) IM5
a) b)
Fig. 9. Intermodulation products of the direct converted mixer for signal spacing 2 MHz, PinRF = -30 dBm, PinLO = -3 dBm: a) IM3;
b) IM5
V. CONCLUSION
This paper describes the linearization method that uses the modified baseband signals for the Gilbert mixer linearization in direct conversion receiver. The main role of this mixer is direct conversion of the input signal carrier frequency to the baseband. The test was performed for the QAM signal whose I and Q components are sinusoidal signals and the spectrum
contains two frequency components separated for 0.2 MHz and 2 MHz. The proposed linearization method utilizes the I and Q signals that are adequately processed in the digital domain at the receiver with the aim to form the signals for linearization. Linearization effects are examined for different input power levels and different frequency spacing between the signal spectral components. The signals for linearization are fed at the transistors' drain of the RF stage differential pair in the Gilbert cell. It should indicate that very good results are achieved in the reduction of the third-order mixer nonlinearity. The fifth-order intermodulation products are deteriorated, but they are still kept at the levels below the linearized IM3 products. Additionally, it is shown that the low-levels of IQ misalignment have almost negligible effect on the linearization results, especially in case of 2 MHz spacing between signals. Also, we analyse the grade in which the linearization effects deteriorate with the increasing imbalance.
ACKNOWLEDGEMENT
This work was supported by the Ministry of Education, Science and Technological Development of Republic of Serbia, the projects number TR-32052.
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