Static realization of reliable positional indication
The highly reliable position information model for optoelectronic display systems is offered. Logical operators that describe static formation of this model are obtained and analyzed. The main features of alphabets for two variants of this information model and information fields for their synthesis...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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irk-123456789-1211272017-06-14T03:06:40Z Static realization of reliable positional indication Bushma, A.V. Sukach, G.A. The highly reliable position information model for optoelectronic display systems is offered. Logical operators that describe static formation of this model are obtained and analyzed. The main features of alphabets for two variants of this information model and information fields for their synthesis are investigated. Also offered are mathematical models for specific devices intended for highly reliable positional imaging information at the display consisting of elements with one common electrode. Analized and represented is their circuit solution. 2002 Article Static realization of reliable positional indication / A.V. Bushma, G.A. Sukach // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2002. — Т. 5, № 1. — С. 119-123. — Бібліогр.: 10 назв. — англ. 1560-8034 PACS 85.60.Bt, 42.79.Kr http://dspace.nbuv.gov.ua/handle/123456789/121127 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The highly reliable position information model for optoelectronic display systems is offered. Logical operators that describe static formation of this model are obtained and analyzed. The main features of alphabets for two variants of this information model and information fields for their synthesis are investigated. Also offered are mathematical models for specific devices intended for highly reliable positional imaging information at the display consisting of elements with one common electrode. Analized and represented is their circuit solution. |
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Bushma, A.V. Sukach, G.A. |
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Bushma, A.V. Sukach, G.A. Static realization of reliable positional indication Semiconductor Physics Quantum Electronics & Optoelectronics |
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Bushma, A.V. Sukach, G.A. |
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Bushma, A.V. |
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Static realization of reliable positional indication |
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Static realization of reliable positional indication |
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Static realization of reliable positional indication |
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Static realization of reliable positional indication |
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Static realization of reliable positional indication |
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static realization of reliable positional indication |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2002 |
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Static realization of reliable positional indication / A.V. Bushma, G.A. Sukach // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2002. — Т. 5, № 1. — С. 119-123. — Бібліогр.: 10 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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AT bushmaav staticrealizationofreliablepositionalindication AT sukachga staticrealizationofreliablepositionalindication |
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119© 2002, Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2002. V. 5, N 1. P. 119-123.
PACS 85.60.Bt, 42.79.Kr
Static realization of reliable positional indication
A.V. Bushma, G.A. Sukach
Institute of Semiconductor Physics, NAS of Ukraine, 45 Prospect Nauky, 03028 Kyiv, Ukraine
Phone: +380 (44) 265 6188; fax: +380 (44) 265 5430; e-mail: bushma@isp.kiev.ua
Abstract. The highly reliable position information model for optoelectronic display systems
is offered. Logical operators that describe static formation of this model are obtained and
analyzed. The main features of alphabets for two variants of this information model and
information fields for their synthesis are investigated. Also offered are mathematical models
for specific devices intended for highly reliable positional imaging information at the display
consisting of elements with one common electrode. Analized and represented is their circuit
solution.
Keywords: positional indication, reliability, modeling, display, LED, bar graph array,
optoelectronics, logic element, digital structure, integrated circuit.
Paper received 31.01.02; revised manuscript received 15.02.02; accepted for publication 05.03.02.
1. Introduction
One of the main parameters of modern information-
measuring systems is high reliability of data transfer to
the operator. This reliability is determined by two major
factors: first, by a configuration and qualitative param-
eters of apparatus means, and, second, by specific fea-
tures of information transfer from an imaging system to
the operator [1, 2].
Estimation of the first component is traditional and
can be carried out using calculation of a probability of
the device fail-proof operation within a definite time in-
terval obeying some analytical or experimental methods
[3, 4]. Taking the second method into consideration is
more complicated and based on man-resourse-loading
experimental methods that envisage using a considerable
number of expert conclusions made by several operator
groups for validity of results obtained. In the course of
the experiment, created are data massifs when reading
information out in different conditions [5, 6]. Practically,
in the most cases, more effective are analysis and evalua-
tion of some information model (IM) that can reflect the
state of a controlled object [7]. Such approach determines
the considerable interest to creation and research of IMs
for displays of different types.
In displays, information is transferred to an operator
via some system of signs corresponding to imaged val-
ues. The set of used symbols forms IM. One of the most
reliable discrete realization for such information process
is based on scale data representation, which is condi-
tioned by both the high level of adequacy between sym-
bol shapes and meanings and an informational excess of
scale indication.
2. Information models of scale indication
Two IM are most widely used in devices for measur-
ing and computational techniques in the case of scale
data representation. These are bar graph and positional
IMs with corresponding specific alphabets for visual sym-
bols. In the first case, indication data is fixed through a
position of an optical non-uniformity in the indicator in-
formation field, and in the second one it is conditioned
by both an length and position of the indication end formed
by the optical non-uniformity relatively scale marks. As
for scales based on active elements, e.g., LEDs, it is ei-
ther an illuminating mark or illuminating line on the
scale, respectively.
It is obvious that in portable and mobile systems with
scales using LEDs, more actual is usage of the positional
IM, since this form of data representation provides their
high efficiency. Within the framework of this model, the
respective level of efficiency and reliability of these de-
vices is reached due to analysis and separation of func-
tional and technical solutions for their units, which is the
most successfully solved using informational process
modeling in imaging systems [2, 7]. Among determinated
mathematical methods, the most widely spread means for
analytic description, while data processing in informa-
tional systems, are theory-of-sets and logical methods [2,
8].
In this work, we made an analysis of logic regulari-
ties that are characteristic for a synthesis of the positional
IM at a bar graph display in optoelectronic informa-
tional-and-measuring systems.
120 SQO, 5(1), 2002
A.V. Bushma et al.: Static realization of reliable positional indication
3. Operation of the information model
Any display is designed to transfer operator some in-
formation I that can be represented by a set of annuncia-
tions
{ }lli III,III ,,,,, 121 −= KK (1)
where Ii is i-th meaning of annunciations ordered in such
manner that ii II <−1 , and li ,1= .
Data from an imaging device are transferred to the
operator per IM elements that are visual symbols νS . As
a rule, each annunciation is corresponded by the unique
symbol. The sense of these symbols is common for the
whole set I , e.g. one deals with a voltage indicator, and
the voltage value runs along a series of meanings. There-
fore, the set (1) can be represented via respective symbols
νS as
{ })(,)(,,)(,)(,)( 121 qq SISISI,SISII −= KK ν
(2)
where )( νSI is the ν-th meaning that corresponds to the
νS symbol, while qí ,1= .
The set used νS symbols forms the IM alphabet
IMΩ . Its length equal to the s number of various sym-
bols in this IM is determined by a final set of allowed
states in the display information area. This area consists
of αi elements that form the set A and can be described as
{ }ppi aaa,aaA ,,,,, 121 −= KK (3)
where p is the total number of information area elements
(IAE).
From the viewpoint of electrical circuits, IAEs are
most often two-terminals, and their mutual connections
have a linear (one-coordinate) or matrix (two-coordinate)
arrangement. In this approach, a spatial location of ele-
ments is determined by the topology of used IM and is
invariant relatively to electric connections.
It is obvious that a visual form of the scale informa-
tion representation assumes the presence of a weighting
factor intrinsic to each display element. As a rule, any
meaning of the weighting factor is linked with a spatial
location of IAE on the display information area and is
proportional to its number i in the scale. Reading infor-
mation out is realized in accord with the weighting fac-
tor meaning relatively to scale marks, while the scale
serving as a multi-channel measure [1].
Image of symbols is formed in the display from dis-
crete elements αi in accordance with a given IM. A con-
trol circuit creates necessary optical non-uniformity us-
ing excitation of optoelectronic elements αi per respec-
tive electric signals. To reach it, formed is the set ( )íG of
αi elements, composition of which is determined by the
number ν of the visual symbol νS .
In the case, the set ( )íG is a sub-set of the set A , one-
to-one correspondence between the synthesized symbol
νS and the set ( )íG being functionally provided. It is
the main condition to adequately represent the meaning
of a measured value and data authentically read by an
operator. This representation of data on a bar graph ar-
ray for the IM with a continuous visual pattern can be
written using the following unification operator
íS ⇔ ( ) U
2
1
i
ii
iaíG
=
= (4)
where i2,i1 are positional numbers of the initial and final
elements in the formed νS symbol.
The operator (4) describes the most general represen-
tation of the visual pattern, which corresponds to absence
of limitations imposed on formation of the ( )íG set. It is
equivalent to static realization of the IM.
4. Features of the positional IM
Our analysis of practical solutions for displays built
on bar graph arrays showed that realization of the dis-
crete-analogous data representation is determined by two
main factors, namely: a visual form of information map-
ping and arrangement of mutual electric connections be-
tween display elements.
The analytical form of IM representation describes
realization of νS symbols from αi elements of the set A
as well as determines i1 and i2 meanings in (4). Widely
spread is the positional IM, optical non-uniformity of
which is formed from the only excited element of the dis-
play information area [9, 10]. The weighting factor of
this indication index coincides with the meaning of an
imaged value. Therefore, for this sort of the positional
IM, numbers of initial and final excited elements of indi-
cator in the formed νS symbol visual pattern coincide in
(4), i.e. i1=i 2=ν. As a result, some dynamical realization is
possible, but it loses its technical expediency, as the set
( )íG converts into the unity set.
Our comparison of reliability performances for the
positional and bar graph IMs shows that the probability
of developing situation when the operator does not get
any information about the parameter controlled in the
first case is much higher. A failure or degradation of even
one IAE or one of the corresponding circuits in a display
driver when using the positional IM consisting from one
excited indication index results in full vanishing of dis-
play information. But in the same situation, using the
bar graph IM, the operator obtains information about
controlled parameter, although with some additive inac-
curacy in the data mapped.
However, usage of the positional IM based on two
adjacent excited IAE provides an opportunity to consid-
erably increase the reliability of data representation. This
approach enables to realize two IM versions. In the first
one, excited in the scale is the element with the weighting
factor that corresponds to the represented meaning as
well as the element with that exceeding by unity the first
meaning.
In the second case, data are represented by excited
elements, the first of which has the weighting factor cor-
responding to the indicated value, and the second one
that is less by unity than the main one. Realization of
these IM versions can be represented in the following
A.V. Bushma et al.: Static realization of reliable positional indication
121SQO, 5(1), 2002
forms stemming from (4):
ΣíS ⇔ ( ) U
1+
=
Σ =
ν
ν
ν
i
iaG (5)
∆íS ⇔ ( ) U
ν
ν
ν
1−=
∆ =
i
iaG (6)
where ΣíS , ∆íS are visual symbols from alphabets for
the two-element positional IM containing additive sen-
ior and junior indication indexes, respectively;
( ) ( )νν ∆Σ GG , are IAE sets αi that are excited when form-
ing, accordingly, the first and second IM versions.
Symbols of these IMs synthesized in accord with (5)
and (6) create alphabets:
{ }∆∆−∆∆∆∆ =Ω pp SSS,SS ,,,,, )1(21IM KK ν
{ }ΣΣ−ΣΣΣΣ =Ω pp SSS,SS ,,,,, )1(21IM KK ν
(7)
(8)
An analysis of (5) and (6) in combination with (3)
shows that formation of such IMs needs display informa-
tion areas consisting of αi -element sets having the fol-
lowing forms:
{ }121 ,,,,, +Σ = ppi aaa,aaA KK (9)
{ }ppi aaaaaA ,,,,,, 110 −∆ = KK (10)
where ∆Σ AA , are IAE sets on which, respectively, the
first and second versions of the considered IM are formed.
As seen from definitions (5) � (10) above, realization
of the two-element positional IM with the alphabet length
s=p needs indicator with an information field consisting
of (p+1) elements. Their weighting factors change be-
tween 1 to (p+1) for IM with an additive senior element
and from 0 to p for that with an additive junior element.
Juxtaposition of symbols from various IM versions
by taking into account weighting factors of forming them
IAE shows that they are identical except the most junior
term ∆1S in one version and the most senior term ΣpS
for another one, i.e., ∆+Σ ≡ )1(νν SS when )1(,1 −= pí .
At the same time, considering an information aspect of
data representation and taking into account (1) and (2),
one can write the equality )()( ∆Σ ≡ νν SISI . It is indica-
tive of informational equivalency of symbols with identi-
cal positional numbers in these two versions of IM.
5. Hardware realization of a highly reliable
positional IM
Let us consider some features of the device circuit tech-
nique that form suggested positional IM in a display with
linear connections between IAE.
The most widely spread and practically applicable is
the variant of bar graph array element connections with
a common bus. To synthesize a visual symbol νS using
this indicator, it is necessary to form a single-coordinate
matrix (vector) of electric signals possessing the follow-
ing appearance
qi eeee ,,,,, 21 KK=E , (11)
where ei is an excitation signal of the i-th IAE and
qi ,1= .
In dependency on the used element type, either direct
(alternating) voltage or current can serve as a signal.
Such signal is generated with appropriate driver. Its func-
tions comprises buffer transformation of logical signals
from a control circuit. The number of driver channels is
equal to the amount of display elements q. Absence of
logical and mutual processing of control signals in chan-
nels determines identity of realized functions that can be
described by the following operator
( )ii zfe = , (12)
where f is a function describing transformation of control
signals into the form corresponding to the IAE type; zi is
the i-th output signal of a digital control circuit.
Usually, in currently optoelectronic information-
measuring systems, displayed data are represented by
the parallel binary code [9]. As a rule, it provides minimi-
zation of circuit solutions for processing signals due to
excessless of such a form for digital data representation.
To obtain display control signals in accord with (11), it
is necessary to form a code with the number of digits equal
to IAE amount. It is used to control the driver that real-
izes the condition (12). Consequently, the digital circuit
for controlling the display consisting of q IAEs fulfills
logical processing signals of the following form
( )XøZ z= , (13)
where Z is the q-digit output code,
{ }qi z,,z,,z,zZ KK21= ; zø is the code transla-
tion operator; X is the k-digit input code,
{ }ki x,,x,,x,xX KK21= .
Let us assume the existence of a symbol reflecting
zero value of an input signal and ascribe it the conven-
tional positional number 1=í . Then circuit realization
of highly reliable positional IM, which correspond to
operators (5) and (6), taking into account the way to ob-
tain display excitation signals described by (11) and (12),
can be written as follows:
ΣíS ⇔ ( ) ( ) == +Σ 0,,0,,,0,,0 1 KK ννν zfzfE
( )Σ== ii zfe , (13)
∆íS ⇔ ( ) ( ) == −∆ 0,,0,,,0,,0 1 KK ννν zfzfE
( )∆== ii zfe , (14)
where ∆Σ νν EE , are vectors of electrical signals pro-
viding formation of two-element positional IM with an
additive senior and junior IAE, respectively; ∆Σ ii zz ,
correspond to the i-th code digit at the output of digital
control circuit when synthesizing the IM with an addi-
122 SQO, 5(1), 2002
A.V. Bushma et al.: Static realization of reliable positional indication
tive senior and junior IAE, respectively.
Following (13), to excite display in accord with (14)
and (15), digital control circuit should form the binary
code Z. It is obvious that for considered variants of
íS visual symbol formation, the transformation (13) with
taken into account (14) and (15) can be converted into
the following forms:
ΣíS ⇔ { }== +Σ 0,0,,00 1 ,z,z,,Z KK ννν
( )νXøzΣ= , (16)
∆íS ⇔ { }== −∆ 0,0,,00 1 ,z,z,,Z KK ννν
( )νXøz∆= . (17)
Let us develop some mathematical model of a digital
structure that forms a two-element positional IM in the
display consisting of ( )1+p IAEs with a common elec-
trode. Control signals for the display are formed from the
k-digit input code when implying ( )[ ] 11log2 +−Ε= pk ,
where E=Entire. Then, stemming from (13) and taking
into account (16) and (17), this structure can be described
by the following models:
1+Σ += iiiz µµ , (18)
iiiz µµ += −∆ 1 , (19)
where mi is the i-th minterm of output signals, and
010 == +pµµ , as the input k-digit code has p minterms.
The structural solution realized by the models (18)
and (19) is depicted in Fig. 1. The decoder 1 forms p
minterms pµµ K1 from k input variables kxx K1 . Ob-
tained signals are processed by OR elements 2. As
01 =+pµ for (18) and 00 =µ for (19), the amount of ele-
ments 2 is by unity less than the number of an input code
minterms, i.e. it is equal to ( )1−p . On their outputs, the
code ΣνZ ( ∆νZ ) is formed. This code controls the array
consisting from ( )1+p drivers 3. Their output signals are
connected with ( )1+p display elements ia 4 that have
one common output electrode.
They provide formation of íS symbol (in the kind of
ΣíS or ∆íS ), which is corresponded to the input code
νX . Our analysis of (7) � (10) as well as (18) � (19)
showed that considered synthesis of ΣíS symbol on the
set ΣA of IAE ia accordingly to (9), and ∆íS symbol
on ∆A in accord with (10), from the practical viewpoint,
differs by the measure that is considered here as a scale
relatively to the display information area. Therefore, both
models (18) and (19) are realized by the same digital
structure. The difference consist in connection elements
ia 4 to the control circuit. In Fig. 1, designations of ia
elements 4 from the set ΣA described by (9) are given
without parentheses, and those from (10) are given in
parentheses.
Fig. 1. The structural solution for reliable two-element positional indication, where
1 is decoder, 2 are OR elements, 3 are drivers and 4 are display elements.
3 42
ep
3 42
ep-1
3 42
ep-2
3 42
3 42
3 42
3 4
ep+1
zp
zp-1
zp-2
zp+1
3 4
e4
e3
e2
e1
z
4
z3
z2
z1
(ap-1)
(ap-2)
(ap-3)
(ap)µp
µp-1
µp -2
µ 1
µ 2
µ
3
xk
x1
x2
1
ap
ap-1
ap-2
ap+1
(a3)
(a2)
(a1)
(a0)
a4
a
3
a2
a
1
A.V. Bushma et al.: Static realization of reliable positional indication
123SQO, 5(1), 2002
6. Conclusions
Thus, analyzed is the highly reliable positional in-
formation model and represented are logical operators
that describe static formation of both its versions for dis-
plays with linear electrical connections between elements.
We studied peculiarities of an arrangement of their infor-
mation areas and alphabets of both information model
versions. Offered and realized are mathematical models
of respective circuit solutions for displays consisting from
elements connected with a common electrode.
It is ascertained that the main properties of the elabo-
rated information model and its hardware realization are
as follows:
1) simplicity of visual symbol formation and used for
that circuit solutions based on series IC regular struc-
tures;
2) realization of both IM versions by the same dig-
ital structure for any display consisting of elements with
a common electrode;
3) to synthesize IM with an alphabet comprising p
symbols one needs the display with an information area
consisting of )1( +p elements.
The results obtained enable one to create highly reli-
able and effective display devices for optoelectronic in-
formation-measuring systems and to analytically describe
the processes taking place in them. It gives designers of
mass-produced devices and complex systems new means
to analyze and separate the most effective structural and
functional solutions providing a fast and reliable trans-
fer of obtained data to an operator.
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