Matrix models of bar graph data display for bicyclic excitation of the optoelectronic scale
In this work, being based on the theory of sets and matrix formulation of the information area for a bar graph display the author obtained a matrix description for electric signals necessary to form two variants of bicyclic excitation of the optoelectronic scale elements under dynamic realization...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2008
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| Цитувати: | Matrix models of bar graph data display for bicyclic excitation of the optoelectronic scale / A.V. Bushma // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 2. — С. 188-195. — Бібліогр.: 12 назв. — англ. |
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irk-123456789-1188832017-06-02T03:04:30Z Matrix models of bar graph data display for bicyclic excitation of the optoelectronic scale Bushma, A.V. In this work, being based on the theory of sets and matrix formulation of the information area for a bar graph display the author obtained a matrix description for electric signals necessary to form two variants of bicyclic excitation of the optoelectronic scale elements under dynamic realization of a bar graph information model. 2008 Article Matrix models of bar graph data display for bicyclic excitation of the optoelectronic scale / A.V. Bushma // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 2. — С. 188-195. — Бібліогр.: 12 назв. — англ. 1560-8034 PACS 85.60.Bt, 42.79.Kr http://dspace.nbuv.gov.ua/handle/123456789/118883 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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English |
| description |
In this work, being based on the theory of sets and matrix formulation of the
information area for a bar graph display the author obtained a matrix description for
electric signals necessary to form two variants of bicyclic excitation of the optoelectronic
scale elements under dynamic realization of a bar graph information model. |
| format |
Article |
| author |
Bushma, A.V. |
| spellingShingle |
Bushma, A.V. Matrix models of bar graph data display for bicyclic excitation of the optoelectronic scale Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Bushma, A.V. |
| author_sort |
Bushma, A.V. |
| title |
Matrix models of bar graph data display for bicyclic excitation of the optoelectronic scale |
| title_short |
Matrix models of bar graph data display for bicyclic excitation of the optoelectronic scale |
| title_full |
Matrix models of bar graph data display for bicyclic excitation of the optoelectronic scale |
| title_fullStr |
Matrix models of bar graph data display for bicyclic excitation of the optoelectronic scale |
| title_full_unstemmed |
Matrix models of bar graph data display for bicyclic excitation of the optoelectronic scale |
| title_sort |
matrix models of bar graph data display for bicyclic excitation of the optoelectronic scale |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2008 |
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http://dspace.nbuv.gov.ua/handle/123456789/118883 |
| citation_txt |
Matrix models of bar graph data display for bicyclic excitation of the optoelectronic scale / A.V. Bushma // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 2. — С. 188-195. — Бібліогр.: 12 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT bushmaav matrixmodelsofbargraphdatadisplayforbicyclicexcitationoftheoptoelectronicscale |
| first_indexed |
2025-07-08T14:50:00Z |
| last_indexed |
2025-07-08T14:50:00Z |
| _version_ |
1837090683035320320 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 2. P. 188-195.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
188
PACS 85.60.Bt, 42.79.Kr
Matrix models of bar graph data display
for bicyclic excitation of the optoelectronic scale
A.V. Bushma
State University of Information and Communication Technologies
7, Solomjanska str., 03110 Kyiv, Ukraine
Abstract. In this work, being based on the theory of sets and matrix formulation of the
information area for a bar graph display the author obtained a matrix description for
electric signals necessary to form two variants of bicyclic excitation of the optoelectronic
scale elements under dynamic realization of a bar graph information model.
Keywords: bar graph display, information model, matrix description.
Manuscript received 28.02.08; accepted for publication 15.05.08; published online 30.07.08.
An essential part of modern radioelectronic facilities is
oriented to man-controlled interaction. Combination of
optical and digital methods for processing signals in
these facilities provides a high efficiency of message
passing to an operator in such ergatic system [1, 2].
Among various types of means for information display,
it is necessary to separate the group of facilities for
discrete-analog (scale) data presentation, which possess
the best complex of ergonomic characteristics [2-4].
Placed at the heart of their functioning is an information
model (IM) that defines the system of rules for coding
the messages [5, 6]. Most often, used in serial
radioelectronic equipment are two forms of IM for
discrete-analog data imaging: positional and additive
ones that are synthesized, respectively, from one or set
of excited elements inherent to the display information
area (IA) [2]. Apparatus realization of IA is some
electron-optical image converter (EOIC) providing
formation of an optical pattern when exciting respective
elements. Most widely used for displaying information
in modern radioelectronic equipment are EOICs based
on light-emitting diodes, liquid crystals and vacuum
cathodoluminescent displays [2, 5, 7].
Reliability of data presentation with a high level of
discreteness (more than 20 – 25 meanings), when rigorous
limitations of power consumption for imaging are absent,
can be functionally reached using a bar graph IM due to
its information redundancy [8]. The apparatus component
of reliability is provided, first of all, by matrix electric
connection of EOIC elements, which allows to essentially
shorten the number of scale control lines and respective
signals to excite it [7]. However, it is not poissible to
simultaneously excite all the elements necessary to form
the bar graph IM. Therefore, used is the dynamic regime
to form images in IA, which is usually realized by multi-
cyclic scanning the matrix along one of its coordinate [5,
9]. As an alternative, developed were bicyclic methods for
synthesizing a visual image for discrete-analog
presentation of information on the display [10, 11].
Minimization of the number of cycles to excite IA
elements considerably increases reliability of data output
and lower the level of high-frequency electromagnetic
noises caused by EOIC control unit. Thereof, modelling
the bicyclic additive discrete-analog data imaging to
design highly efficient facilities for information output has
a great practical interest.
In this work, being based on the theory of sets and
matrix formulation for display IA obtained are analytical
models allowing to describe electrical signals necessary
to realize two variants for bicyclic excitation of
optoelectronic scale elements with dynamic synthesis of
imaging the bar graph IM.
The discrete-analog form to code messages
assumes that every ai element of p IA ones has the
weight function )( ii aϖ=ϖ , the value of which is
associated with its space position in IA and is in
proportion to its number i in a fully ordered set of A
elements. This can be described as
{ }ppi aaaa,a ,,,,, 121 −= KKA . Besides, this set
is characterized by the condition )()( 1+ϖ<ϖ jj aa at all
)1(,1 −= pj . In the heart of this way to code
information, there are values of the weight function for
IA elements, which are determined relatively to the
spatial multi-channel measure [1].
Presentation of messages in IA is realized starting
from IM and using the finite set l of Sν BG symbols where
l,1=ν that form the alphabet of the bar graph model
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 2. P. 188-195.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
189
{ }.,,,,,, BGBG 1)(BGBG2BG1BG ll SSSSS −ν= KKΩ
Synthesis of images for alphabet symbols BGΩ takes place in IA. To provide that when exciting EOIC, the
subsets BG
~
νA are formed from the elements of the set IA A , that is for all l,1=ν the condition AA ⊆νBG
~ is
fulfilled. As every message should be decoded uniquely, every symbol from BGBG Ω⊂νS should be one-to-one
corresponded with ai elements of the subset BG
~
νA beloning to the set A : BGBG
~
νν ⇔ AS .
The bar graph form of IM assumes formation of SνBG symbols from a set of ai elements with serial values of the
weight function, originating from its minimum value )( 11 aϖ=ϖ up to the value )( νν ϖ=ϖ a that corresponds to
the output information relatively to the spatial measure. These symbols can be described on the set A as follows
U
ν
=
νν =⇔
1
BGBG
~
i
iaS A { }ν−ν= a,aaaa i 121 ,,,,, KK . (1)
To increase reliability of the data output facility, one can use an electric organisation of EOIC, when
its elements are connected as a two-dimensional matrix from n groups every of m elements where m·n = p.
Each group contains elements the weight function of which in serial pairs differs by unity. In this case, their common
bus is the output termination of one of n high-order bits. Values of the weight function both for each group and for
their elements are determined by their position in IA relatively to the spatial multi-channel measure. Joint outputs of
all the elements with the same relative value of the weight function inside each group serve as the bus for one of m
low-order bits. As a result, EOIC elements form IA consisting of the set MA with elements axy that has the number y
in the group of the number x, while n,x 1= and m,y 1= , that is { }mnmnxy aaaaa ,)1(1211M ,,,,, −= KKA , or in
the matrix form
mnmnynnyynnn
mnmnynynynnn
mxmxyxyxyxxx
mxmxyxyxyxxx
mxmxyxyxyxxx
mmyyy
mmyyy
aaaaaaa
aaaaaaa
aaaaaaa
aaaaaaa
aaaaaaa
aaaaaaa
aaaaaaa
)1()1()1(21
)1()1()1()1()1()1()1()1(2)1(1)1(
)1()1()1()1()1()1()1()1(2)1(1)1(
)1()1()1(21
)1()1()1()1()1()1()1()1(2)1(1)1(
2)1(2)1(22)1(22221
1)1(1)1(11)1(11211
M
−+−
−−−+−−−−−−
+−++++−+++
−+−
−−−+−ν−−−−−
−+−
−+−
=
KK
KK
MMMMMMMMM
KK
KK
KK
MMMMMMMMM
KK
KK
A
(2)
When the number of element is the same, the sets A and MA are equipotent, and there is a one-to-one
correspondence between their elements xyi aa ⇔ . Then, for the elements with the equal value of the weight function
)()( xyi aa ϖ=ϖ=ϖν one can write that the positional number of the element ν in the set A is determined by the
expression ν = m(x – 1) + y, and ν-th element in the set MA stands in the matrix as yν = ν – m· E(ν/m) within the
group with the number xν = E(ν/m) + 1, where E is Entier. It is obvious that the subsets BG
~
νA and M
BG
~
νA
( AA ⊆νBG
~ , AA ⊆ν
M
BG
~ ) will be equipotent, too, and the symbols Sν BG are synthesized from their elements. Then,
for the matrix electric connection of EOIC elements the expression (1) can be rewritten in the following form
( )
( ) ⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
=⇔⇔
Ε⋅−=
+Ε=
ν
=
ννν
mimiy
mix
i
xyaS 1
1
M
BGBGBG
~~
UAA }
νννν −= yxyxxy aaaaa ,,,,,, )(1211 1KK . (3)
Presentation of M
BG
~
νA as a subset of the set MA described with the matrix (where the elements belonging to
M
BG
~
νA are marked with tilde) with account of IA matrix description (2) will have the following form
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 2. P. 188-195.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
190
mnmnynynynnn
mnmnynynynnn
mxmxyxyxyxxx
mxmxyxyxyxxx
mxmxyxyxyxxx
mmyyy
mmyyy
aaaaaaa
aaaaaaa
aaaaaaa
aaaaaaa
aaaaaaa
aaaaaaa
aaaaaaa
)1()1()1(21
)1()1()1()1()1()1()1()1(2)1(1)1(
)1()1()1()1()1()1()1()1(2)1(1)1(
)()()(
)1()1()1()1()1()1()1()1(2)1(1)1(
2)1(2)1(22)1(22221
1)1(1)1(11)1(11211
11121
~~~~
~~~~~~~
~~~~~~~
~~~~~~~
M
−+−
−−−+−−−−−−
+−++++−+++
−+−
−−−+−−−−−−
−+−
−+−
ννν
ννν
νννννννννν
νννννννννν
νννννννννν
ννν
ννν
=
=
KK
KK
MMMMMMMMM
KK
KK
KK
MMMMMMMMM
KK
KK
A
(4)
Two-dimensional matrix electric construction of EOIC superpose some limitations on simultaneous excitation
of the set M
BG
~
νA elements that serve to form the image of the symbol Sν BG. In this case, it is possible to
synchronically turn on only all the elements (without exceptions) with arbitrary chosen identical numbers in any set
of groups. Therefore, to realize the bicyclic synthesis of an image, the elements of the set M
BG
~
νA described by the
matrix (4) with taking this limitation into account are separated in two non-intersecting subsets that are excited in
different cycles of Sν BG symbol formation
⎭⎬
⎫
⎩⎨
⎧== νννν
D2
BG
D1
BG
D
BG
M
BG
~~~~ AAAA , , (5)
where D
BG
~
νA is the set identical to M
BG
~
νA and is its dynamic equivalent, D2
BG
D1
BG
~~
νν AA , – are the subsets of the set
D
BG
~
νA with elements axy, and ∅=νν
D2
BG
D1
BG
~~ AA I .
An obligatory condition to form a persistent sight image of any visual symbol is a relative height of the
frequency corresponding to image regeneration SS Tf 1= over the critical frequency of flicker fusion [2, 5]. In this
case, each group of axy elements that belongs to the respective subset is excited only one time during every period for
symbol regeneration within the time interval rTSg =τ , where r is the number of cycles to synthesize a visual image
on the display.
In the case of a two-dimension IA matrix, it is possible to realize two variants of formation of non-intersecting
subsets for display elements: using the partition by high-order [10] and low-order [11] bits of the scale. Dynamic
joining the elements into groups in accordance with the first version assumes realization of the logic IM in the form
[10]
[ ]
,
~~~
1
02
0
11
0
0
1
D21
BG
D11
BG
D
BGBG
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
=
==⇔
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ ν
Ε=
−τ+=
+τ+=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ ν
Ε−ν
=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ ν
Ε
=
−τ+=
+=
=
νννν
U UUU U
U
m
x
tt
tt
m
m
y
xy
m
x
tt
tt
m
y
xy
T
gs
gs
gs
S
aa
S
S
AAA
(6)
where D21
BG
D11
BG
~~
νν AA , are the non-intersecting subsets of axy elements; t – current time of image dynamic synthesis; tS
– onset of the period of Sν BG symbol formation in IA.
It is seen that, in accord with this type of logic IM (6), synthesis of the SνBG symbol in IA is realized in the
dynamic bicyclic regime, and two groups of IA elements are separated in this case. During the first time interval
gss ttt τ+<< , excited are all m elements of all high-order bits from the first up to E(ν/m)-th one. The second
interval gsgs ttt τ+<<τ+ 2 corresponds to formation of a visual signal by using [ν – mE(ν/m)] elements of one
[E(ν/m) + 1]-th IA order. Obtaining the extended visual image in IA that corresponds to the symbol Sν BG is provided by
inertial properties of a human sight analyzer when excitation of scale elements in two groups is repeated by cycles
with the frequency exceeding that of flicker fusion.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 2. P. 188-195.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
191
Now, let us proceed from set logic presentation of IM (6) to the matrix one by using the respective form (4) to
describe the excited IA when forming the symbol Sν BG. As a result, we obtain the matrix of n×m dimensions:
;
0000000
0000000
000~~~~
~~~~~~~
~~~~~~~
~~~~~~~
~~
)1(21
)1()1()1()1()1()1()1()1(2)1(1)1(
2)1(2)1(2)1(22221
1)1(1)1(11)1(11211
MD
BG
M
BG
2
KK
MMMMMMMMM
KK
KK
KK
MMMMMMMMM
KK
KK
νννννν
νννννννννν
ννν
ννν
−
−−−+−−−−−−
−+−
−+−
νν
=
==
yxyxxx
mxmxyxyxyxxx
mmyyy
mmyyy
aaaa
aaaaaaa
aaaaaaa
aaaaaaa
AA
(7)
If using the considered logic IM, the searched description of subsets M11D
BG
~
νA and M21D
BG
~
νA can be deduced from
the matrix (7) with taking account of the operator (6) in the form of matrixes with the dimension n×m
,
0000000
0000000
~~~~~~~
~~~~~~~
~~~~~~~
~
)1()1()1()1()1()1()1()1(2)1(1)1(
2)1(2)1(22)1(22221
1)1(1)1(11)1(11211
M11D
BG
KK
MMMMMMMMM
KK
KK
MMMMMMMMM
KK
KK
mxmxyxyxyxxx
mmyyy
mmyyy
aaaaaaa
aaaaaaa
aaaaaaa
−−−+−−−−−−
−+−
−+−
ν
νννννννννν
ννν
ννν
=
=A
(8)
.
000000
000000
00~~~~
000000
000000
~
)1(21
M21D
BG
KK
MMMMMMMM
KK
KK
KK
MMMMMMMM
KK
ννννν −νν = yxyxxx aaaaA (9)
With account of the matrixes (7)-(9), for non-intersecting subsets in the framework of this bicyclic logic IM, the
following equality is valid:
M21D
BG
M11D
BG
MD
BG
M
BG
~~~~
νννν +== AAAA . (10)
To realize IM, when using dynamic formation of subsets for IA elements by separation of groups by low-order
bits of the display matrix, analytic presentation of image synthesis can be written in the form [11]
[ ] ==⇔ νννν
ST
S U D22
BG
D12
BG
D
BGBG
~~~ AAA
.
1
02
0
11
0
0
1
1
⎪
⎪
⎪
⎭
⎪⎪
⎪
⎬
⎫
⎪
⎪
⎪
⎩
⎪⎪
⎪
⎨
⎧
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
⎪
⎪
⎪
⎭
⎪⎪
⎪
⎬
⎫
⎪
⎪
⎪
⎩
⎪⎪
⎪
⎨
⎧
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
=
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ ν
Ε−ν=
−τ+=
+τ+=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ ν
Ε
=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ ν
Ε−ν
=
−τ+=
+=
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ ν
Ε
=
U UUU U
m
m
my
tt
tt
m
x
xy
m
m
y
tt
tt
m
x
xy
gs
gs
gs
s
aa (11)
This operator describes formation of the symbol Sν BG in the dynamic bicyclic regime and defines two sets of IA
elements. During the first time interval gss ttt τ+<< excited are [ν – mE(ν/m)] low-order elements of all
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 2. P. 188-195.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
192
[E(ν/m) + 1] matrix low-order bits. The second interval gsgs ttt τ+<<τ+ 2 corresponds to formation of a visual
signal by using {m [E(ν/m) + 1] – ν} high-order elements of E(ν/m) IA low-order bits. Due to the lag effect of human
sight analyzer, the repeated cyclic excitation of elements in these two groups allows to form an extended visual image
corresponding to the symbol Sν BG.
Changeover from IM set logic presentation (11) to the matrix one is realized in the identical manner said above
for the model (6) by using the respective form (4) describing the excited IA when forming the symbol Sν BG. It is
obvious that the matrix (7) is valid for this type of IM, too. Consequently, the subsets M12D
BG
~
νA and M22D
BG
~
νA can be
deduced from the matrix (7) with account for the operator (11) in the form of matrixes with the dimension n×m
,
000000
000000
00~~~~
00~~~~
00~~~~
00~~~~
~
)1(1
)1()1()1(2)1(1)1(
2)1(22221
1)1(11211
M12D
BG
2
KK
MMMMMMMM
KK
KK
KK
MMMMMMMM
KK
KK
νννννν
νννννν
νν
νν
−
−−−−−
−
−
ν =
yxyxxx
yxyxxx
yy
yy
aaaa
aaaa
aaaa
aaaa
A (12)
.
0000
0000
~~~00
~~~00
~~~00
~
)1()1()1()1()1(
2)1(2)1(2
1)1(1)1(1
M22D
BG
KK
MMMMMMM
KK
KK
MMMMMMM
KK
KK
mxmxyx
mmy
mmy
aaa
aaa
aaa
−−−+−
−+
−+
ν νννν
ν
ν
=A (13)
Analysis of the matrixes (7), (12) and (13) shows that for non-intersecting subsets in the case of bicyclic logic
IM with separation of IA elements into groups by low-order bits one can write
M22D
BG
M12D
BG
MD
BG
M
BG
~~~~
νννν +== AAAA . (14)
From the expressions (10) and (14) as well as analysis of all four subsets of elements M11D
BG
~
νA , M21D
BG
~
νA ,
M12D
BG
~
νA , M22D
BG
~
νA used to form the Sν BG symbol image, one can write the respective sums of matrixes for every
synthesis way
.~~~~~~ M22D
BG
M12D
BG
M21D
BG
M11D
BG
MD
BG
M
BG νννννν +=+== AAAAAA (15)
It is seen that the bicyclic synthesis of symbols Sν BG is invariant relatively to the choice of the principle for
partition of the set MD
BG
M
BG
~~
νν = AA by two subsets when exciting the visual images of the bar graph IM on the IA
element matrix. In each of these image synthesis modifications, IA elements with the same numbers in the respective
group set are switched on simultaneously, which does not contradict to the imposed limitations for synchronical
controlling the electric matrix of elements.
Formation of IA element subsets belonging to the expression (15) is realized with electric signals generated by
the display driver in the dynamic regime. To synthesize an image in IA for every time moment, the respective group
q
νA~ of scale matrix elements is excited, which, as shown in [12], is described by the vector product
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 2. P. 188-195.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
193
qqq HL~
ννν ×= EEA
rr
, (16)
where qq HL , νν EE
rr
are m- and n-dimensional vectors of electric signals that control low- and high-order bits of the
matrix, respectively. The elements of vectors are defined as eli and ehj, where mi ,1= , nj ,1= , and their values are
equal to eL and eH for buses of display low- and high-order bits excited at this moment. Here, qL
νE
r
presents a row
matrix, while qH
νE
r
does the column one. The group q
νA~ consists of elements placed at the intersection of buses with
applied electric stimuli eli and ehj corresponding to respected voltage levels or currents with necessary directions, in
the dependence on the used IA type.
As a result, realization of a bar graph IM with bicyclic image formation by separation groups in high-order bits
of display matrix, if starting from (10) and taking into account the matrix (8) and (9) as well as the expression (16),
can be provided by electrical signals of the following form
[ ] =+== νννν
sT
M21D
BG
M11D
BG
MD
BG
M
BG
~~~~ AAAA
[ ] [ ] =
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
×
⎭
⎬
⎫
⎩
⎨
⎧
×=
−τ+=
+τ+=
νν
−τ+=
+=
νν
02
0
21H
BG
21L
BG
0
0
11H
BG
11L
BG
gs
gs
gs
s
tt
tt
tt
tt
EEEE
rrrr
U
×
⎪⎩
⎪
⎨
⎧
⎢
⎢
⎣
⎡
= −+− mlmlilililll eeeeeee )1()1()1(21 KK
×
⎪⎩
⎪
⎨
⎧
⎢
⎢
⎣
⎡
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎭
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎬
⎫
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
×
ννν
ν
−
−τ+=
+=
−
−
000
0
0
0
)1(21
0
0
)1(
)2(
2
1
KKU
M
M
ylylll
tt
tt
xh
xh
h
h
eeeee
e
e
e
gs
s
(17)
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎭
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎬
⎫
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
×
−τ+=
+τ+=
ν
02
0
0
0
0
0
0
0
gs
gs
tt
tt
xhe
M
M
.
By analogy, we can obtain an analytic description for synthesis of a bar graph IM with bicyclic image formation
by using separation of groups by low-order bits of the display matrix. In this case, we shall start from (14) with
account of the matrixes (12) and (13) as well as the expression (16), which allows to represent the necessary electric
signals in the form
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 2. P. 188-195.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
194
[ ] =+== νννν
sT
M22D
BG
M12D
BG
MD
BG
M
BG
~~~~ AAAA
[ ] [ ] =
⎭
⎬
⎫
⎩
⎨
⎧
×
⎭
⎬
⎫
⎩
⎨
⎧
×=
−τ+=
+τ+=νν
−τ+=
+=νν
02
0
22H
BG
22L
BG
0
0
12H
BG
12L
BG
gs
gs
gs
s
tt
tt
tt
tt
EEEE
rrrr
U
U
M
M
KK
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎭
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎬
⎫
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
×
⎪⎩
⎪
⎨
⎧
⎢
⎢
⎣
⎡
=
−τ+=
+=
−
−
ν
ν
νν
0
0
)1(
2
1
)1(21
0
0
0
000
gs
s
tt
tt
xh
xh
h
h
ylylll e
e
e
e
eeee (18)
⎪⎩
⎪
⎨
⎧
⎢
⎢
⎣
⎡
−++ νν mlmlylyl eeee )1()2()1(000 KKU
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎭
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎬
⎫
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
×
−τ+=
+τ+=
−
−
ν
ν
02
0
)1(
)2(
0
0
0
2
1
gs
gs
tt
tt
xh
xh
h
h
e
e
e
e
M
M
.
These analytic expressions obtained in the matrix
form describe the process of dynamic bicyclic image
synthesis for bar graph IM on the scale of matrix
electric connection of elements. Analyzed and
represented are both possible variants for IM of this
type: with partition of IA elements onto groups by
low- and high-order bits of the display matrix.
Considered are information conversion stages
the most interesting from a practical viewpoint and
those requiring to be modelled, starting from
formation of electric signals controlling the display
and finishing with formation of visual images in IA.
The analytic expressions obtained possess good layout
and are convenient for computer modelling the
radioelectronic facilities.
The results presented above create an analytical
base extremely necessary in designing, investigation
and complex optimization of functional, structural and
circuitry solutions for information display facilities
aimed at radioelectronic equipment of various
purposes. This equipment can be used both in mobile
objects and information-measuring as well as
controlling systems exploited mainly in complex
conditions. It serves also as a base for efficient
solution of the task to increase the level of technical-
and-economical performances of serial and
specialized products as well as to simplify their
integration into perspective automated control means
for complex objects and processes.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 2. P. 188-195.
© 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
195
References
1. P.P. Ornatsky, Theoretical Principles of
Information-measuring Techniques. Vyshcha
shkola, Kyiv, 1983 (in Russian).
2. S. Gage, M. Modapp, D. Evans, H. Sorenson,
Optoelectronics Applications Manual. McGraw-
Hill Book Company, New York, NY, 1977.
3. A.V. Bushma, G.A. Sukach, Light-Emitting
Diode Position Scale – a Highly Efficient Tool
for Representation of Information in Metrology
// Measurement Techniques, 45 (5), p. 494-499
(2002).
4. A.V. Bushma, G.A. Sukatch, Analysis and
optimization of integrated optoelectronic
discrete-analog devices for information output //
Radio electronics and communications systems,
45 (7), p. 21-25 (2002).
5. F.M. Yablonsky, Yu.V. Troitsky, Information
Imaging Tools. Vysshaya shkola, Moscow, 1985
(in Russian)
6. L.F. Kulikovsky, V.V. Motov, Theoretical
Basics of Information Processes. Vysshaya
shkola, Moscow, 1987 (in Russian).
7. Liquid Crystal Displays of the Firm Data
International / Ed. by V.M. Khalikeev. Dodeka,
Moscow, 1999 (in Russian).
8. A.V. Bushma, Information redundancy of data
visualization forms as a means to improve
reliability of electronic equipment // Radio
electronics and communications systems, 46 (2),
p. 5-10 (2003).
9. A.V. Bushma, G.A. Sukach, Formation of
Additive Scale Representation of Information
Using a Multielement Light Emitting Diode
Display of a Measuring Instrument // Mea-
surement Techniques, 46 (1), p. 23-27 (2003).
10. A.V. Bushma, G.A. Sukach, Yu.M. Gavrilyuk,
Estimation of the reliability of optoelectronic
systems with multi-element LED bar graph
displays // Novi tekhnologii, 3 (6), p. 20-28
(2004) (in Russian).
11. A.V. Bushma, G.A. Sukatch, Optimization of
dynamic discrete-analog representation of data //
Radio electronics and communications systems.
46 (7), p. 49-53.
12. A.V. Bushma, Modelling the process of LED
matrix excitation // Izvestiya vuzov. Priboro-
stroeniye, 46 (10), p. 40-44 (2003) (in Russian).
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