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Hbw Report No, 270
frv. Z70
jTULtft
JUL 2 4 1968
OPTOELECTRONICS SWITCHING MATRIX
by
TUH KAI K00
May 28, 1968
Report No. 27O
OPTOELECTRONICS SWITCHING MATRIX
by
TUH KAI K00
May 28, 1968
Department of Computer Science
University of Illinois
Urbana, Illinois 6l801
Ill
ACKNOWLEDGMENT
The author wishes to express his gratitude to his advisor,
Dr. W. J. Poppelbaum, for his invaluable advice, illuminating suggestions
and encouragement throughout the period of research for this dissertation,
Thanks are also due to Dr. L. Van Biljon and Mr. D. P. Casasent
for their comments and improving the manuscript. The author also
appreciates to his wife, Ping, for her help on programming.
Thanks are also extended to Mrs. Carpenter who typed the
manuscript in its final form.
IV
TABLE OF CONTENTS
Page
ACKNOWLEDGMENT ...................... iii
1. INTRODUCTION. .................... 1
2 . GENERAL DESCRIPTION OF SYSTEM AND OPERATION ..... 3
2.1. Organization of The Opto-Electronic
Switching Matrix System. ........... 3
2.2, Structure of The Photoconductive Cell
Matrix Panel ................. 5
2.3« Principle of Operation ............ 5
3. TRANSIENT CHARACTERISTICS OF PHOTOCONDUCTOR ..... 13
3.1. Photoconductivity Phenomenon ......... 13
3.2. Solution to Single SRH Center Level. ..... 20
3«3' Transient Problem With Multi-level
SRH Centers. ................. 26
k. ANALYSIS OF PHOTOCONDUCTIVE CELL MATRIX ....... 3^
4.1. Equivalent Circuit of Pulsed
Photoconductor ................ 3^
4.2 o Transmission Efficiency, Injection Noise
and Cross -talk 4 9
4.3. Important Factors in Matrix Design ...... 57
5. OPTICAL SOURCE AND SCANNING . 62
5.1. Light Sources. .... ....... 62
5.2. Light Deflection Methods ..... 70
5.3. Resolution of Light Deflectors ........ 80
5.4. Comparison of Light Deflecting Methods .... 83
5.5. Optical. Scanner. ............... 86
6. CONTROL SIGNAL PROCESSOR. .............. 95
6.1. Scanning Pattern and Driving Signals ..... 95
6.2. Driving Signal Generation. .... 97
6.3. Control Signal Memory and Regeneration .... 99
7- EXPERIMENTAL RESULTS. ..... ...... 104
8. SUMMARY ....................... Ill
LIST OF REFERENCES .................... 112
VITA .................... 113
OPTO -ELECTRONIC SWITCHING MATRIX
Tuh Kai Koo, Ph.D.
Department of Electrical Engineering
University of Illinois, 1968
A cross -"bar type switching matrix system with photo-
conductive cells as basic switching elements and. an optical signal
as the switching driving source has been studied and developed .
The matrix itself has the form of a two-dimensional panel with a
basic switching unit at each cross point in the matrix. The basic,
switching unit contains three photo-conductive cells in T-connection,
in which the center branch is grounded and the two arm branches
are connected to input and output channels, respectively . Switching
action is accomplished by scanning the matrix panel with a programmed
helium-neon laser beam. The state of a switching unit depends upon
whether the center branch or the arm branches are being excited by
the light beam.
The basic characteristics of the photo-conductive cells
required for this application are a large ratio of off (dark) -resistance
to on-resistance and large ratio of decay time to rise time. A better
transmission efficiency and cross-talk factor will be obtained with
a larger ratio of off to on resistance and the injection noise level
as well as the transmission efficiency will improve with a large
ratio of decay time to rise time. The equivalent circuit of a photo-
conductive cell under the specific application has been developed .
The complete equivalent circuit contains harmonic terms which are the
consequence of optical beam scanning. These harmonic terms interact
mutually with each other. First degree approximation has to be used
to reduce the equivalent circuit to a practically usable form- All
the theoretical evaluation of the system performance is based upon
the approximated equivalent circuit .
A small scale system which consists of a k by k matrix, an
eiectro-mechanical light deflector with 20 kHz frequency response
and a k mv helium-neon continuous laser has been constructed and
tested. The performance of this system matches the theoretical
expectation closely. Feasibility study shows that larger scale operation^
say 100 x 100, is possible when the photo -conductive cell matrix is
constructed with the technique of integration yielding a matrix panel
of several inches square and when an optical scanning system of
higher resolution is used.
1 . INTRODUCTION
An opto-electronic system which transfers information
between given input and output channels is discussed in this thesis .
The system basically contains a switching matrix panel, optical
scanner, light source and control unit. The switching matrix panel
is a cross-bar type matrix with photoconductive cells as the switching
elements . Switching is initiated by a scanning light beam from the
optical scanner which is controlled by the control unit,, The basic
principle of operation is the asymmetrical relaxation process of
longer decay time than rise time, which is observed in some photoconductive
materials . This system was proposed by W, J. Poppelbaum some years ago.
The transient characteristics of photoconductors are analyzed
using the simplified physical model of SRH centers and it is shown that
under certain conditions the deep traps and heavy trapping activity
give rise to the longer decay time than rise time. The equivalent
circuit of a single photoconductor with periodic excitation is then
developed using the assumption that the relaxation processes of the
photoconductors are an exponential function of time but with different
time constants for rise and decay transients. This equivalent circuit
can be represented by a constant conductance and either induced voltage
sources or induced current sources. These induced sources have frequency
spectrums similar to the Fourier spectrum of the fluctuating photo-
conductance and amplitudes which are functions of the relaxation time
constants of the photoconductor and the condition of excitation.
A network analysis of the switching matrix of photoconductors
is then presented. The characteristics of the system are described by
defining transmission, efficiency, cross-talk factor and noise injecting
2
factor. Satisfactory performance is possible only with a high load
impedance at the output channels and when the ratio of the decay time
constant to the rise time constant of the phot oconduc tor is larger I
the ratio of off -time to on-time of the stimulating light pulses,
A prototype system with four input channels and four output
channels has "been constructed. The optical scanner consists of two
electro-mechanical deflecting mirrors with frequency response to
20 kHz. A novel alternate interlaced scanning method is used to
eliminate the requirement of blanking the light beam during fly-fcack
as in conventional raster scanning systems A dynamic memory unit,
called Phastorj, can be used to store the information of input-output
channel connection „ In the Phastor, the information is preserved
in the form of time delay with respect tc standard timing, A direct
excess to control the light beam can be obtained = It, therefore $
offers a more efficient means than other memory units
2 o GENERAL DESCRIPTION OF SYSTEM AND OPERATION
2 o 1 . Organization of The Opto-Elsctronic Switching Matrix Sys'
The opto-electronic switching matrix system can be used to
direct information from various input channels onto properly selected
output channels. It can be divided into four major parts? (ij optical
source, (2) optical beam scanner , (3) control signal processor a
(h) switching matrix panel, as shown in the block diagram in Fig, 1.
The optical source is required to provide an intense narrow light beam
with small beam divergence . A continuous gas laser serves this purpose
adequately., The function of the optical scanner is to modulate the
propagating direction of the light beam from the light source according
to the information received from the signal processor such that the
trace of the beam spot on a plane perpendicular to the non-modula1
beam follows a pre -determined two-dimensional scanning pattern . The
control signal processor is a unit which processes the informati
concerning the switching between input and : bput channels on
switching matrix panel, and it generates the proper signals to dri
the optical scanner. The switching matrix panel is the most essent
section of the system. It is an array of properly interconnected
photoconductive cells, and it carries bcth input channels and output
channels. Upon receiving the control signal carried by the light- team
from the optical scanner, it responds by allowing information to be
transmitted from the proper input channel to the selected output channel..
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2.2. Structure of The Photoconductive Cell Matrix Panel
The photoconductive cell matrix is in the form of a
two-dimensional panel with an array of photoconductive cells „
Electrically, it is simply a cross -"bar type formation of input and
output channels, as shown in Fig. 2. At each cross-point, there is
a "basic photo -switching unit connected to the input and output
channels as illustrated. The basic switching unit consists of three
photoconductors in T-connection with one branch grounded , The branch
connected to the input channel may be termed the "input branch' 1 ,
the one connected to the output channel the "output branch" and the
grounded one the "center branch" , Physically, all photoconductive
cells are located on the front surface of the matrix panel, and the
relative location of the cells is such that the center branches are
situated in rows which are separated from the rows of input and output
branches, as illustrated by Fig. 3° The packing density of photocells
is limited by the resolution of the optical scanner and the photo-
conductive material. The relative location of the matrix panel, and
the optical scanner is such that the panel is perpendicular to the
undeflected light beam path. The distance between the panel and. the
scanner depends upon, the dimensions of the matrix panel and amount of
energy density fluctuations received by the photoconductive ceil
surfaces between the edge un.it and center unit.
2.3. Principle of Operation.
It is well known that the basic characteristic of photo -
conductors is the change of its resistance when excited by light energy,
In general practice, a phot oconduc tor can have a very high yet finite
INPUT CHANNELS
-A
OUTPUT BRANCH
INPUT BRANCH
CENTER
BRANCH
BASIC
SWITCHING
UNIT
Figure 2. Electrical Connection of Photoconductive Cell Matrix
INPUT BRANCH
OUTPUT BRANCH
MATRIX PANEL
INPUT 8 OUTPUT
BRANCH ROWS
GROUNDING BRANCH ROWS
7
resistance state when it is in dark, and can reach a low yet non-zero
resistance state when it is excited by intense light. In comparison
with a perfect switch, which is characterized by allowing total
information transmission when closed and no information passage when
open, a photoconductor acts as an imperfect switch where information
may flow through it with attenuation caused by its non-zero resistance
in the on state and a small part, though negligible, of information may
leak through due to its finite high resistance in the off state.
To maintain a photoconductor at the low resistance state, one
can excite it either with continuous light or a train of light pulses.
In the latter case, the resistance of the photoconductor fluctuates
along an average value as illustrated in Fig. h. The level of the average
resistance and the amplitude of fluctuation are determined by the transient
characteristics of the photoconductor and the amplitude, pulse width and
period of the light pulses. With a proper combination of these factors,
a low average resistance with small fluctuations in amplitude can be
obtained. The interaction between these factors will be detailed in
Chapter 4.
The switching action of a basic switch unit on the matrix pane]
namely, the structure of the T-connected phot oconduc tors as shown in
Fig. 5> can be phenomenolcgicaily described as follows % Assuming all
photoconductors are identical, and the intensity of exciting light is
high so that a large dark-to-on resistance ratio can be obtained, then,
as far as terminals A and B are concerned, the information transmission
will be negligibly small when the center branch is excited as shown in
Fig. 5a, and information transmission occurs only when both input branch
and output branch are excited simultaneously as in Fig. 5b. Therefore,
U-UJ
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Figure U. Steady State Photoconductance of Photoconductive Cell
■with Periodic Light Pulse Excitation
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into the conduction band as in process "b or it may capture a hole
from the valence band as in process c. The capturing processes are
characterized by capturing coefficients C,, C and the emission
ir
processes are determined by emission coefficients e , e . The capturing
coefficients are proportional to the capturing cross sections cf
the centers. The ratio of the C's and e's are related to the energy-
level of the SRH center, E t , by
e
n
=
exp
P
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C
n
L
kT
e
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(3 = 2)
SRH centers may locate at any energy level in the forbidden band and
may have different capturing coefficients which may not depend upon
the energy level of the center. Although SRH centers may be located
at the same level but they are spatially separated, so that the effective
electron flow between centers may be ruled out.
In addition to the recombination mechanism through SRH
centers, ether recombination processes are also possible such as
direct recombination or impact recombination. The direct recombination
is characterized by the electron and the hole combining in a single
step. In other words, the free electron "drops 11 back to the valence
band right across the forbidden gap. However, In most phot oconduc tors,
this process is not likely to be a dominant mechanism if it exists at
all. From conservation of energy, the excess energy of a free electron
must be given away when it is recombined. While no photon emission
is observed for most phot oconduc tors and releasing energy in the form
17
of high energy phonons is also not likely, it is strongly suggested
that the direct recombination across the gap is at least in a negligible
amount .
The impact recombination is a result of three-body inter-
action. It involves either two electrons and one hole or two holes
and one electron. When this process happens, two carriers recombine
and the excess energy is transferred to the third carrier. However,
this process may be observed only under proper conditions [3> ^] s
such as high equilibrium carrier density. It, therefore, does not
appear significant under normal conditions.
Since SRH centers play a dominant role in both equilibrium
and non-equilibrium conditions for most photoconductors, understanding
their characteristics will, therefore, be most essential to understand
photoconductors o From the four basic capturing and emitting processes
it is obvious that, for an electron captured by a SRH center ; . its
fate would either be to recombine by capturing a hole or to be thermally
emitted back into the conduction band. The occurrence of these two
possibilities has defined probabilities . One may, therefore, divide
the SRH centers into four groups. Those centers, in which the pro-
bability of a captured electron being recombined is higher than "Che
probability of the captured electron being re -emitted back into conduction
band, are termed electron recombination centers. The centers, in
which the above ratio of probabilities is reversed, are termed electron
traps = Similar arguments yield hole recombination centers and hole
traps. For SRH center of the same capture cross-section, it apparently
is the energy level that determines whether the center acts as a
recombination center or a trap. The energy level, at which the
18
probabilities of the fates of the captured electrons are equal
is, therefore, termed the demarcation level. The forbidden band
can, consequently, be divided into three regions by the electron
demarcation level and the hole demarcation level as shown in Fig. 8,
The SRH centers located in region I and II act predominantly as
electron and hole traps, respectively, and the SRH centers in
region II act predominantly as recombination centers. As a reason-
able approximation, one may consider that electrons captured by
traps can only be thermally re-excited back to the conduction band
and electrons or holes captured by recombination centers can only
be recombined.
The location of the demarcation levels are given by
C p
E, = F + kT In -£-
dn n C n
n
(3-3)
E, - F + kT In -2-
dp p C n n
where E, and E , are the demarcation levels for electrons and holes ,
dn dp
respectively, and F and F are the quasi-Fermi levels for electrons
J n p ^
and holes, respectively. The above equations show that the demarcation
levels are not only determined by the capture cross-sections of the
SRH centers, but are also closely related to the carrier densities.
Therefore, one can see that as the densities of carriers increase,
the electron demarcation level and hole demarcation level are moving
towards the conduction band and the valence band, respectively. This
fact has an important effect on photoconductivities when SRH centers are
distributed in the band gap or concentrated near the equilibrium
19
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dt p^ t p^l^ t t' {3>*J
dAP t
— ■ C n n( V n t ) - C^ - C pP n t + Cy^-nJ
21
where f is the generation rate, n is the electron density in SRH
centers , An and Ap are the excess electron and hole densities and
n and p are defined as
n n = N exp
t c
(3.5)
1 c * kT
IE, - E
: N exp |— — rr -
1 v kT
with N and N being the densities of the effective states of the
c v
conduction hand and the valence hand, respectively. The system
equations, Eq, (.3°^)? are completed with the space charge neutrality
condition that
An. + An = Ap . (3° 6)
The solution to Eq. (3°*0 and Eq= (3-6) with the proper initial and
boundary conditions should give a complete picture of the kinetic
characteristics of this single level system. Unfortunately, the
mathematical difficulties with higher order non-linear differential
equation prevent a solution in the genera.i case. A treatment for the
small signal case has been presented thoroughly by Fan [6]. First,
one considers the case
An ~ Ap
This is a good approximation for low SRH center density cr after the
initial stage of a large excitation. Then Eq= (3-^) and Eq« (3°6)
can be reduced to
22
dAa = _ 1_ l+JoAn .
dt T - L + aAn
where
C + C
n p
n + P.
and
1_ Vp^vV
T o "' C n (n i + V + c P U i + V
in which p n and n are equilibrium electron and hole densities.
Equation (3° 7) is valid for both rise and decay transients
with appropriate initial conditions. For the rise transient the
generation rate is greater than zero and the initial conditions is
An = when t = 0. For the decay transient, the generation rate is
equal to zero and the initial condition is An - An , when t = where
st
An is the steady state value before decay transient starts .
S"C
The general solutions to Eq= (3° 7) are then
(i) The rise transient;
bAn 2 + (fT a-l) An + f T I J |^=i I = C ± exp(- f) (3-8)
where
a
oo Ob
; - [(iT a-.l) 2 + 4bf T J £
7= 2b
p =
(fT Q a-l) +
E
fT Q a-l)'
tei,
2b
23
and
¥ ,2 1
5 - «a + ? + ^ r=T
C ;I = + fT Q (&)5
(ii) for the decay transient, one obtains:
(i - =9
(bAn+.l j
(An)
= q exp
(3-9)
where
<*W
\ ll QO (
bAn , + l)
st
d - t 2 )
The solutions of Eq. (3-8) and (3 = 9) have such a complex form that.
real physical meaning can hardly be deduced from them. To gain a
clearer understanding of the transient behavior, one may investigate
a special case where C ~ or C » C , and where the location of
n p n p
the SRH center is such that n ~ n . Considering that the excitation
is larger so that only a short time after the excitation
An » n Q ,
it arrives at the conditions
aAn » 1 and bAn » 1
2k
and then Eq. (3«7) has the form of classical recombination theory [7]
dAn = f-i-An (3.10)
dt " t
where
_1_ . b _1
T oo a " T
it is apparent that both rise and decay transitions are characterized by
same time constant, t and rise time equals decay time. However, if
00
the SRH center level is moved closer to the conduction band so that n
becomes much larger than An, while all others remain unchanged, this
becomes another extreme case
bAn » 1 and aAn « 1 .
It yields the form of classical quadratic recombination theory [7]
= f An-— An . (3.11)
l l
The solution for the rise transient of Eq. (3.11) is
An = -= & (3.22)
with
— + r Coth(rt/2)
1
25
And the solution for the decay transient is then similarly
An =
An exp[- -H
st T Q
1 + An . b[l-exp(- — )]
St T Q
(3-13)
From the above analysis, it is seen that the relaxation processes of
photoconductivity are closely controlled by the location of the SRH
centers. If the centers are located near the dark Fermi-level,
they are predominantly recombination centers and the transient response
to square wave stimulation has same time constant for both rise and
decay. However, if the level of the SRH centers is moving toward the
conduction band, the characteristics of the centers shift toward
more trapping action and thus increase the lifetime of free electrons
and prolongs the decay transient, and thus the relaxation for rise and
decay becomes more and more asymmetry . If one defines the rise time
t as the time required for An to reach ~— of its final steady state
r 1-e
value and the decay time t as the time necessary for An to decay
to - of its initial value then from Eg,. (3.12) and Eq. (3° 13) one finds
1
2,
1
>2-
_d _ l/^ol 2 ^.[e+efl + (l+^fl) J - in[l+2 fl + (l+lj-fl) ]
L CL -, -1 J-
Coth
— [e + (1+hilf 2"] >
(3.H0
with
ft = fb-r,
f[C n ( V n c ) + C p (p 1+ n )]
t
N, C C (n_+p.)'
t n p v
N
ffC n-+C P, )
• n 1 p-l y
t n r> 0'
e - 2.713
26
Equation (3.1k) is plotted in Fig. 9 which shows that the ratio of
decay time to rise time increases as the trapping action of the SRH
center increases.
The previous example is only for the case that the density
of SRH center is relatively low. For the opposite case where the
density of SRH center is relatively large, a mathematical form of
transient response can hardly be reached. However , one can expect
similar conclusion as the low density case, that heavier the trapping
activity of the centers, the larger the ratio of decay time to rise
time.
3 . 3 . Transient Problem^ W ith Multi-level SRH Centers
In the previous section, a model of a single level SRH
center has been considered under some restrictions. Unfortunately,
few practical cases can be represented by this simple model,
especially for the insulating type photoconductors . In the practical
case, one may expect that there are SRH centers of different types
located at different energy levels. An exact analysis to any such
given case is mathematically impossible. To understand the mechanism
of such a complex system, a phenomen-logical argument is needed to
deduce an approximation for semi -qualitative analysis [8].
A relatively simple model, of distributed SRH centers of one
kind is discussed. The energy diagram for this case is shown in
Fig. 10. Assume that there is a high concentration of SRH centers
N near the dark Fermi -level ,. These centers act as recombination
centers . There are also uniformly distributed centers of lower
27
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29
density between the dark Fermi -level and the conduction band. Let
the density of these distributed centers be N per kT. At any free
carrier density level, there corresponds a demarcation level E.,
dn
such that those centers above E, will act mostly as traps and those
below E n will, mostly be recombination centers . Due to the fact
dn
that N is a large quantity, the shifting of E does not effectively
alter the recombination center density. Also, as a result of
Boltzman's distribution law, the density of electrons captured by
the traps is always N during the steady state and is not affected
by the location of the demarcation level. Then,, at steady state,
the lifetime t of the electrons can be determined from the trapped
electron density and the free electron density as:
n t
T = (1 + — ) T
n. (3*15)
where i is the lifetime of electrons when there are no traps but
recombination centers, t~ is determined by N in this case. One
r
can see from Eq. (3*15) that the lifetime is inversely proportional,
to the excitation if the excitation is low (N » n) and approaches
the constant value T n as the excitation intensity is increased.
The above argument on the lifetime t is valid in steady
state. Equation (3. 15) may not hold during the transient process,
however, t is valid as an instantaneous lifetime under certain-
condition [9]» If this is the case, the rate of change of conduction
electrons may be written as
dAn f An
dt t. ,
inst
f -^T^7 •- •
The solution to above equation can easily be found to be
30
(3.16)
(i) for the rise trans ie
nt
An. - T Q f An - t q fN t
An-q!
An-p]
' t \
C exp^- — j
T
(3-17)
with
^fr n • (fx n ) 2 + 4fT Q N t ]
2 V
'0'
= i^T 0+ [(fT ) 2 + ^f
VtH
• I i
[(fT Q ) + ^Tq^]
C .. (f N t ) 2 |a|
The rise time constant can then be found as
(1+A) 2 | 2 - 2(1+A)|
1
i4-N, 2
fT
(1-A)(|-1)
(I^TFTi^A)
(3.18)
31
in which
A =
1
5=1 "e
(ii) For the decay transient, where f=0, and An^An , when t=0
An
An
exp
N
t
An.
.(1 2.)
An v An '
s
= exp(- — )
l
(3-19)
The above equation clearly shows a long decay tail due to the
presence of the exponential term on the right side of the equation,
The effectiveness of this prolonged decay depends upon the initial
excess electron density and N . If An is in the neighborhood of
"0 s
or less than N, , a very long decay can be expected. Assuming that
An is produced by a generation rate f , then
^s - 2 f T
i l
and the time for — - to decay to - — — of its initial value will be
An J 1-e
s
u
2N
1 +
li^ll
f t q 1+A
(3-20)
32
The ratio of the decay time to the rise time can then
be plotted from Eq. (3J-8) and Eq. (3-20 ) as shown in Fig. 11.
This plot reveals that a heavy trap density yields a long decay
time. This is due to the fact that, during the decay process,
there are almost a constant number of electrons freed from traps
which are turning into trap action from recombination while the
demarcation level moves toward equilibrium levels.
The analysis of the two given simple models merely serves
the purpose of demonstrating the effect of trapping on the transient
responses of photoconductivity. They show that both heavy trapping
activity and the existence of deep traps prolong the delay time.
Phenomologically , one sees that if large quantity of electrons are
trapped ;, then during the decay process, these electrons are released
into conduction band by thermal process and. the decrease of conduction
electron density is slowed down by the arrival of electron from traps.
Also, if the electrons are trapped in deep traps, where the exchange
rate between conduction band is slow, the latter part of the decay
transient is, therefore, dominated by this slow process.
In the practical case, few insulator photoconductors have
the simple energy band structure as given. The SRH centers may have
different capture cross -sections and their density distributions
may be non-uniform. A more complicated transient curve can be expected.
But one can expect that the dominating fact by SRH center has the similar
trend.
33
f?
z --
4- o
H
SL'Z
OS'Z
0)
S
•H fn
Eh CD
P
CD £
CO CD
■H O
w
-P CO
(L) 15
S 0>
•H -P
EH 3
>5 -H
c6 U
V -P
01
P
•H >,
P rH
K
rH
o
•rH
c
U P
^ -H
•H
fa
se-c!
oo-z
SL'l
OS' I
S2"l
3^
4. ANALYSIS OF PHOTOCONDUCTIVE CELL MATRIX
k . 1 . Equi valent Circuit, of Pulsed Photoconductor
For phot oconduc tors., which are under the excitation of
periodic light pulses, their instantaneous conductances depends
upon the transient characteristics of the photoconductor as well
as the condition of excitation. As noted in the previous section,
the transient response of a photoconductor cannot be expressed by
any simple mathematical function of time, even for a simple model.
Therefore, an exact analysis of the behavior of the photoconductor
matrix under the given stimulation is beyond our scope due to
mathematical difficulties and complexity. However, a simple
analytical result with rough assumptions will serve as a guide
for the evaluation of system design and performance.
Assuming that the relaxation process of the excess charge
carriers in the photoconductor follows an exponential function of
time characterized by two time constants, the rise (or growth)
time constant, i and decay time constant t.,, then the instant-
r d'
aneous conductance G of a photoconductor can be expressed as
G = G + m s [1 - exp( - ;£-)] (k.l)
'r
for rise transients, and
G G_ + £G exp (- — ) ( (4.2)
S T,
d
35
for decay transients, where G„ is the dark conductance of the
photoconductor and AG is the steady state non-equilibrium con-
s
ductance corresponding to the given intensity of the light. If the
photoconductor is stimulated by periodic pulses, as illustrated
in Fig. 12, then in steady state, the instantaneous conductance
can be written as
G=G^+Z^. + (£G - £G . )[1 - expf- — ) ] (4.3)
mm x s min /L v T v
r
for
< t < T
and
t-T
G - G n + ZX> exp[ - (■ -)] (4. k)
max T,
d
for
T < t < T
where £G and ZG . are the maximum and minimum points of the
wax min
fluctuating instantaneous conductance. Since G is continuous at
t = T and t-T, one finds
36
O (o
It
T ,
sp_j~i n n r
1 1 1 II II II m
Figure 12. Steady State Photoconductance of Photoconductive Cell
with Periodic Light Pulses Excitation
37
T l
Sinh'
-U- -^.^L,
"Wn ' ^s " \X T ^ 6XP( " ^
Sinh — i — + —
2 Vr T d,
The peak-to-peak amplitude of fluctuation, AG „, is, therefore,
AG = AG - AG .
f max mm
Sinh I =■ . — Sinh
0<7)
2 t / \2t,
» r/ \ d
sinh §k + v
Since the conductance G is periodic, it may, therefore, be expanded
in a Fourier series such that
G = G + G (4.8)
av ac
where G is the average conductance given by
av
T
+ 2
G = ^ /' G(t)dt (l+„9)
av T
't
2
and G is the combination of all harmonic terms given by
ac
38
G = Z
ac n=l
?mr 2nn .
a Cos -7=- t + b Sin — 7- t
n T n T
(1+. 10)
where the a 's and b 's are the Fourier coefficients
n n
+
= - / G(t) Cos -~- t dt
T
2
n T
(4.11)
2
b n = |/ G(t)SinfL t dt
>.12)
Equation (4.10) may also be expressed as
G = Z C Cos
ac . n
n=l
T n
(4.13a)
with
C =
fa + b )
■ n n '
(4.13b)
and
i b
-- tan"~ —
n b
a
(4.14)
39
Assuming that the excitation condition satisfies
AG . » G„ ,
mm
the Fourier components are then given by
and
AG
'av " T
T T
2 1
Sinh t: — Sinh —
2t, t
\ + 2(t,-t )
'1 ' d r'
Sinhi(^ + ^-)
2 T T,
r d
(4.15)
ey,
T T T
= 2AG . °^P. Sin e, exp( — ). Sin(nit+e, )+Sin(nit— ^ — --0, )
mm d | t j d
T d
exf
T T -T
2fAG -AG . ) —Sine |exp(-~ )sin(n«-e )-Sin(mr 2 m 1
s mm T r|^T r T
AC T -T
s a . / 2 1 N
— - Sin (nit — - — )
nit T .
(4.16)
b = 2AG . -^ Sine,
n mm T d
T T -I
exp( — )cosfnir+e, )-Cos(nit— — e _, )
T, k d T d'
d
r „.
+ 2 (AG -AG . ) ~ Sin Q
s mm' T r
m T -T
1 2 1
exp(- — )Cos(nit-e r )+Cos(nit T ' -Q^)
r
AG
nit
T -T
2 1
Cos nit - Cos (nit ■ — — -)
(4.17)
with
m "I T
Q, = Tan
d 2nn t,
d
■>.18)
-1 T
9 = Tan
r 2nn t
r
Tf a voltage V is applied across the terminals of the
phot oconduc tor which is excited "by periodic light pulses as shown
in Fig. 13a, the instantaneous voltage -current relationship is then
I = V(G + G ) ^ 19a )
av ac
using the instantaneous conductance expression Eq . (4.8). Equation
(4.19a) may be rewritten as
G
I = V(l + ^--) G . (4.19b'
G av -
av
This equation shows that the photoconductor may be considered to
possess only a constant conductance G . The fluctuating part,
G , may be considered as a series "induced" internal voltage source
ac
and the magnitude of its voltage is
G
-S£ v
G
av
Ui
LU
(/>
_l
3
a.
x
H
<
CD
g
i-
<
■ LU
t or
5E
o
UJ
I
3
o
Ixl
UJ
u
or
8
O
>
o
•H
P
C5
P
•H
O
T3
O
•H
P
O
-P
o
g
C
o
o
o
p
o
>
o
CD
-I
Z
o
z
LU
(/>
LU
or
Q.
£ or
o
LU
o
or
3
O
if)
CO
LU
-J
i
3 H
O Z
LU LU
or
or
3
O
O
w
p
•H
o
•H
o
p
a
H
a
>
•H
en
■H
k2
By defining the inducing factor [i, that
av
and equivalent circuit for the photoconductor under periodic
excitation may, therefore, be represented by an induced voltage
source in series with a constant conductance as shown in Fig. 13b.
Equation (4.19) 'may also be considered from the viewpoint of current
flow. Since VG is the current generated by a voltage V across a
3. v
conductance G , another equivalent circuit can be formed with the
av
parallel combination of an "induced'' current scarce and a constant
conductance as shown in Fig. 1.3c where
G
i = VG and u = — - ■
av G
aA^
The inducing factor u. actually consists of the Fourier components
normalized with respect to the average conductance G , and is a
av
periodic function of time, and, therefore, the induced sources merely
represent noises injected, by the periodic stimulation. Since p.. is
the combination of all the harmonic terms in the Fourier expansion,
it may also be separated according to +he frequencies of the Fourier
components. The induced sources may thus be represented by either
series :ombination of induced voltage sources of single frequencies
T
n . ,
m> as shown in Fig, 14a, or by a parallel combination of induced
U3
<$ ® ® ® iilGov
M4' ^3' M2 1 Ml 1
(a) CURRENT SOURCE REPRESENTATION
5>nV
(b) VOLTAGE SOURCE REPRESENTATION
Figure lU. Equivalent Circuit Representation
kk
current sources of single frequencies =■, as illustrated in
Fig. 14b. The inducing factor for each single source is given
by
C
n
U- = ~ CO£
n G
av
g
2nr^
(4.21)
In the practical application of the opto-electronic switching
system, one requires that, with a periodic excitation, the photo-
conductor yields a high average conductance and small amplitudes of
inducing factors. To show the relations between the equivalent
circuit quantities , the photoconductor parameters and excitation
condition, Eq. (4.15) and Eq. (4.13b) are plotted in Fig, 15 through
Fig. 17. Figure 15a to Fig. 15c show the normalized average conductance
T d T 2
as a function of — with — as parameters . The normalization is with
r 1
respect to the steady state non-equilibrium conductance zX> corresponding
to same light intensity as the amplitude, of the light pulses. The
four figures are for four different light pulse widths, expressed by
T l
— . One notices that the average conductance decreases as the pulse
T r T 2
width increases if — is unchanged. This is due to the fact that one
1
allows longer T for the photoconductor to decay, but the decreasing
of the average conductance is not so drastic that it would, be a condition
for concern However, for the amplitudes of the inducing factors,
which are shown in Fig. 16 and. Fig. 17 for first and second harmonics,
one no ; Lc several important facts, (l) The inducing factors increase
*•?
U6
15.00 60.X 75.00 90.00
^'T
(a)
-i — i — i i
-> — i — i
00 15.00 30.00 MS.00 60.00 75.00 90.00 105.00 120.00
(b)
^'T
90.00 105.00 120.00
(c)
Figure 16. Inducing Factor of First Harmonic Frequency
1+7
-t — i — i — i — i — i — i — ►-
H 1 1 1 1 1 1
.00 15.00 30.00 HS.OO 60.00 75.00 90.00 105.00 120.00
(a)
Mi-
1.
■05
io s .
T,
30
■ 20
Ti
Ti
■10
ID-*-
-•
10 ■
Ti
• 1
io""-
,o".
1 1 1 I 1 1—
— 1 1 1-
— 1 1
1 1
1— —
1 1
.00 15.00 90.00 1(5.00 60.00 75.00 90.00 105.00 120.00
(b)
I I I 1 1 I t 1 1 1 1 1 1 I
.00 15.00 30.00 15.00 60.00 75.00 90.00 105.00 120.00
(c)
Figure 17. Inducing Factor of Second Harmonic Frequency
T l
rapidly when the pulse width increases (for — unchanged). For
T T 2
1 1
example from — = .1 to — = .1.0, the first harmonic inducing factor
T r Tr +2
increases by a factor of nearly 10 , (2) For a given pulse width,
the harmonic inducing factor increases as the pulse period increases,
but the rate of growth decreases as period becomes large, (3) The
inducing factor decreases rapidly as its order increases. For both
the inducing factors and average conductance; it is found that they
will always have a satisfactory value as long as
T t
T 2 \
Additionally, one may neglect the higher order harmonics when
considering the inducing factor.
Furthermore, although the term ''current source" and "voltage
source" are used in the equivalent circuit presentations, they do not
have the conventional meaning. It is clear that the sources
corresponding to different harmonic terms interact with each other
since they are directly associated with the current flow in G
J av
(in case of current source representation) or voltage across the
whole element (in case of voltage source representation). These
induced sources are not effective unless external forcing is
applied, therefore, for further analysis, Thevenin's theory is not
valid. However, in the practical case, |_i * s are designed to be small
and the regenerative effect may be negligible.- If this is the case,
then the conventional theory of voltage sources or current sources
may be applied and should yield an approximate analytical result.
^9
k .2° Transmission Efficiency, Injection Noise and Gross- talk
Under the operating scheme described in Chapter 1, the
characteristics for a cross-bar type matrix with T-connected
photoconductor units at each cross-point, as shown in Fig. 2, can
be analyzed with the equivalent circuit developed in the previous
section. It is understood that, during the system operation, it is
either the center branch or both the input and output branches of
the switching unit that are being stimulated by periodic light pulses.
Since the light pulses to a given photoconductor result from scanning,
the photoconductor instead of receiving a light pulse which fully
illuminates its sensitive area at once sees a light spot moving
across its sensitive area. Therefore, before and after the photo-
conductor is fully illuminated, there is a period of time that the
photoconductor is only partially illuminated. The effect of partial
illumination not only complicates the treatment, but also introduces
additional noise into the system if the period of partial illumination
is comparable to that of full illumination. However, if the sensitive
area of the photoconductor is small in comparison with the light spot
size or if a step scanning system is used to increase the ratio of
full illumination period to partial Illumination period, one may
neglect the partial illumination effect.
It is assumed that the scanning light beam has such an intensity
and scanning rate that the inducing factor p. of each photoconductor
is small and the ratio of dark resistance to the average resistance R
is very large. The average resistance is defined, as the reciprocal
of the average conductance G . Under the restriction that each output
av
50
channel may not receive information from more than one input channel
but one input channel may feed more than one output channel , the
interaction among output channels can be neglected .
Considering any output channel Y., which is receiving
information from input channel X , one can draw an equivalent circuit
m
for the situation as in Fig- 18, in which u(n) denotes the inducing
factor for the photoconductor of the switching unit associated with
the nth input channel. Since p's have been assumed small, super-
position is approximately valid and one can consider the effect of
information voltage V 's and noise sources separately. From the
equivalent circuit in Fig. 19* which considers V 's only, the voltage-
current relations are given by
V" - V . ' V s V . - V '
m i m oj m
R R , R
av d av
V - V ' V 8 V.-V* r / m
r r r oj r
R^ R R., r = 1, . . . m-1, m+1 . „.n
d av d
V ' - V . n V ' - V
av r=l d
/m
r^m
(4.22)
51
Vm> •
Vi> •
V 2 >
V 3 >
v r >
jVWin
Figure 18. Approximated Equivalent Circuit at an Output Channel
52
A
-•
w
•H
O
o
T3
■a.
'H^ » ||l = >>
H
■P ctf
C C
•H
o
CM
U
w
4
"O <
(T <
>
o
~^<
>
c
"O <
a: <
<
c
IX
o
•H
ra
w
•H
e
w
§
rl
EH
U
O
Ch w
•h
-P w
PS H
o cr3
•H <
O
-P
a)
rH
>
•H
ON
rH
•H
Pn
53
Equation (4.22) leads to the voltage V . at Y . as
oj j
n-1 d. 1 av n-1
+
or
with
oj \R T R R , R 2R^+R R^ P^+2R
° \L av d av d av d d
av.
R, V R 1 n
d * + J?L^L^ £ V (4.23)
R 2R,+R R^ 2R +R^ . r
av d av d av d r=l
^
r^ra
n
V . = TV + p E V (4.24)
r=l
r = A
R (2R +R ) 1 _1_ n-1 _d_ 1 av n-1
aV aV R T + R + R, "R °2P,+F. "R, - R^+?R
av a av d av d d av
(4.25)
R V /2-R^ + R
In the practical case,, the condition
R, » R
d av
.s always satisfied and yields
^
2R
X
(4.27)
! + _±I + 2(n-l)
av
(W
p*2 s^l r
The current flowing through the branches of R can then te found
cL V
,'R, + P R,
1 ( d av d „
ml P V 2P + R i 2R + R oj
av V d av d av
_A_(____^ rv + v.) - -\
m2 R \2R J + R ^ oj V oj
av V d av
(k.29)
V . + V r = 1,
r R , + 2R '
d av
. , m-1, m+1, . . . n
For the case R , » R , Eq. ( J 4.29; "becomes
d av
i -, = i
ml ' m2 2R
av
n
(i - r) v - p Z v
^ ' m r
r=l
~~ r^m —
(4.30)
i = ~ 1 rv - v
r R . V m r
d
n
P Z V
r~l
r/-m
55
When the currents are known- the effect of the "induced sources"
can then he evaluated with the help of the equivalent network of
Fig. 2C. The system equation
V . V V "
sj m m
P~ " FT " R~
av d av
V
sj r r
u(r) i = ' 4.3i;
R, R R^ r
d av d
r =■ 1, ... m-1, m+1, ... n
r fc m
n V - v " V V - "
v s j r sj si ra \ , _
r-1 d '- av
r^m
leads to the solution for the voltage V . appearing at the output
channel Y. due to the induced sources. Since the inducing factors
J
M-(r) are out of phase with each other due to the fact that all the
photocells are excited, sequentially, a complex form for V ., which
s j
can hardly be interpreted clearly, will be obtained if the phase
shift is considered. However, one may create a worst case' by
assuming that all |i ' s are in phase. This cannot happen to the
first harmonic term, which is the most important one, with the given
scanning scheme, but it is possible for higher order ones. The
worst case analysis gives a possible upper limit of noise. By assuming
that the |i(r)'s have the same amplitudes and. are in phase., the maximum
noise at the output for the case R n » R becomes
d av
56
n
v„< = n< (i - r) rv m - pr(n-i; v^ + (1- p Z v
sj m • m r
or by const ip-ri n g t~ne practical case condition 6 « 1 > one has
V . = n(l - r) T • V (^-32b)
sj m
Therefore, the total signal V appearing at the output is the
superposition of V„ . and V
Oj sj
n
v - rv + p Z v + J, - r) rv ^3;
Oj m p r= , r • • m JJ/
r /'n
A] examination of the terms on the right side of the above equation
eals that the first term, TV , carries the information. V to be
m m
transmitted despite being modulated by a scaling factor I\ Therefore,
may be defined as the 'Transmission Efficiency and it has a
numerical value between and 1. The second term on the right clearly
carries the information from input channels other than the mth one ;
this inJ rmal ion is not supposed to be received by the output as it
re}.' the i ross-talk from other channels. The constant 3 is,
57
therefore, defined as the "cross-talk factor". From Eq< (4,28),
it is clear that the cross-talk may be suppressed to a negligible
level if a large ratio of R, to R can be provided The Last term
d av
V . is the noise caused by the periodic stimulation. It may be
s J
termed "injection Noise" in the ser.se + hat it is injected by the
scanning beam with a noise injection factor n. = (i(l - V) F,
This noise contains a spectrum of u.. By examining the three
quantities; F given by Eq. (4.27)> p given by Eq , (4.28) and
t] = n(l - r) r, one finds that the matrix functions better when the
load impede nee P on the output channel increases. Since the value
R L
of — — is usually very small, on the order of .10"'' or less, the
R d R
3 V
transmission efficiency F becomes highly affected bv - — , The
larger the R T , the closer the F to unity. Improving the transmission
efficiency F may also increase the cross-talk factor P, but it
/R V 2
/ av *
becomes less important due to the fact (3 is governed by[ r —
\ F d
which is one the order of 10" or less. However, the injecting noise
can be heavily suppressed when F approaches unity, The relation
P R
between ~- and ~- with V and n as parameters is plotted in Fig, 2.1
P- ^j
L d
to show their interactions.
4.3. I mportant Factors in Matrix Design
From the above analysis, the basic characteristis of the
switching matrix can be described by three quantities, namely, the
transmission efficiency F, cross-talk factor P and noise injection
factor T]« An ideal system should, have unit transmission efficiency,
zero cross-talk factor and zero noise injection factor. By examining
58
o
cr
■o
-■ tr
IfllOrfOl S m
cj> 0> (7) CO CD OD
d 6 6 6 d d
II II II II II II
C_UE-.UL.J-.--
i\\\\\
o
-I
o
CM
— o
o
r4
59
Eq. (4.27), Eq. (4.28) and Eq. (4.31), it becomes clear that a
R d R L
system requires large - — , - — and small u.
av av
It is not unusual to find photoconductors which can furnish
h
a ratio of 10 or higher for dark resistance R, to full-on resistance
R (= 777^) with only moderate light intensity. From Fig, 18, it is
s
obvious that as long as the scanning satisfies
r 1
the average conductance G satisfies
av
G > k £&
av 2 s
R d 3
Therefore, the quantity - — still is of the order of .10' or higher.
R
av
To maintain this large ratio requires complete dark on the photo-
conductor when it is not. scanned. Since the photo-resistance is
very sensitive in low light intensity region, as shown in Fig. 22
for a typical photoconductor, any background light will reduce the
R d
effective - — drastically and degrade the performance of the system.
R
av
For example, if the photoconductor has a resistance - light intensity
relation as in Fig. 22 and the light beam has an intensity of
2 P d
22.9 mw/cm , with periodic excitation, R =10Ko This gives a - — ■
' ' ' av R
av
6o
Hi
o
z
S
* ID
2
O
-P
O
C
o
o
o
-p
o
o
6
8
d
2 H0/SllVM|-niN 6'22 01 103dS3W HUM Q3ZnVNM0N ' Ai.ISN31.NI 1H9H
CVI
CM
f l '
63
e
CD
-P
w
>>
CO
bo
•H
-P
B
•H
H
H
O
o
0)
PQ
•P
■a
•H
on
CM
CD
S,
•H
1
z
H
oo:
uj o
-Jflc
Jc
o 5
o2
the output beam diameter I , beam divergence angle 9 and energy
density e of the collimated beam are given by
6k
or
and
where
9 - d
Z 3 \ i
9 = Tan
(5-1)
(5.2)
l h
£q Tan e = _ Ai __
(5-3)
E = 2+jtE
.i -
(5-M
f r f 2
d^d.,
c
diameter of radiating source
aperture of condensing lens
effective focal lengths of condensing
and collimating lenses, respectively
distances, as illustrated in Fig, 25
radiating energy per ster radian from the
radiating source .
65
A well collimated beam for moderate specifications can be obtained
by optimizing Eq. (5-1) "to Eq. (5»^)» However, if the specifications
of the required beam are extreme, for example very small £ and 9 and
very large E, an optimum condition may not exist at all. From the
above equations, it is seen that lenses of small f -number are
required to produce a small, intense light beam. On the practical
technology side, this imposes an additional limitation on the avail-
ability of lenses with near ideal quality. Therefore, obtaining an
intense, well collimated small light beam from a conventional light
source is difficult and its broad spectrum also imposes difficulties
in effectively controlling it (such as deflecting or modulating)
without introducing color dispersion.
The alternative is a continuous laser [10]. A laser beam
is characterized by highly monochromatic and coherent light. The
laser beam can be in different modes depending upon the resonant
cavity structure. For the fundamental mode, which is the most important
and most used, the laser beam is approximately defined by a Gaussian
wave [11]. If the beam is propagating in the z -direct ion, it may be
described by a wave function in cylindrical coordinates
U = $(r,(j),z) • exp(-jkz) (5-5)
where j = \l - 1
66
which satisfies the wave equation
- 2 2
v u = k u = o
(5-6)
2tt
where k = - — is the wave propagation constant . This wave function
A.
has the approximate solution
{
U = ^exp4-j(kz- 4-
x
72
z
2 c
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UJ
cr
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The elctro-mechanical deflector has the highest resolution
potential due to its large deflection angle. But its scanning rate
is the lowest of all. For the higher scanning rate units, the
deflection angle is limited by inertia or other mechanical restrictions,
thus the resolution decreases as scanning rate increases. Acousto-
optical deflectors can reach a resolution comparable with TV scanning,
their main restrictions are the frequency response of the ultrasonic
transducer and the necessity of rotating the acoustic wavefront to
keep track with the Bragg angles. Electro-optical devices have the
highest scanning rate but their resolution is limited by the voltage
gradients and crystal size that can be used.
The range of resolution and scanning rate for the different
deflectors is indicated graphically in Fig. 29. This indicates that,
for all types of deflectors, the resolution and scanning rate are not
independently controllable. One may have a wide range to choose
deflector according to the requirement.
5.k. Comparison of Light Deflecting Methods
Among the light deflection methods described in previous
sections, none can be considered adequate for general practical use.
Although each method offers some advantages over the others, they all
have some serious disadvantages which limit their application.
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85
The electro-mechanical scheme has a unique advantage in
that it does not introduce color dispersion and its deflection is
insensitive to the light frequency. It may also have a wider
scanning angle and, therefore, higher resolution. But its frequency
response is limited to a relatively low range due to the mechanical
inertia present. The rotating mirror offers only one type of
scanning -- namely, saw-tooth. Each trace cannot be triggered
separately and, therefore, synchronization to an external time base
requires good phase and frequency stability of both the deflector
and the external time base. The vibrating mirror suffers from
thermal effect since the expansion of the suspension system displaces
the beam in the direction perpendicular to the scanning,, This becomes
more severe for higher frequency units in which the suspension is
stiffer, also, in high frequency units, the mirror is immersed in a
damping fliud to provide critical damping operation which unavoidably
creates color dispersion in a broad spectrum beam.
Both the electro-optic and the birefringent methods are
different applications of the electro-optical properties of some
materials. The sensitive nature of the materials to the light
frequency makes both deflectors usable for monochromatic light . Since
they require a high electric field to produce the electro-optical
effect, a high voltage control source is necessary and yet the result-
is a relatively small deflection, approximately 1 . However, these
two methods do have attractive aspects as high speed deflectors.
Their frequency response is limited only by the thermal dissipation
36
due to dielectric losses and the driving electronics. A frequency
9
response up to 10 Hz can "be expected. Deflectors employing
b.irefringent methods are the only ones that offer random access-
ability without the need for an additional light shutter to blank
out the light during the beam position transition.
The acous to -optical deflection system has a frequency
response into the MHz range. It is also rather insensitive to
thermal effects but requires a critical alignment of the optical
beam and the acoustic wavefront to maintain the beam intensity.
To compensate for any deviations from the required alignment, an
array of cells may be used to generate a rotating acoustic wavefront
to match the angle. This method also su f fers from color dispersion.
When the light power handling capacity is considered, the
electro-mechanical types cf deflector emerges in a leading role among
all deflectors. The main factor which limits the power capacity is
the thermal effect which introduces a non-uniformity in either the electro-
optical crystals or the transducers = The .^oss of light power through
the deflector is not. a. sufficient reason to reject any of the methods
becfe high optical quality components are available to insure high
y in each case .
5° 5° leal Scanner
The basic requirements for the light beam, scanning system in
pto-electronic switching matrix are determined by several factors:
(l) The beam diameter is specified by m>< criterion that at the edge
87
-3
of the beam the energy density is 10 of its value at the maximum
point (usually the center of the beam). This definition is different
from the conventional definition of ~ attenuation. The reason for
e^
such a rigid criterion is that the operation of the system requires
3
the light on-off states having a contrast of at least 10 . A Gaussian
beam with radius a for —r- attenuation, has a beam radius of 1.8.5a
e
in the new criterion. This also implies that the distance between
photoconductors on the matrix panel cannot be less than the radius
of the light beam. On the other hand, the size of the sensitive area
of the photoconductor should be kept smaller than the -r attenuation
e
dimension in order to have the unit as uniformly illuminated as
possible. (2) The system must provide a resolution of n-element
per line where n is the number of photoconductive elements per line.
(3) The system must provide a two-dimensional scanning pattern.
(k) The periodic light pulses experienced by the photoconductors
must satisfy Eq» (4.33) from which the requirement of scanning rate
is determined. (5) The background light caused by scattering inside
-3
the beam scanner should be less than 10 of the maximum bean intensity.
Any higher background light intensity will degrade the matrix per-
formance .
The optical scanner used in the prototype system was constructed
with two vibrating mirrors. The vibrating mirrors have a frequency
response of 20 KHz with 5 deflect i.on angle and an aperture of
approximately 1 mm by 1 mm. Two dimensional scanning is accomplished
88
by the optical arrangement shown in Figo 30. Both 1*41 and M2 are
fixed first surface mirrors insuring proper incident and exit beam
directions, GM1 and GM2 are the vibrating mirrors whose axes of
vibration are at right angles to each other, and lens L serves the
prupose of collimating and guiding the light beam. GM1 and GM2 are
located in the conjugate planes of the lens L so that the beam
deflected by GM1 is guided onto GM2 to be deflected again. The
detailed optical path in the scanner is shown in Fig. 31' The laser
beam with 0.7mm diameter and i.^ millradian divergence angle is
converged by a lens with focal length of 203-2 mm. The optical
distance between the converging lens and GMl is such that the focused
light spot falls on the focal plane of the collimating lens whose
focal length is 25^ mm. Therefore, the light spot on GMl is
approximately 0.^ mm in diameter, just small enough to avoid
diffraction by GMl, and the focused light spot in the focal plane
is approximately 0*3 mm in diameter . The center of the light beam
passes the conjugate point on the right side of the collimating lens
and it is independent of the deflection angel — of GMl, Furthermore,
the light beam image A or B in the focal plane is equivalent to a
light source and radiates a cone of light rays which .is coliimated
into a parallel beam by the lens, The coliimated beam has a diameter
of approximately 0.4 mm and. a divergence angle of nearly 6 mi.liirad.ian
due to the finite spot size at A or B. The direction of the coliimated
beam d Ls on the location of the image in the focal plane, and in
this case it has the same magnitude as the deflection angle 5- of GMl.
89
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91
All of the center lines of the deflected beam from GM1 pass through
the conjugate point 0. The vibrating mirror GM2 is located at
this point to pick up the beam and deflect it in a direction per-
pendicular to that of GM1, thus providing a two-dimensional scanning
system.
The use of a converging beam and a collimating lens reduces
the diffraction caused by the small mirror aperture and removes the
limitation on the deflection angle of GM1. Two -dimensional deflection
could be obtained by having two mirrors face to face, but either the
second mirror must have a larger aperture to accommodate the beam
deflected by the first mirror or the deflection of the first mirror
must be limited so that the beam will not sweep out of the aperture
of the second mirror. The two lenses used in this canning system
reduces the beam size, but increases the beam divergence by a factor
of the ratio of their focal lengths which is 8 in this case. The
resolution of the scanner will also be reduced by the same factor.
The fact that the locus of the focused beam spot A is an arc instead
of a line when GM1 vibrates, as shown in Fig, 32, introduces an
additional divergence into the exit beam. To the first order
approximation, this divergence is given by
5 = wl
which results in a beam divergence of approximately 0,1 > mill! radian
in the worst case. Therefore, the exit beam of the scanner will have
92
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93
a diameter of 0.4- mm with a divergence angle of 6.5 milliradian
in the worst case. A resolution of 130 lines in either scanning
direction may be expected if the remainder of the optical system is
ideal .
Unfortunately, the resolution of the system is less than
expected due to the optical condition of the vibrating mirror
structure. A cross-sectional view of the vibrating mirror is shown
in Fig. 33 > the mirror is immersed in a damping fluid and sealed
in a tube. The light beam exists through a window which is tilted
to separate the first reflected beam as shown in Fig. 33a. However,
successive reflections between the interfaces of the window as
indicated in Fig. 33b, interferes with the main beam and results in
interference fringing in the far-field pattern. The intensity of
the fringing depends upon the reflective it ies at the interfaces.
Unless the window is optically flat, the scattered light will also result
in a serious background illumination.
9h
i— DAMPING FLUID
CYLINDER WALL
INCIDENT BEAM AND
EXIT BEAM
MIRROR
SUSPENSION
CROSS -SECTIONAL SIDE VIEW
CROSS -SECTIONAL TOP VIEW
Figure 33. Cross-sectional Views of Vibrating Mirror
95
6. CONTROL SIGNAL PROCESSOR
6.1. Scanning Pattern and Driving S ign als
To scan the switching matrix, several alternate sequences
may he considered. In conventional raster scanning, in which the beam
starts at one edge of the panel and retreats back to the same edge
to start the second row, there is both horizontal and vertical
fly-back. During the fly -back, the beam must be blanked so that
it will not interfere with the switching units it passes over. This
requires additional components such as a beam shutter. To avoid
this, one may use an alternate interlacing scanning pattern in which
there is no fly-back or retrace as illustrated in Fig= 3^a. Such a
scanning pattern requires a more complicated driving signal than a
simple saw-tooth wave for raster scanning and an. even number of
horizontal lines to produce continuous scanning with no fly-back.
Since the scanning beam spot is to be discrete in order to
reduce the transition time between units and to provide a large ratio
of full -illumination time to partial illumination time for the scanned
photoconductor, a step-shaped driving signal is necessary for both
horizontal and vertical deflections. To illustrate the sequential
relation between driving signals, one may consider the scanning of a
4x4 matrix without loss of generality. The ideal signal for both
the horizontal and vertical driving signals for a linear scanner are
shown in Pig- 3^ . The driving signals are shown for the condition of
no information transmission being allowed between input and output
GATE n
ANALOG
ADDER
CLOCK OUT FOR VERTICAL DRIVING
(0)
D*
I
/
CLOCK OUT
i
m_
JLtL
U
(d)
u
.5. Block Diagram of Horizontal-driving Signal Generator
and Wave Forms at Different Staees
99
the number of columns to be scanned, on the matrix panel, relative
frequency drift between these signals cannot be tolerated. It would
be very difficult to stabilize the beam position if free running
oscillators were used.
The method of generating vertical driving signals is
similar to that for the horizontal driving signals and is shown in
Fig. 36. The only difference is that the output D of the control
un.it is a wide pulse which shifts one side of the staircase wave to
provide an asymmetry staircase (.Fig. 3^c) for the interlacing scheme.
The clock is fed by the control unit of the horizontal, driving circuit
and its frequency is r— -- of that for horizontal driving.
6.3. Control Signal Memory and Regene ration
The driving signals generated, by the above scheme provide
the basic scanning, which maintains all the switch units in an off state
To turn on a selected, switch unit, the beam, scanning has to be
displaced in each scanning cycle until that switch unit is to be off.
The information on selection may come on. a separate control
channel or as part of the information on the input channels and its
form may be in any code. It is reasonable to assume that it can be
broken down to two parts which designate the input channel and the
output channel to be connected. "Phastor" [19]j offers an elegant
and. economical method, for storing this information and for regenerating
the corresponding distrubing signal, every scanning cycle.
C LOCK
FROM HORIZONTAL
DRIVING
TRIANGLUAR
WAVE
GEN.
1
SAWTOOTH
WAVE
GEN. I
1
SAWTOOTH
WAVE
GEN.H
CONTROL
GATE I
GATEH
ANALOG
ADDER
♦ t
C*
D*
-►t
Figure 36. Block Diagram of Vertical-driving Signal Generator
and Wave Forms at Different Stages
101
Phastor is a high speed high precision analog memory unit
in which the information is stored in the form of phase shift with
respect to a standard reference. It is basically a regenerative
constant delay loop. If the information is in analog form, the
operation of phastor can he described with the aid of Fig* 37-
The information voltage (Fig. 37d) to be stored is compared with
a standard ramp voltage (Figo 37c ) to generate a single narrow
pulse (Fig. 37e ) whose phase with respect to the standard reference
pulses (Fig. 37b) is proportional to the amplitude of the information.
This single pulse circulates in the active delay loop. The delay time
of the loop is clocked so that its output pulses (Fig. 37-t ) has same
period as that of the standard clock. Therefore, the output is a
pulse train with same frequency as the reference pulses but with a
phase shift between them, A phastor with an operating frequency in
MHz region and ±00 memory levels has been reported.
For n x m matrix channels, 2N phastors are used. For each
input channel two phastors are used, to register the input and the
output channel between which the information is to be transmitted.
Those are designated as the X-phastor and the Y-phastor, respectively..
The X-phastor has N memory levels while the Y-phastor is divided into
M levels. The X-phastor is controlled by the clock used in the
horizontal driving and the Y-phastor by the clock used in the vertical
driving. The output pulse widths of both phastors are set to equal
the period of their respective clocks. Therefore, by sending the output
of both phastors through an AND-gate , a single pulse with width
102
INFORMATION
INPUT
c
COMPARATOR
D
ACTIVE
E
DELAY LOOP
i
u a
«
»B
oA
A*
RAMP
REFERENCE
(a)
ERASE CLOCK
Figure 37. Phastor Block Diagram and Wave Forms
103
corresponding to the matrix cross-point is obtained. This pulse,
if its amplitude is standardized, may be added directly to the
vertical driving signal to produce displacement at proper location.
Since geometrical position on the matrix corresponds
to the time delay in the driving signal, and since the phastor
registers information in the form of time delay, it offers a
directly usable access signal thus eliminating the process of trans-
formation required by other memory methods.
104
7. EXPERIMENTAL RESULTS
To prove the feasibility of the suggested switching system,
a prototype system with four input channels and four output channels
has been constructed and tested.
The light source used in the system is a continuous
helium-neon gas laser with wavelength of 632.8 nm at TEM m mode.
The output beam of the laser is measured at 4.5 milliwatts with the
-2
beam diameter at 0,7 mm for e points at the exit aperture and the
full divergence angle of 1.6 milliradians . The optical scanner is
constructed as described in section 5«3«
The phot oconduc tors used on the matrix panel are commercial
grade EM1508 manufactured by Raytheon, They are caldium selenide
cells primarily for control circuit use. The dark resistance of the
9 /
cells has typical value of 10 ft in low voltage (around 50 volts or
less) operation. All cells are selected so that their resistance
and transient response are within 25$ of uniformity. The photo-
resistance of the cell with response to the laser beam is measured
at the room temperature and one typical case is shown in Fig. 38.
Nature density filter and beam expansion are used to provide low energy
density illumination. The transient time constants, t-,, t are
d r
measured with light pulses provided by rotating chopping wheel. The
t and t is determined by comparison method. The circuitry for the
measurement is simple as shown in Fig. 39- For such circuit the output
105
-i o.oi -
0.001
10 6 RESISTANCE fl
Figure 38. Photo -response of a Photoconductor
Id
60
50 -
40 -
30 -
20 -
10 -
1
RISE TIME CONSTANT T r :
O
DECAY TIME CONSTANT T d
:
? : '
/x
-
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NORMALIZED
LIGHT INTENSITY
Pi mifo QQ t3iao o-n^ TIopqv Timo frvn c-han +■ :s nf a Phr>-hr>r>rmr1'nr > "hr)"r
106
voltage V n is
R l
v ___ v
R(t) + R
1
in which R(t) is the instantaneous resistance of the photo-
s'
conductor, one set the value of R n being —r of the final steady
7 1 e-1
state value R(°°) of the photoconductor for rise transient time
constant and set R "being eR.(°°) for decay time constant measure.
With proper value R, one obtains
V = — V
v 2 v
when t = t in rise transient and t = T n in decay. By this relation,
r d
both t and t, are determined on the oscilloscope with constant
r d
voltage supply. The measured data of a EMI 5 02 is given in Fig. 39-
The scale of light intensity is normalized with respect to 22, 95
milliwatts/cm .
The scanning pattern and driving signal wave forms are as
that suggested in Chapter 5- But the circuits to generate the driving
signals did not follow the recommended method because the total units
to be scanned is only l6 that no economic factor is to be considered.
To generate the horizontal scanning signal, a ring counter is used
to register the corresponding horizontal beam position, as shown in
the upper part of Fig. kO, outputs of each flip-flop of the counter
processed by a group of NAND gates so that the output of the gate
107
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has pulse sequence as shown in Fig. kl. The output pulses of the
four NAND gates activate four diamond gates which allow their analog
input voltages transmitted to the output terminals. The analog voltages
input to the diamond gates have precise step difference from one to
another. Therefore, at the output joint of the four diamond gates,
a staircase wave is obtained by their proper turn-on sequence. To
drive the light beam off the area of photo elements during the
vertical transition, an "edge-detector" is designed to generate
pulses with correct polarities when it receives signal from the
counter. The outputs from diamond gates and edge detector are added
through a wide band operational amplifier whose output is amplified
by a variable gain amplifier that provides critically damped driving
current to drive the horizontal deflector in the scanner.
The vertical driving signal generator, lower part of Fig. hO
is basically same as the horizontal driving signal generator except
it is clocked four times slower than the horizontal generator. The
vertical displacement perturbation signal is added to the basic
scanning signal through its analog adder. The channel switching
information signal is simulated with a simulator of mechanical switches.
The scanning rate is controlled by changing the frequency
of clock, it ranges from few lines per second to 10 lines per second,
limited by the response of light deflector. Since the light deflector
; electro-mechnical devices operated at critical damping condition,
the transition time of light spot from, one switching unit to another
constant, measured at 25-7 i^sec . becausi the driving signal
109
changes level faster than the deflector response. Then, the
T
2
parameter =— is related to the clock frequency f by
1
T 2 16
T ' ^E
1 1 - f x 25.7 x 10
To measure the transmission efficiency T and injecting noise factor r\ ,
one applies a d-c voltage V to one of the input channels and grounds
the rest of them. Then, switching the input channel to one of the
output channels, the output voltage "becomes
v Q = rv + t^V
The first part on the right is then a d-c term (information transmitted)
and the second part is an a-c term (noise). Therefore, by measuring
both d-c and a-c component, one can determine both r\ and I\ The
measurement of one of the channels is shown in Figc kl. Since rj
is an a-c term, peak-to-peak value is plotted.
To determine the cross -talk factor, the switched input channel
is grounded and the rest of input channels are applied with d-c
voltage V. Then the output is
V Q = p(n-l)V
in which n is the number of input channels. In the measurement one
cannot determine the meaningful quantities, because it is smaller than
the noise picked up by the panel and leads . It is negligibly small
as expectedo
110
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8 . SUMMARY
The aim of this work is to present a new approach of
switching matrix system. Theoretical analysis of various factors
in this system has "been done. It leads to several general con-
clusions, (l) The photoconductor must have large decay to rise
time ratio. (2) The photoconductor must have large dark-to-on
resistance ratio. (3) The system must not suffer from high
background light, and (h) To have the system operate properly,
high load resistance at output channel is required.
An experimental model has been constructed and tested.
It proved that the system is feasible indeed .
The capacity of the system can be extended to the order
3 h
with 10 ~ 10 switching unit per panel is the integration technique
is used to construct the matrix panel. A high resolution and high
speed light deflecting system is then necessary for proper system
performance.
LIST OF REFERENCES
[1] Wo Shockley and W. T. Read, Jr., Phys . Rev ,, 87,
PP. 835; 1952.
[2] R, N. Hall, Phys. Rev ., 87, pp. 387; 1952 .
[3] L. Bess, Phys. Rev ., 105, PP« 1469; 1957-
[4] L. Bess, Phys. Rev .;, Ill, pp. 129; 1958.
[5] Ao Rose, Phys. Rev ., 97. PP° 322; 1955-
[6] H. Y. Fan, Phys. Rev., 92, pp. 1424; 1953
[7] R. Ho Bube , Photoconductivity of Solid , John Wiley
and Sons, New York; i960.
[8] A. Rose, Concept in Photoconductivity and Allied Problem ,
I nt e rscience; 1963 •
[9] G. A. Dussel and R. H. Bube, J. of Appl . Phys., 37 . PP.
934; 1966.
[10] A. L. Bloom, Proc. IEEE, 54, No. 10, pp. 0262; 1966.
[11] T. S. Chu, B. S.T.J.,, 45, pp. 2.87; .1.966.
[12] H. Kogelnik and T, Li, Proc. IEEE , 54, No. 10, pp. 1312; 1966.
[13] K. Wo Boer, Physica S tatus Solid! , 8, pp. K179; 1965.
[14] Midwestern Instruments Bulletin OE-1053> Tulsa, Oklahoma.
[15] Ao Korpel, R. Adler, etc., IEEE J. of Quantum Electronics ,
QE-1, pp. 60; I96S o
[16] A. Korpel, etc, Free.. IEEE, Vol. 54, Ko„ 10, pp. 1429; 1966.
[17] W. Haas, R. Johannes, and P. Cholet, Applied Optics , Vol. 3,
Nco 12, pp. 1504; 1964.
W. Kulcke, To J. Harris, K. Kosanke and E. Max, IBM Journal ,
65; January 1964.
L , Wallman , Storage of Analog Vari ables in Delay Lines ,
M.S-. Thesis, University of Illinois; 196*8.
112
113
VITA
Tuh Kai Koo was born on September lk, 1936, in
KainSu, China . He received the Bachelor of Science degree
from National Taiwan University, Taipei, Taiwan, China, i960.
In 1962, he enrolled with the School of Mines and Metallurgy,
University of Missouri, Rolla, Missouri, where he received the
Master of Science degree in 1963°
He joined the Circuit Research Group of the Computer
Science Department at the University of Illinois in the fall of
1963. He has been a half-time research assistant to continue his
graduate work since then.
He is a member of Sigma -Xi, Kappa -Mu-Epsi Ion and the
Institute of Electrical and Electronic Engineering.
UNCLASSIFIED
Security Classification
DOCUMENT CONTROL DATA - R&D
(Security claealtlcatlon of title, body of abatract and Indexing annotation muat be entered when the overall report ia classified)
I ORIGINATING ACTIVITY (Corporate author)
Department of Computer Science
University of Illinois
Urbana, Illinois 61803
2a. REPORT SECURITY CLASSIFICATION
Unclassified
2b CROUP
3 REPORT TITLE
Optoelectronic Switching Matrix
4 DESCRIPTIVE NOTES (Type of report and inclusive datea)
Technical Report; Ph.D. Thesis
5 AUTHOR^) [Last name, first name, initial)
Koo, Tuh-Kai
6 REPORT DATE
June, 1^68
7a- TOTAL NO. OF PAGES
113
7b. NO. OF REFS
19 ■
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6. PROJECT NO.
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10 AVAILABILITY/LIMITATION NOTICES
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None
12. SPONSORING MILITARY ACTIVITY
Office of Naval Research
219 South Dearborn Street
Chicago, Illinois 60604
A cross-bar type switching matrix system with photoconductive cells as
basic switching elements and an optical signal as the switching driving source has
been studied and developed. The switching unit at each crosspoint in the matrix
contains three photoconductive cells in T-connection, in which the center branch is
grounded and the two arm branches are connected to input and output channels re-
spectively. Switching action is accomplished by scanning the matrix panel with a
programmed light beam. The state of a switching unit depends upon whether the
center branch or the arm branches are being excited by the light beam.
The equivalent circuit of a photoconductive cell under the specific application
has been developed. The complete equivalent circuit contains harmonic terms which
are the consequence of optical beam scanning. These harmonic terms are responsible
for the noise appearing at the output.
The performance of the system is analyzed with the equivalent circuit. Its
characteristic is described by defining transmission efficiency, cross-talk factor
and injection noise factor. One finds that satisfactory functioning of the system
requires a photoconductive cell with a large ratio of off (dark) -resistance to on
resistance and a large ratio of decay time constant to rise time constant. The
scanning rate of the light beam is also an important factor in the good performance
of the system.
A prototype system with a capacity of four input channels and four output
channels has been constructed to demonstrate the feasibility of the idea. Experi-
mental results were very satisfactory.
DD
FORM
1 JAN 64
1473
UNCLASSIFIED
Security Classification
UNCLASSIFIED
Security Classification
14
KEY WCRDS
Optoelectronic Switching Matrix
inducing factors
LINK A
ROLE
LINK C
ROLI WT
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