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unknown variable Kj. (i.e. g,(Kr)= g,K, + go, g , , go are two integers.) Now suppose f is a one-way function of degree d. Then the
coeflicient g,(K,) in eqn. 1 is substituted for the functionf. Consequently, we have
f(gi(Ki)) = K j
=(e,dKt e j ( d - , ) K f ’ +. ’ .
ejlK, ejo) mod P for j = 1.2. . . , d
Measuring technique for characterising the
electrical properties of piezoelectric tubular
A.M. Sabatini and P. Dario
Indexing terms: Piezoelectric devices, Polymers
We have d equations and d variables, by the Gauss elimination
method [3], thus when d immediate successors of the security class
C, collude, the secret key K, of C, is revealed. In fact, only one
security class is needed to break the scheme when the one-way
function is in quadratic residue modulo (i.e.flX) = g,X + g , X + go
mod P.)[4]. Therefore, when the one-way function is a polynomial
of degree d, they need d - 1 immediate successors for conspiracy
Modijications and discussions: From the above statements and
example, we see that d - 1 security classes can attack the one-way
function of degree d . We now give two modifications for withstanding this attack.
(i) Modifieation 1: Each security class has its own private one-way
function. This means that the one-way function 1; has to be kept
secretly by the security class C, and the third party.
Modification 2: Choose a one-way function of degree d + 2
where d is a maximal number of immediate successors of each
security class in the whole system.
Although Modification 1 can prevent conspiracy attack, it
wastes a large amount of storage space to store these one-way
functions. Modifcation 2 not only keeps the advantage of the proposed scheme but also enhances the security.
Acknowledgment: This research was partially supported by the
National Science Council, Taiwan, ROC, under contract no.:
NSC82-0408-E-009-161, and by the Telecommunication Laboratories, Taiwan, ROC, under contracts no.: TL-NSC-82-5206.
The Letter describes a simple measuring technique which is useful
for characterising in a nondestructive manner the electrical
properties of tubular devices made from piezoelectric polymers.
The proposed measuring technique allows us to estimate the socalled d3J’ constant, a parameter often used for evaluating
piezoelectric activity.
Introduction: Recent substantial advances in the production of
synthetic polymers have made possible the conception, fabrication
and testing of a variety of medical devices to be used in basic
research as well as in clinical investigations. Among them, piezoelectric materials, such as polyvinylidene fluoride (PVDF) [I], or
electret materials, such as polytetrafluoroethylene (FTFE) [2], have
been proposed and used as guidance channels, that is small tubular devices, in a number of applications that require some physical
agents for promoting regenerative processes. The ability of piezoelectric materials to enhance tissue regeneration is believed to be an
effect of their electrical properties. Hence, simple means for characterising these properties in a nondestructive manner are
required. A thorough investigation of the properties of piezoelectric materials requires considerable effort [3]; in some cases, however, a simple characterisation is sufficient for the purpose of
comparing different devices under identical operating conditions
[4], so as to select samples with roughly equivalent properties for
the intended application.
Theory of measurement: The aim of this Letter is to describe the
simple apparatus we propose for measuring the so-called 4,’ constant of piezoelectric tubular devices. Refer to Fig. 1 for an explanation of the terms and notation usually adopted in dealing with
piezoelectric planar films [3]. The transverse and machine directions refer to the directions along which the mechanical stretching
of the film must be exerted; the poling direction relates to the
direction of the electric field to be applied to the stretched material
during the fabrication of the device. Both processing steps are necessary for inducing proper conformation changes in the crystalline
structure of the polymer so as to make it piezoelectrically active.
8 IEE 1993
20 September I993
Electronics Letters Online No: 19931391
M.-S. Hwang and W.-P. Yang (Department of Computer and
lnformation Science, National Chino Tung University, Hsinchu, Taiwan
300. Republic of China)
C.-C. Chang (Institute of Computer Science and Information
Engineering, National Chung Cheng University, Chiayi, Taiwan 621,
Republic of China)
M.-S. Hwang is also with the Directorate General of
Telecommunication Laboratories, Ministry of Transportation and
Communications, Chung Li, Taiwan 320, Republic of China
HWANG,R.I., and W . T . C . : ‘Cyptographic key
assignment scheme for access control in a hierarchy’, Information
Systems, 1993, 17, (3), pp. 243-247
2 KNUTH. D.E.: ‘The art of computer programming, Vol 2:
seminumerical algorithm’ (MA Addison-Wesley, 1980)
3 NOBLE. E., and DAW, J. w.: ‘Applied linear algebra, 2nd Edn.’
(Prmtice-Hall, 1977)
4 SCHROEDER. M.R.: ‘Number theory in science and communication,
2nd Edn.’ (Springer-Verlag, 1985)
2 %&chine direction
Fig. 1 Axis nomenclaturefor piezoelectric films
Piezoelectric measurements on polymer films are usually made
by properly applying a mechanical tension to the sample and
measuring the short-circuit charge or the open circuit voltage on
opposing electrodes. Owing to the anisotropy of piezoelectric
materials, it is important to specify the directions along which the
mechanical tension is applied or the electrodes are placed. The d3;
constant is defined as
4 3
where A Q is the charge developed in a double-sided metallised f h
of piezoelectric material with surface area A, as a consequence of a
force AF applied in the normal direction, that is direction 3 in Fig.
1. Let E denote the transverse electric field existing between the
two electrodes. The underlying boundary condition E=O is
assumed for eqn. 1, therefore the electrodes must be shortcircuited: when the charge A Q is measured by a charge amplifier,
the short-circuit conditions are virtually met. The d3; constant is
25th November 1993
Vol. 29
No. 24
only an approximation to the true d3)value:
where T3 is the normal stress in a point of the film surface, D3 is
the electric displacement and the boundary conditions imply that
no clamping of the film is assumed: the film is free to expand
along directions 1 and 2 (in contrast to the definition of d3;, where
the impinging probe may be responsible for some clamping
In spite of being just an approximation to d3,, 4,’ is often used
in order that the apparatus used for making the measurement can
be simplified. For planar films, a non-metallised piezoelectric film
is sandwiched between an aluminum plate, acting as the ground
reference, and a flat impinging metallic probe forming the second
electrode needed for the measurement. By connecting the two electrodes to a charge amplifer, A Q can be measured. The force convertor AF exerted on the polymer film is usually measured by a
load cell, incorporated in the impinging probe.
BNC connector
paraffin wax
Fig. 2 Schematic view of measuring apparatus
Description of measurement cell: To implement the described measurement technique on tubular devices, we have designed an ad hoc
measuring apparatus, see Fig. 2. The chamber is formed by a hollow brass cylinder, threaded at both its ends; one end is capped
with a BNC connector (Amphenol RG 178), endowed with a
metallic needle soldered to its hot lead. At the other end the cylinder can be connected to a simple pneumatic circuit consisting of a
compressor capable of injecting air into it; a manometer measures
the air pressure in the circuit. Before screwing the BNC connector
to the cylinder, the tubular device to be measured is snugly fitted
into the needle; small pieces of an insulating material such as parafEn wax are then spread over that metallic part of the needle
which remains exposed. After the BNC connector has been placed
in situ, the hollow cylinder is filled with mercury and then vertically positioned by means of a suitable support: note that the
shield of the BNC connector is connected to the outer liquid electrode through the brass cylinder itself. Provided that any short-circuit condition between the two electrodes has been avoided by the
wax covering, the pneumatic circuit is connected to the cylinder by
means of its threaded end. For the pressures p of interest to our
application, ranging between 0.5 and Satm, the mercury leakage is
easily prevented by placing two 0 rings at both threaded ends.
Finally, a coaxial cable allows us to connect the measuring chamber to a charge amplifer (Kystler Type 5011). The.measurement is
made when the mercury is pressurised within the cylinder; given
that the length of the tubular device portion exposed to the liquid
mercury is L,and the outer diameter of the tubular device is Q, we
Conclusions: The measuring technique described in this Letter represents an inexepensive means for evaluating the piezoelectricconstant d33*of tubular devices. The proposed measuring technique
allows us to select batches of devices with similar electrical characteristics. It should be pointed out that:
(i) it is difficult to compare the results of our measurements to the
figures currently given for commercially available films, because
they are subjected to a mechanicay thermal process quite different
from the process to which we subject our devices
(ii) our home-made procedure of preparing samples is unable to
provide a degree of uniformity and reproducibility in the electrical
properties of the proposed tubular devices comparable to that
obtained in films of industrial origin: this might account for the
observed spreading in the measured values.
q3= -
the cylindrical surface of the tube at a distance of d = 2 mm from
it. A brass wire fitted into the lumen of the tube is used as an
inner electrode. A high intensity electric field (15-20kV) is applied
to the sample for -12h. After poling, the PVDF tubular device is
placed in the measuring chamber for performing the d3,+measurement. We have obtained d?)* values from d to -IOpC/N (values
for piezoelectric films of PVDF manufactured by Solvay are d33*=
-13.5pC/N [5]); inert devices, that is devices not subjected to the
poling procedure, were unable to elicit any significant readings
from the charge amplifier at any pressure.
0 IEE 1993
29 September 1993
Electronics Letters Online No: I9931362
A.M. Sabatini and P. Dario (Advanced Robocics Technology & Systems
Loboraiory (ARTS Lob), Scuola Superiore di Studi Universitari e di
Perfezionamenio S. Anna, Via Carducci, 40, 566127 Pisa, Italy)
P. Dario is also with the Centro ‘E. Piaggio’, University of Pisa
GALLETTI, P.M.: ‘Piezoelectric
P., WMENICI. c., and
guidance channels enhance
regeneration in the m o w sciatic nerve after axotomy’, Brain
Research, 1987,436, pp. 165-168
‘Polymer electret guidance channels enhance peripheral nerve
regeneration in mice’, Brain Research, 1989, 480,pp. 300-304
SESSLER, G.M.:‘Electrets’ (Springer-Verlag, 2nd Edn., 1987)
SABATINI, A.M.,and FIORILLO, A.s.: ‘A system for measurement of
surface charge densities on tubular electrets’, J. Measurement
Science & Technology, 1990, 1, (l), pp. 1099-1101
SOLVAY: ‘Piezoelectric SOLEF PVDF polyvinylidene fluoride
films’. Technical Note. 1991
1.5V BiCMOS dynamic multiplier using
Wallace tree reduction architecture
J.B. Kuo, K.W. Su and J.H. Lou
Indexing ierms: BiCMOS integrated circuits, Multiplying circuits
1.5V BiCMOS dynamic multiplier is presented which is free
from race and charge sharing problems, using Wallace tree
reduction architecture and a 1.5V full-swing BCMOS dynamic
logic circuit. Based on a lpm BiCMOS technology, a designed
1.5V 8x8 multiplier shows a x2.3 improvement in spcd as
compared to the CMOS static multiplier.
Experiment: The preparation of an electrically active piezoelectric
device made from PVDF is quite complex. Starting from an
extruded tube of PVDF (SOLEF XION, Solvay, Brussels, Belgium), the stretching phase of the material processing consists of
stretching the material at ll0”C (drawing ratio 1:3.5). The material is then subjected to a thermal annealing, a procedure of maintaining the sample clamped at constant tension for a while (3h at
llO”C), in order to heal the damage induced in the material by the
stretching phase. After stretching, the tubular device, presenting
an outer diameter CP = 0.9mm, is submitted to the corona poling
procedure for making it piezoelectrically active. An array of regularly spaced needle electrodes is circumferentially arranged around
ELECTRONICS LETTERS 25th November 1993
Introduction: High-speed multipliers are usually realised by
parallel architectures [I], where a Wallace reduction structure [I]
and carry look ahead circuit have been used to enhance the speed
performance. In a high-speed parallel multiplier using the Wallace
tree reduction structure, the most important building cells arc the
full adder circuit and the carry look-ahead circuit. Although the
CMOS dynamic technique [2] can provide a speed advantage over
the static technique for implementing serial adders, it is not
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