2003 IEEE Aerospace Conference, Big Sky, Montana
Transmitting Antenna Modules Refusals Reaction on Wireless Power
Transmission efficiency
Sergey S. Shaposhnikov
Moscow Radiotechnical Institute of
The Russian Academy of Sciences
132 Warshawskoe Shosse
Moscow, RU 117519 Russia
7 095 315-3125
ssshmrti@orc.ru
Dimity M. Sazonov
Moscow Power Engineering Institute
(Technical University)
14 Krasnokazarmennaja
Moscow. RU, 111250. Russia
7 095 362-7242
dsazonov@postman.ru
Abstract—Research of influence of the transmitting antenna modules refusals on Wireless Power
Transmission (WPT) efficiency and on an angular distribution of side lobe radiation is one of the
important questions for WPT systems. In the WPT radiating antennas always there is a part of
array elements, which are refused. Here an admitted percent was calculated. An influence of the
refused array elements number on the WPT efficiency was found. Pictures of field distribution
on the transmitting and receiving antennas were shown. The number results were obtained due to
essential modernization of the Computer Aim Design (CAD).
TABLE OF CONTENTS
1. INTRODUCTION AND G ENERAL STATEMENTS 2
2. TRANSMITTING ANTENNA ARRAY WITH R ECTANGULAR APERTURE 4
3. TRANSMITTING ANTENNA ARRAY WITH CIRCULAR APERTURE
4
CONCLUSIONS ...............................................10
ACKNOWLEDGMENT.....................................12
REFERENCES .................................................12
1. INTRODUCTION AND GENERAL STATEMENTS
The given research was carried out with reference to idealized model of WPT system shown on
Fig. 1.
Y
Y
X
X
Z
tg (RA) = D/2R
Rectenna Angle (RA)
L
D
Distance R
Transmit Array
Rektenna
Fig. 1. Idealized model of the WPT system
It was supposed, that transmitting antenna array has flat aperture and consists of separate
modules each with rectangular radiating aperture. Excitation phase of each module is adjusted in
an appropriate way for focusing radiation to the center of reception rectenna. This means, that
exact required (so-called “ideal”) excitation phase Φ opt for each module is determined from the
condition of in-phase addition each module partial radiation in the given focusing point. Ideal
excitation phase distribution appears square-law when transmitting antenna array and rectenna
are posed exactly as on Figure 1. Value of a required square-law outstripping phase Φ 2 at
aperture edge in comparison with its central point is under well-known approached formula
Φ 2 ~ π L2 /4λ
λR proceeding from given distance between antennas R, aperture size of transmitting
antenna L and working wave length λ The value . Φ 2 = 2π
π corresponds to the distance between
antennas L2 /8λ
λ.
Specially modernized Computer Aided Design (CAD) for the Wireless Power Transmission
(WPT) systems (WPTCAD) created by D.M. Sazonov was used as the basic tool for
calculations. The WPTCAD tool was described earlier [1]. Modernization was directed on
achievement mathematical modeling of random removal of elements in a transmitting antenna
array.
The input data at calculations of WPT systems with randomly deleted modules by means of
WPTCAD are:
1. Transmitting antenna array parameters. They are: form and sizes of the aperture, excitation
type, the type of array grid (rectangular or triangular), parameters of one element, and the
overall number and positions of deleted modules in array aperture;
2. Reception rectenna size, available in a vicinity of a field focusing point transmitting antenna
array. The reception rectenna in WPT system is modeled by round aperture ideally matched
with free space. It means acceptance of assumption that the rectenna will transform
completely all falling microwave power to direct current and does not create reradiated field
in a direction on transmitting antenna array. Calculations of WPT efficiency (it is the Power
Transfer Ratio) were carried out simultaneously in 5 various rectenna diameters in the chosen
range of sizes. It enables a fast finding of the optimum rectenna size, providing required field
intensity according to the technical requirements.
The following output data are of primary interest at calculations of WPT systems with randomly
deleted modules:
1. WPT efficiency between transmitting antenna system and reception rectenna with variable
size (5 variants simultaneously are used). It is assumed, that rectenna center coincides with
field focusing point of a transmitting antenna array.
2. The required field concentration in a focus point. This parameter is an analogue of directivity
factor for usual antennas.
3. Bi-dimensional and three-dimensional electromagnetic field distribution patterns around
focusing point.
The main basic result of our investigations is the creation of the computing subroutine to
examine WPT efficiency of the transmitting antenna arrays with randomly deleted modules. This
subroutine was organically included in the structure of WPTCAD.
Numerical research of influence of random removal or refusal of some modules in transmitting
array on parameters of WPT system was carried out on two types of transmitting arrays: with
rectangular aperture and with circular aperture. There were applied as function in each case: both
uniform and falling down to edges quasi-Gauss distribution of excitation: 0.21+ 0.79 cos 2 (π
πx/L),
where L = full aperture size.
Array steps in a square grid and sizes of radiating elements were chosen identical. For the best
comparison of results it was supposed, that in rectangular and circular array it should be used
about identical quantity of transmitting modules. Removal of elements in each realization of
transmitting array was modeled by means of a specially picked up uniform random number
sensor, a generator with zero mean random value and with standard deviation equaled to one.
Results of researches the efficiency for varying percentage of deleted modules were included in
the Figures 4 and 7. Each figure contains WPT Efficiency for 5 various rectenna sizes and for
independent realizations of elements removal in transmitting array. Illustrative field distributions
in focal area, showing changes of side lobe radiation level, also were considered for 10% of
deleted modules.
The algorithm of elements refusals modeling was extremely simple. Random number in range
from 0 to 1 was received from random number generator for each array element during cycle of
elements amplitudes evaluation.
If the received random number was less then the present threshold then the given element was
deleted, and its amplitude of excitation was adjusted to zero. Special test has shown, that this
algorithm gave enough uniform distribution of deleted elements in the array aperture.
The analysis of the results shows an opportunity of preservation of serviceability transmitting
antenna arrays for WPT systems at full refusals up to 5–10% of transmitting modules. The
increase of the percent of defected modules up to 10–20% results in essential decrease of power
transfer ratio in WPT system.
2. T RANSMITTING ANTENNA ARRAY WITH RECTANGULAR APERTURE
Research was made on precisely same antenna array, as in the previous paper [2] on research of
influence of random phase aperture errors. The array under test contains 41 × 41 = 1681
elements. Aperture dimensions of each module are 0.85 from array step. Each side of the
aperture in transmitting antenna array is 41.17ë Array steps as in X-direction and in Y-direction
both are 0.895ë.
Array aperture picture when the percent number of deleted elements was δ N/N = 10% is shown
on Figure 2a and 3a. These figures were captured from the screen of monitor at running
WPTCAD. Field distributions on focal surface are shown on Figure 2b and on Figure 3b when
δ N/N = 10%, and on Figure 3c and on Figure 4c when δ N/N = 0%.
The full analysis of WPT system was made for each given percent of deleted modules with
several independent realizations of distribution of the deleted modules in the aperture. It was
necessary for an estimation of dispersion of efficiently. It was found out, that the dispersion is
very small, however it tends to increase at increase of percent of deleted modules.
Dispersion grows appreciably for quasi-gauss aperture distributions in comparison with uniform
amplitude distribution. And this is natural, as deleted modules with small amplitudes have low
influence on the efficiency in comparison with modules with high amplitudes of excitation.
Results of calculations were shown on diagrams (see Figure 4). Conclusions by the received
results are given in final section of the report.
3. Transmitting Antenna Array with Circular Aperture
The array under test contains (46 × 46) – 452 = 1664 elements. Aperture dimensions of each
module are 0.85 from array step. The aperture diameter in transmitting antenna array is 41.17ë
Array steps in X- and Y-directions are 0.895ë. The circular aperture form was formed due to
removal of 452 angular elements from the square aperture. We shall notice that the number of
elements is less in the given circular array approximately for 1%, than in the rectangular array
considered in section 2.
Array aperture pictures when the percent number of deleted elements was δ N/N = 10% are
shown in Figures 5a and 6a. These figures were captured from a monitor screen running
WPTCAD. Field distributions on focal surface are shown on Figures 6b and 7b when
δ N/N = 10%, and in Figures 5c and 6c when δ N/N = 0%.
(a)
(b)
(c)
Fig. 2. Square Aperture Transmitting Array with uniform amplitude excitation with δ N/N =
10%; a) aperture view; b) field on focal surface δ N/N = 10%; c) field on focal surface δ N/N =
0%
(a)
(b)
(c)
Fig. 3. Square Aperture Transmitting Array with Quasi-Gauss excitation and with δ N/N = 10%:
(a) aperture view, (b) field on focal surface δ N/N = 10%, (c) field on focal surface δ N/N = 0%.
(a)
(b)
Fig. 4. Square Aperture Transmitting Array Efficiency (a-Uniform, b-Quasi-Gauss). Rectenna
Angular Size in Degrees: 1–0.8, 2–1.0, 3–1,2, 4–1.6, 5–2,0.
(a)
(b)
(c)
Fig. 5. Circular aperture transmitting array with uniform amplitude excitation with δ N/N = 10%:
(a) aperture view; (b) field on focal surface δ N/N = 10%; (c) field on focal surface δ N/N = 0%;
(a)
(b)
(c)
Fig. 6. Circular aperture transmitting array with Quasi-Gauss excitation and with δ N/N = 10 %;
a) aperture view; b) field on focal surface δ N/N = 10 %; c) field on focal surface δ N/N = 0 %;
The full analysis of WPT system was made for each given percent of deleted modules with
several independent realizations of distribution of deleted modules in the aperture. It was
necessary for an estimation of dispersion of efficiency. It was found out that the dispersion is
very small; however it tends to increase by the growth of deleted modules quantity. Dispersion
grows appreciably for quasi-gauss aperture distributions in comparison with uniform amplitude
distribution. And this is natural, as deleted modules with small amplitudes have low influence on
efficiency in comparison with modules with high amplitudes of excitation. Results of
calculations were shown on diagrams (see Figure 7).
(a)
(b)
Fig. 7. Efficiency for Circular Aperture Transmitting Array (a) Uniform excitation (b) QuasiGauss) Rectenna Angular Size in Degree: 1–0.8, 2–1.0, 3–1.2, 4–1.6, 5–2.0.
CONCLUSIONS
1. The main basic result is the essential modernization of the WPTCAD for the investigation of
the behavior of transmitting antenna arrays with failure modules. The demo version
WPTCAD was created with opportunities of deleting some percent of overall number of
modules in transmitting antenna array. This version can be situated on 3.5” diskette.
2. The carried out numerical researches enable to establish quantitative connections between the
decrease of the WPT efficiency and percent of the deleted modules in transmitting antenna
array.
3. It is established, that the efficiency of WPT system in separate realizations at identical
number of deleted modules has insignificant dispersion of values.
4. It was shown, that it is allowed refusal up to 5–10% from the general number of array
modules.
5. It follows from submitted results that the physical reason of efficient decrease in WPT
system with failure modules is the increase of uniformly distributed on space background
side lobe radiation. Side lobe radiation extracts power from the central focal beam. The
extracted power is distributed approximately uniformly on space.
6. Accompanying changes of focal beam width and increase of maximal side lobe level are
insignificant at presence no more than 5–10% of failure modules.
7. Antenna array with circular aperture form has advantage in comparison with the rectangular
aperture array at identical number of transmitting modules and identical percent of failure
modules.
8. Use of quasi-gauss excitation in transmitting antenna arrays of WPT systems is justified only
at aspiration to extremely high efficiency (more than 0.7–0.8). For smaller allowable
efficiency the transmitting antenna array with uniform excitation has an advantage in
comparison with quasi-Gauss array at identical percent allowable efficiency. The
transmitting antenna array with uniform excitation has advantage in comparison percent of
with quasi-gauss array at identical deleted modules.
ACKNOWLEDGMENT
The authors would like to thank, engineer E. A. Tsaturyan for the paper edition and International
Science and Technology Center (ISTC) who supported this research.
REFERENCES
[1] Sazonov D.M., Microwave Circuits and Antennas. Mir Publishers, Moscow, (ISBN 5-03001411-X), 1990.
[2] Development of the Method for Producing Electromagnetic Wave Beam with Small
Divergence, 2001 International Science and Technology Center Annual Technical Report on the
Project 386-2, May, 2001.