NASA Technical Reports Server (NTRS) 19970001823: Computer Analysis of Electromagnetic Field Exposure Hazard for Space Station Astronauts during Extravehicular Activity

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by  NASA Technical Reports Server (NTRS)

NASA-CR-202587
AI AA-95-1 049 .
Computer Analysis of Electromagnetic
F=eld Exposure Hazard for Space Station
Astronauts During Extravehicular Activity
S. Hwu and J. Kelley
Lockheed Engineering & Sciences Company
Houston, TX
R. Panneton and G. Arndt
NASA/Lyndon B. Johnson Space Center
Houston, TX
Life Sciences and Space
Medicine Conference
April 3-5, 1995 / Houston, TX
For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics
370 L'Enfant Promenade, S.W., Washington, D.C. 20024
AIAA-95-1049
COMPUTER ANALYSIS OF ELECTROMAGNETIC FIELD EXPOSURE HAZARD FOR
SPACE STATION ASTRONAUTS DURING EXTRAVEHICULAR ACTIVITY
Dr. Shian U. Hwu*,James S. Kelley
Lockheed Engineering& Sciences Company, Houston, TX 77058
Robert J. Panneton, Dr. G. DickeyArndt
NASA/Lyndon B.Johnson Space Center, Houston, TX 77058
Abstract Computational Electromagnetics (CEM)
techniques were presented intheir studies.
In order to estimate the RF radiation hazards to
astronauts and electronics equipment due to There are concerns about the levels of electric
various Space Station transmitters, the electdc field strength produced by the Space Station
fields around the various Space Station antennas communication andtracking systems transmitters.
are computed using the rigorous Computational Users of the Space Station designing scientific
Electromagnetics (CEM) techniques. The Method experiment payloads need to know the levels of
of Moments (MoM) wasapplied tothe UHF andS- electromagnetic fields in the Space Station
band lowgain antennas. The Aperture Integration environment. Astronauts are required to assemble
(AI) method and the Geometrical Theory of and maintain the Space Station. To ensure the
Diffraction (GTD) method were used to compute astronaut safety and mission success, the
the electric field intensities for the S- and Ku-band
electromagnetic fields produced by the Space
high gain antennas. As a result of this study, The
Station varioustransmitters need to be quantified.
regions in which the electric fields exceed the
This studyistoquantify and analyze the near-field
specified exposure levels for the Extravehicular
strengths and power densities around the Space
Mobility Unit (EMU) electronics equipment and
Station various UHF, S-, and Ku-band antennas,
Extravehicular Activity (EVA) astronaut are
as shown in Fig.l, based on the rigorous
identified for various Space Station transmitters.
computational electromagnetic methods.
I.Introduction
In recent years, due to the advance of computer
and computational electromagnetics, rigorous
Predicting the near-field intensities (strengths)
prediction methods have been developed which
around an antenna and structures is important in
can be used in the early design stage to
assessing personnel and electronic equipment
complement the costly experiment process. A
Radio Frequency (RF) exposure hazards. 1Gdffin
reliable computational tool provides for the early
experimentally studied the electromagnetic fields
detection of problems and helps to find the
in the Space Shuttle payload bay due to the Ku-
solutions. Predicting the electric field strengths
band antenna. 2'3Murphy analyzed and presented
closeto an antenna is not trivial. Within the near
the obtained Space Shuttle flight experiment data
field, far-field approximations are no longer valid,
for the electromagnetic fields produced by the
and hence more rigorous numerical techniques
Space Shuttle S- and Ku-band antennas. No
and more complex antenna models have to be
prediction techniques based on the rigorous
applied. In this study, the Method of Moments
"Principal Engineer
Senior Member, AIAA
Copyright© American Institute ofAeronautics andAstronautics, Inc., 1995. All rights reserved.
(MoM), the Aperture Integration (AI) method, and
A= l, ] #s,+fs z #s' (2)
the Geometrical Theory of Diffraction (GTD)
, w2_a(s') R
method were used to compute the electric field
intensities.
1 dl e-JkR
dS'J
The regions in which the electric fields exceed the 2_m(s' ) ds' R
specified maximum permitted RF exposure to the
(3)
Extravehicular Mobility Unit (EMU) electronic
equipment and Extravehicular Activity (EVA)
and R=[r-r'[ is the distance between an arbitrarily
astronaut are identified for the Space Station
located observation point r and a source point r'
various UHF, S-, and Ku-band antennas. Contour
on S. In (2) and (3), the wavenumber k=-2_/X,
curves of equal electdc field strength are
where X is the wavelength, s and g are the
presented at selected field strength levels.
permittivity and permeability, respectively, of the
surrounding medium, s' is the arc length along the
II. Low Gain Antenna Analysis
wire axis, and a isthe radius of the wire.
A technique to predict the near field strengths has
The current is written as a linear combination of
been developed by Wilton and Hwu 47. The
subdomain basis functions with unknown
electric field integral equation (EFIE) is formulated
expansion coefficients. These unknown
in the frequency domain using the vector and
coefficients are obtained by applying the method
scalar potential description for an arbitrarily
of moments for solving the integral equation,
shaped, perfectly conducting structure consisting
of surfaces and wires. The surfaces are modeled
The vector and scalar potentials A and _ can be
by planar triangular patches, and thin wires are
calculated at any point in space according to the
modeled by piecewise linear segments. The
formulas (2) and (3). Finite differences were used
integral equations are formulated via the
to approximate the gradient and curl operations,
equivalence principle, and the method of
and hence to determine the near electric and
moments is applied to solve for the currents
magnetic fields at a given point. Detailed
induced on the boundary surfaces of the system.
procedures may be found in Wilton and Hwu.7.
The current distribution on the structure can be
obtained for each specified excitation by solving
II.a. UHF Low Gain Antenna
the resulting matrix equation. From these
currents, the near field can be obtained.
The Space Station UHF antenna transmit
frequency is 413.5 MHz. The electric field
Let S denote a configuration of an antenna
strength levels that an EVA astronaut or sensitive
immersed in an incident electromagnetic field. In
electronic equipment might experience from UHF
general, S may consist of a collection of
antenna system operation are required to comply
conducting bodies SB and wires Sw. An electric
with specified RF radiation protection criterion.
field E_, defined to be the field due to an
impressed source in the absence of S, is incident
A radiated power of 5 watts is used for the UHF
on and induces surface current J and total current
quadrifilar helix antenna for the high power
I on SB and Sw respectively. A pair of coupled
communication link between the Space Station
integral equations for the configuration of wires
and Shuttle Orbiter. The maximum permitted RF
and bodies may be derived by requiring the
exposure to the EMU at the UHF frequencies is
tangential component of the electric field to vanish
3.16 Vim peak, as shown in Fig. 2. The maximum
on each surface. Thus we have
permitted RF exposure to the EVA astronauts at
the UHF frequencies is shown in Fig. 3. The
w),.. (1)
regions in which the electric fields are greater than
the maximum permitted RF exposure to the EMU
where
at the UHF frequencies are identified in Fig. 4.
For 5 watts radiated power, a cylindrical region of
14 meter diameter and 10 meters in length,
extending 9 meters forward and 1 meter backward
from the
antenna and centered about the Traditionally, the AI method has been widely used
boresight axis, should be avoided to reduce the for calculating aperture antenna patterns in the
risk associated with excessive UHF antenna RF forward region, which includes the main beam and
exposure to the EMU electronic equipment. the near-in sidelobes. The physical optics
approximation is used. The approximation fails in
As shown in Fig. 3, the maximum permitted RF the shadow region of the aperture antenna
exposure to the EVA astronaut is an avera_le because the currents on the shadow side of the
power density of 1.378 mW/cm 2 (13.78 W/m'), antenna are neglected. For the calculation of
which is an electric field intensity of 102 Vim peak these wide-angle sidelobes, the GTD has been
(or 72 Vim rms) at the UHF frequency of 413.5 found very efficient and accurate. The
MHz. For 5 watts radiated power, the electdc field combination of AI and GTD methods was applied
intensity criterion will not be exceeded by the UHF in this study for the numerical analysis of the high
antenna if the EVA astronaut stays further than gain horn and reflector antennas.
0.5 meter from the antenna.
The AI technique has been widely used for
ll.b. S-Band Low Gain Antenna calculating aperture antenna patterns in the
forward region. The approximations used in this
The Space Station S-band omni antenna transmit technique are: The current density is zero on the
frequency is 2.265 GHz. The electric field shadow side of the antenna. The discontinuity of
strength levels that an astronaut or sensitiv_ the current density over the rim of the antenna is
electronic equipment might experience due to S- neglected.
band antenna system operation are required to
comply with specified RF radiation protection The radiation field of an aperture antenna can be
criterion. computed by integrating the field distribution on
the aperture. For an aperture antenna with
Forty watts of maximum radiated power is used in aperture defined in the X-Y plane and pointed
this analysis for the S-band quadrifilar helix along the Z-axis, the radiation field (E) can be
antenna. The maximum permitted RF exposure to computed by
the EMU at the S-band frequencies is 106 Vim
peak as shown in Fig. 1. The regions in which the
electric fields are greater than the maximum E =Jkjj[Fxe x +F e _e-j*R dxdy, (4)
21r _ Y Yl R
permitted RF exposure to the EMU at the S-band
frequencies are identified in Fig. 5. Based on the
where exand eyare the x- and y-components of the
results obtained for the 40 watts radiated power, a
aperture field. Fx and F, are the modified vector
cylindrical region of 1.1 meter diameter and 0.8
element patterns associated with two Huygen's
meter in length, extending outward from the
sources. R is the distance between a field point
antenna and centered about the boresight axis,
and a source point. The wavenumber k = 2mr.,t,
should be avoided to protect the EMU electronics.
where _.is the wavelength.
As shown in Fig. 2, the maximum permitted RF
In the numerical integration, the aperture is
exposure to the EVA astronaut at the S-band
treated as a collection of overlapping
frequencies is an average power density of 5
subapertures. Each subaperture is square in
mW/cm 2 (50 W/m2), which is an electric field
shape and consists of four adjacent grid squares.
intensity of 194 Vim peak (or 137 Vim rms).
The field distribution for each subaperture is
Based on the results obtained for 40 watts
triangular which permits a piecewise linear
maximum radiated power, as shown in Fig. 5, the approximation to the overall aperture field
electric field intensity criterion for the EVA
distribution. Detailed descriptions of the method
astronaut will not be exceeded by the S-band can be found in Rudduck e.
antenna provided the EVA astronaut stays further
than 0.5 meter from the S-band omni antenna.
GTD gives valid results in the shadow region of
horn and reflector antennas since the currents on
III. Hi,qh Gain Antenna Analysis
either side of the edge are accounted for
implicitly. This method is finding increasing
applicationto hornandreflectorantennasforthe and the specified minimum antenna gain (13
antennapatternsinfar-outsidelobeandbacklobe dBic):
regions.
Pr_.rnax(16dBW)+G(13dBic)=EIRP_BaX(29dBW)
At high frequencies the scattering fields depend Pr._m,n(13.3dBW)+G(13dBic)=EIRP._m_n(26.3dBVV)
on the electrical and geometrical properties of the
scatterer in the immediate neighborhood of the In the aperture integration, a TEll mode aperture
point of reflection and diffraction. Thus, the total field distribution is assumed for the S-band conical
fields (E°f) can be obtained by summing up the horn antenna. The square grid size was set to be
individual contributions of the direct field (L_"), 0.01 X2. The results correlate well with that using
reflected field (E'f), and diffracted field (E_f), as 0.0025 ;_2square grid size. To further validate the
follows: S-band antenna model used in the computer
simulation, experimental measurements were
E'°'=E + + gzEE. . (5) performed in the antenna test range. Good
agreement is obtained for the computed and
n=l m=l
measured antenna radiation patterns. Detailed
descriptions and data can be found in Hwu 1°.
The diffracted fields are related to the incident
fields by means of diffraction coefficients. In a
The maximum permitted RF exposure to the EMU
similar way, the reflected fields are obtained using
reflection coefficients. Since the diffracted field is is 106 Vim peak at the S-band frequencies. The
regions in which the electric fields are greater than
determined solely by the incident field and the
the maximum permitted RF exposure to the EMU
local nature of the scattering surface, it is possible
at the S-band frequencies are identified in Fig. 6.
to derive a diffraction function relating the incident
Based on the results obtained for the maximum
field to the diffracted field for a certain scatter
radiated power (40 watts or 16 dBW), a cylindrical
geometry, a so called canonical configuration.
Detailed descriptions of the method can be found region of 1 meter diameter and 2.3 meters in
in Rudduck 8and Kouyoumjian 9. length, extending outward from the antenna and
centered about the boresight axis, should be
avoided to reduce the risk associated with
lll.a. S-Band Steerable Hi,qh Gain Antenna
excessive S-band antenna RF exposure to the
EMU electronic equipment. The maximum
The S-band subsystem, also known as the
permitted RF exposure to the EVA astronaut is an
Assembly/Contingency Subsystem (ACS), is a bi-
average power density of 5 mW/cm 2(50 W/m 2) or
directional RF link utilizing the Tracking and Data
an electdc field intensity of 194 Vim peak (or 137
Relay Satellite System (TDRSS) S-band Single
Vim rms) at the S-band frequencies. Based on the
Access (SSA) service to receive audio, software
results obtained for a maximum radiated power
uploads, and commands from the ground station,
and to transmit audio and core element telemetry (40 watts), the electric field intensity criterion will
not be exceeded by the S-band antenna if the
to the ground station. In addition, the S-band
EVA astronaut stays outside of a cylindrical region
subsystem is utilized to support ground based
of 0.5 meter diameter and 1.3 meters in length,
tracking services for station orbit determination.
extending outward from the antenna and centered
The transmit frequency for the S-band antenna is
2.265 GHz. The near-field intensity levels around about the boresight axis.
the Space Station produced by the S-band high
III.b. Ku-Band Steerable Hi,qh Gain Antenna
gain antenna are a real concern because of the
high radiated power.
The Ku-band subsystem is a single direction RF
A maximum of 40 watts (16 dBW) and a minimum link utilizing the TDRSS Ku-band Single Access
of 21.4 watts (13.3 dBW) radiated power (Pr) at (KSA) service to transmit payload data and video
to the ground station. The transmit frequency for
the antenna aperture were estimated for the S-
the Ku-band antenna is 15 GHz. The near-field
band high gain steerable horn antenna. These
estimates are based on the maximum estimated intensity levels around the Space Station
Effective Isotropic Radiated Power EIRP (29 produced by the 6-ft. reflector antenna are a
matter for concern.
dBW), the minimum specified EIRP (26.3 dBW)
A maximum of 10 watts(10 dBW) anda minimum EVA astronautstaysoutside of acylindrical region
of 4 watts (6 dBW) radiated power (Pr) at the of 2.5 meters diameter and 5 meters in length,
antenna aperture were estimated for the Ku-band extending outwardfrom the antenna and centered
reflector antenna. These estimates are based on aboutthe boresightaxis.
the maximum allowable EIRP (56 dBW), the
minimum allowable EIRP (52dBW), and the IV. Concluding Remarks
specified minimum antenna gain (46 dBic):
In thispaper,the electric field strengths due to the
Pr._rnax(10dBW)+G(46dBic) = EIRP._max(56dBW) Space Station UHF, S-band and Ku-band
Pr._min(6dBVV)+G(46dBic)= EIRP_.min(52dBVV) transmitters was presented. The rigorous method
of moments, aperture integration method and the
Inthe aperture integration process,the square grid geometrical theory of diffraction method were
size wassetto be 1X2.The results agreewell with applied in this study. These computational
that using 0.25 X2 square grid size. In the techniques can be used in the early design stage,
numerical integration, the aperture field is when the hardware is not yet available, to identify
approximated by a collection of overlapping and solve problems earlier. They can also
subapertures withtriangular field distribution.As a complement the costly experiment process in the
consequence of this piecewise linear system performance evaluation. As a result of
approximation of the aperture field, the grid size this study, the regions in which the electric fields
can be increased to reduce the field sample exceed the specified maximum permitted RF
number without losing accuracy. The simulations exposure to the EMU electronic equipment and
were carried out on a Cray X-MP/EA 464 astronaut are determined. This information is
supercomputer. To further validate the Ku-band important in assessing personnel and electronic
antenna model used in the computer simulation, equipment RF exposure hazards and is useful for
experimental measurements were performed on the usersofthe Space Station designing scientific
the antenna test range. Good agreement was experiment payloads to be operated inthe Space
obtained for the computed and measured antenna Station environment.
radiation patterns. Detailed descriptions and data
can be found inHwu11. Acknowledqments
The maximum permitted RF exposure tothe EMU This workwas supported byNASA/Johnson Space
is20 Vim peak (or 14.14 Vim rms) atthe Ku-band Center under contract NAS9-19100. The authors
frequencies. The regions in which the electric would like to acknowledge Dr. Teh-Hong Lee of
fields are greater than the maximum permitted RF the Ohio State University, James A. Porter of the
exposure to the EMU at the Ku-band frequencies NASA/JSC and Jon S. Foumet of the Lockheed
are identified in Fig. 7. Based on the results Engineering and Sciences Co. for their valuable
obtained for a maximum of 10 watts radiated discussions.
power, a cylindrical region of 2.5 meters diameter
and 230 meters in length, extending outward from References
the antenna and centered about the boresight
axis, should be avoided to protect the EMU 1Griffin, B. L., and Blount, R. L. "The
electronic equipment and reduce the risk Electromagnetic Environment for the Space
associated with the Ku-band antenna RF Shuttle Orbiter," AIAA Paper 83-0332, Jan. 1983.
exposu re. 2Murphy, G. B., and Shawhan, S. D., "Radio
Frequency Fields Generated by the S-Band
The RF radiation protection criterion specified for Communication Link on OV102," Journal of
the EVA astronaut is an average power density of Spacecraft and Rockets, Vol. 21, July-Aug. 1984,
5 mW/cm 2(50 W/m 2)or an electric field intensity pp. 398-399.
of 194 Vim peak (or 137 Vim rms) at the Ku-band 3Murphy, G. B., and Cutler, W. D. "Orbiter
frequencies, same as for the S-band frequencies. Environment at S- and Ku-Band Frequencies,"
Based on the results obtained for a maximum of Journal of Spacecraft and Rockets, Vol. 25, No. 1,
10watts radiated power, the 194 Vim peak (or 137 1988, pp. 81-87.
Vim rms) electric field intensity criterion will not be 4Wilton, D. R. and Hwu, S. U. "JUNCTION
exceeded by the Ku-band antenna so long as the Code User's Manual," Technical Document No.
1324,NavalOceanSystemsCenter,SanDiego,
CA92152-50001,988.
_Hwu, S. U. and Wilton, D. R.,"
ElectromagneticScatteringand Radiationby
ArbitraryConfigurationosfConductinBgodiesand
Wires," TechnicalDocumenNt o. 1325,Naval
OceanSystemsCenter,SanDiego,CA92152-
5000,1988.
6Hwu, S. U. and Wilton, D. R.,"
ElectromagneticNear Field Computationfor
ArbitraryConfigurationosfConductinBgodiesand
Wires, "TechnicalReportNo. 88-11,Applied
ElectromagneticsLaboratory,Departmentof
ElectricalEngineering, University of Houston, __
1988.
7Hwu, S. U., Fournet, J. S., Eggers, D. S., Arndt, _:'_'__.
G. D., "Space Shuttle EMI Analysis :_
Electromagnetic Field Strength Around WISP v_r_
Payload," 1992 IEEE International _
Electromagnetic Compatibility Symposium, and - an
Anaheim, CA, August 1992.
8Rudduck, R. C., and Chang, Y. C., "Numerical
Electromagnetic Code - Reflector Antenna Code
(NEC-REF)," ElectroScience Laboratory, The Fig. 1.Space Station various antennas.
Ohio State University, Dec. 1982.
9R. G. Kouyoumjian, R. G., and P. H. Pathak,
P. H., "A Uniform Geometrical Theory of
Diffraction for an Edge in a Perfectly Conducting
Surface," Proceedings of the IEEE, Vol. 62, No.
11, 1974, pp. 1448-1461.
l°Hwu, S. U., Lu, B. P., Johnson, L. A.,
Fournet, J. S., Panneton, R. J., Eggers, D.S., Maximum Pern-liLI.ed ]2FExposure on Ule F.MU
Arndt, G. D., "Scattering Effects of Space Station retiredE_31C111T92,,Cperr,,LEtnp,u.lOw,,TbEy,_S.d,TW,'hYStfcro.r,nbEqUIA.E2.W,6C[6__0",HIIA.M-.S,T_D.C,,,]
Structure on Assembly/Contingency Subsystem "'JIH,,,| IIIlt,, } Illl)lll I ll}|]l]m_
(ACS) Antenna Performance," AIAA Paper 92- _ ,_,--
1538, Mar. 1992.
11Hwu, S. U., Johnson, L. A., Fournet, J.S., ml,,, ,,-o,o'.,.,,-,...-.,...o,,,,,,,o,.o..,_.,.,.,,,,,.._.
Panneton, R. J., Eggers, D. S., Amdt, G.D., __llJlrll[J rfl[ll[I Illl_l_
"Scattering Effects of Solar Panel on Space ,_,
Station Space-to-Ground (SGS) Antenna _-]-II/ll/I I II1(1111_Jllljllllll ! l ltllll _o
Performance," AIAA Paper 92-1941, Mar. 1992. -' -_ ]_t_ll_tt__ ,°
l:_1 4
, ,olIIIHI,I I ,olllllo,],
_z..-¢ ._.,_ce _.t.v._Tjz FREQUENCY in GIGAHERTZ xjr_j_L_,..,vp_
Fig. 2. The maximum permitted RF exposure on
EMU electronics.
0.8
.... 106
07 ."" "''""
°° i",
05- , ",
Average Power Density In MIIliwatts/Centlme ter2 JSC-le79e
. April 1981 0.2 -
I00.
I ,1I/:_I:''"IHlllITl[IlA.VItfsii,JI,lIl+l_'-iTli":Wl1,:.f1lYYT1ii'[iil_,:II'_P'I']+I:II',R_llnl._."_i.'_.".ro"mn_"I'mEm''PmmlPiil.l.l_..'.[.'_l'IX'tq'o'lli4_REFqIM_JIlC:llIh|Oh+W":A'lVE Il'l'"_[__,_.l_J'lI.]l`'t O0.]0 -- ",,, _,+_ _._:_,]
-+.. Acre. (,_.),,m., _t_!!i!a.... g.d.... 01..... t._,.,,t..P._tLtI!I"II_E ..........
I0.
101<14.... lheRF,,,,,, .... I_;II_II!_I!HI_I_ iJl _ iI_li_i_iM_,o EMU _xposurelimit = 106V/m
5
.!, I _IilllIIPN,I,",.,:_ltJHll+.4;E!+_tliJtt#_l+I1'_.tt.llt,°+_o.7o -o1++ oloo o:++
0.70
ItIl_ll_;_f:i']:llCJ_6' ,,ors/melerl[.]l_L1l_3+_v]:oLltsl/e£'
I.
: +t I : ++: l P+++! Fig. 5. The electric fields produced by the S-band
A^CNGSlItt =A:mAen,Ilce.ln'icarl N.llCoonaall ....StaCndearedlsGoreI s..l...l.ule Inl and Induslrlal HYge.'s',_Ir'l_,'L+:_{].L_T+'pItl"low gain antenna with 40 watts radiated power.
1985, Iho Federal Commtlntcallon Commlaslon adopted Ihe 1982 ANSI standard, t
In 1986, Ihe NaIIon_=II Co.nclt for Rndlallon Prolecllort adopted Ihe 1982 ANSI slandard.i
0.1
lOOKl4z IMHz 10Ml4z 100MHt 16}lz lO6tlt
FREQUENCY Space Station S-Band High Gain Antenna
Peak E-Field _//m), Radiated Power = 40 Walls
Fig. 3. The maximum permitted RF exposure on
EVA astronauts.
0+_-
_j co-
>.-
-- 62 ---.___ 62
+..--'3 "-+.+ .O+I
8- .. ...
o, Z (METERS)
•" EMU exposure limit = 3]6 V/m
7-
Fig. 6. The electric fields produced by the S-band
6 high gain antenna with 40 watts radiated power.
5
4
Space Station Ku-Bend 6-ft Reflector Antenna
Peak E-field (V/m), Radialad Power _ 10 Watts
us _ /::2" ..o--- 2o
N 2 +: ........... ....................
I -_-._:.,.,._-_ '--,. o ".,. _o
! ,
0
-I
...... _ __ _o
-2
-B -6 -4 -2 0 2 4 6 5O _oo I_.o _b;30 2_0 3GO
Y (METERS)
Z {METERS)
Fig. 7. The electric fields produced by the Ku-
Fig. 4. The electric fields produced by the UHF band high gain antenna with 10 watts radiated
low gain antenna with 5 watts radiated power. power.