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The Applied Technology Institute (ATIcourses.com) specializes in training
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Learn From The Proven Best!
Satellite Communication Systems Engineering
A comprehensive, quantitative tutorial designed for satellite professionals
March 16-18, 2009
Boulder, Colorado
June 15-17, 2009
Beltsville, Maryland
$1740
(8:30am - 4:30pm)
"Register 3 or More & Receive $10000 each
Off The Course Tuition."
Instructor
Dr. Robert A. Nelson is president of Satellite
Engineering Research Corporation, a consulting firm in
Bethesda, Maryland, with clients in both
commercial industry and government.
Dr. Nelson holds the degree of Ph.D. in
physics from the University of Maryland
and is a licensed Professional Engineer.
He is coauthor of the textbook Satellite
Communication Systems Engineering,
2nd ed. (Prentice Hall, 1993) and is Technical Editor of
Via Satellite magazine. He is a member of IEEE, AIAA,
APS, AAPT, AAS, IAU, and ION.
Additional Materials
In addition to the course notes, each participant will
receive a book of collected tutorial articles written by
the instructor and soft copies of the link budgets
discussed in the course.
Testimonials
“Great handouts. Great presentation.
Great real-life course note examples
and cd. The instructor made good use
of student’s experiences."
“Very well prepared and presented.
The instructor has an excellent grasp
of material and articulates it well”
“Outstanding at explaining and
defining quantifiably the theory
underlying the concepts.”
“Fantastic! It couldn’t have been more
relevant to my work.”
“Very well organized. Excellent
reference equations and theory. Good
examples.”
“Good broad general coverage of a
complex subject.”
Course Outline
1. Mission Analysis. Kepler’s laws. Circular and
elliptical satellite orbits. Altitude regimes. Period of
revolution. Geostationary Orbit. Orbital elements. Ground
trace.
2. Earth-Satellite Geometry. Azimuth and elevation.
Slant range. Coverage area.
3. Signals and Spectra. Properties of a sinusoidal
wave. Synthesis and analysis of an arbitrary waveform.
Fourier Principle. Harmonics. Fourier series and Fourier
transform. Frequency spectrum.
4. Methods of Modulation. Overview of modulation.
Carrier. Sidebands. Analog and digital modulation. Need for
RF frequencies.
5. Analog Modulation. Amplitude Modulation (AM).
Frequency Modulation (FM).
6. Digital Modulation. Analog to digital conversion.
BPSK, QPSK, 8PSK FSK, QAM. Coherent detection and
carrier recovery. NRZ and RZ pulse shapes. Power spectral
density. ISI. Nyquist pulse shaping. Raised cosine filtering.
7. Bit Error Rate. Performance objectives. Eb/No.
Relationship between BER and Eb/No. Constellation
diagrams. Why do BPSK and QPSK require the same
power?
8. Coding. Shannon’s theorem. Code rate. Coding gain.
Methods of FEC coding. Hamming, BCH, and ReedSolomon block codes. Convolutional codes. Viterbi and
sequential decoding. Hard and soft decisions.
Concatenated coding. Turbo coding. Trellis coding.
9. Bandwidth. Equivalent (noise) bandwidth. Occupied
bandwidth. Allocated bandwidth. Relationship between
bandwidth and data rate. Dependence of bandwidth on
methods of modulation and coding. Tradeoff between
bandwidth and power. Emerging trends for bandwidth
efficient modulation.
10. The Electromagnetic Spectrum. Frequency bands
used for satellite communication. ITU regulations. Fixed
Satellite Service. Direct Broadcast Service. Digital Audio
Radio Service. Mobile Satellite Service.
11. Earth Stations. Facility layout. RF components.
Network Operations Center. Data displays.
12. Antennas. Antenna patterns. Gain. Half power
beamwidth. Efficiency. Sidelobes.
13. System Temperature. Antenna temperature. LNA.
Noise figure. Total system noise temperature.
14. Satellite Transponders. Satellite communications
payload architecture. Frequency plan. Transponder gain.
TWTA and SSPA. Amplifier characteristics. Nonlinearity.
Intermodulation products. SFD. Backoff.
15. The RF Link. Decibel (dB) notation. Equivalent
isotropic radiated power (EIRP). Figure of Merit (G/T). Free
space loss. WhyPower flux density. Carrier to noise ratio.
The RF link equation.
16. Link Budgets. Communications link calculations.
Uplink, downlink, and composite performance. Link budgets
for single carrier and multiple carrier operation. Detailed
worked examples.
17. Performance Measurements. Satellite modem.
Use of a spectrum analyzer to measure bandwidth, C/N,
and Eb/No. Comparison of actual measurements with
theory using a mobile antenna and a geostationary satellite.
18. Multiple Access Techniques. Frequency division
multiple access (FDMA). Time division multiple access
(TDMA). Code division multiple access (CDMA) or spread
spectrum. Capacity estimates.
19. Polarization. Linear and circular polarization.
Misalignment angle.
20. Rain Loss. Rain attenuation. Crane rain model.
Effect on G/T.
Register online at www.ATIcourses.com or call ATI at 888.501.2100 or 410.956.8805
Vol. 97 – 53
Satellite 2001 Daily
What Is the
Radius of the
Geostationary
Orbit?
by Robert A. Nelson
Most communications satellites operate
from the geostationary orbit, since from
this orbit a satellite appears to hover over
one point on the equator. An Earth
station antenna can therefore be pointed
at a satellite in a fixed direction and
tracking of the satellite across the sky is
not required. The basic question to be
discussed is, “What is the radius of the
geostationary orbit?”
The geostationary orbit must satisfy
three conditions: (1) the velocity must be
in the direction and sense of the Earth’s
rotation; (2) the velocity must be
constant; and (3) the period of revolution
must exactly match the period of rotation
of the Earth in inertial space. The first
condition implies that the orbit must be a
direct orbit in the equatorial plane. The
second condition implies that the orbit
must be circular. To satisfy the third
condition, the radius of the orbit must be
chosen to correspond to the required
period given by Kepler’s third law.
According to this law, the square of the
orbital period is proportional to the cube
of the semimajor axis.1
The problem reduces to determining
the value of the orbital period. However,
it is not simply 24 hours, or one mean
solar day. The mean solar day is equal to
the average time interval between
successive transits of the Sun over a
given meridian and is influenced by both
the rotation of the Earth on its axis and
the motion of the Earth along its orbit.
Instead, the appropriate period of the
geostationary orbit is the sidereal day,
which is the period of rotation of the
Earth with respect to the stars. One
sidereal day is equal to 23 h 56 m
4.0905 s of mean solar time, or
86 164.0905 mean solar seconds. Using
this value in Kepler’s third law, we
compute
the
orbital
radius
as
42 164.172 km.
Relationship between the sidereal day and the mean solar day.
Yet even this value for the orbital
period is not quite correct because the
Earth’s axis precesses slowly, causing the
background of stars to appear to rotate
with respect to the celestial reference
system. The Earth’s axis is tilted by
23.4° with respect to a line perpendicular
to the orbital plane and executes a conical
motion with a precessional period of
about 26 000 years.
Therefore, the
sidereal day is less than the true period of
the Earth’s rotation in inertial space by
0.0084 seconds. On this account, the
period of the geostationary orbit should
be 86 164.0989 mean solar seconds. The
corresponding
orbital
radius
is
42 164.174 km.
There is also a correction due to the
unit of time itself. The mean solar
second is defined as 1/86 400 of a mean
solar day. However, in terms of the
second of the International System of
Units (SI), defined by the hyperfine
transition of the cesium atom, the present
length of the mean solar day is about
86 400.0025 seconds. The mean solar day
exceeds a day of exactly 86 400 seconds
by about 2.5 milliseconds due to slowing
of the Earth’s rotation caused by the
Moon’s tidal forces on the shallow seas.
This extra time accumulates to nearly one
second in a year and is compensated by
the occasional insertion of a “leap
second” into the atomic time scale of
Coordinated Universal Time (UTC).
Adding this increment to the orbital
period, we obtain 86 164.1014 seconds.
The corresponding orbital radius is
42 164.175 km.
The analysis so far has assumed that
the Earth can be regarded as a perfect
sphere. However, in reality the Earth’s
shape is more nearly oblate.
The
equatorial radius is 6378.137 km, while
the polar radius is 6356.752 km. The
gravitational
perturbation
due
to
oblateness causes the radius to be
increased by 0.522 km.2 The resulting
geostationary
orbital
radius
is
42 164.697 km.
In practice, once the satellite is
operational in the geostationary orbit, it is
affected by a variety of perturbations that
must be compensated by frequent
stationkeeping maneuvers using thrusters
onboard the spacecraft.
These
perturbations are caused by the
gravitational attractions of the Sun and
the Moon, the slightly elliptical shape of
the Earth’s equator, and solar radiation
pressure. Because the orbit is constantly
changing, it is not meaningful to define
the orbit radius too precisely. By
comparison, using recent data for 16
Intelsat satellites, we obtain a semimajor
axis with a mean of 42 164.80 km and a
standard deviation of 0.46 km.
A perfectly geostationary orbit is a
mathematical idealization. Only the
distinction between the mean solar day
and the sidereal day needs to be taken
into account. Therefore, it is customary to
quote a nominal orbital period of 86 164
seconds and a radius of 42 164 km. The
height above the equator is 35 786 km
and the orbital velocity is 3.075 km/s.
_________________________________
1
Mathematically, Kepler’s third law may
be expressed as T 2 = (4 π 2 / GM) a 3,
where T is the period, a is the semimajor
axis, and GM is the gravitational constant
for the Earth, whose value is 398 600.5
km3 / s2. For a circular orbit, the
semimajor axis a is equal to the radius r.
2
The correction is ∆r = ½ J2 ( RE / r )2 r,
where r is the orbital radius, RE is the
Earth’s radius, and J2 is the Earth’s
oblateness coefficient, 0.001 083.