JED - October 2016 - 69

E W

101

From the law of sines for plane triangles:
b/sin B = a/sin A
so, sin A = a sin B / b =
(6371/8059) sin(110°) = .7429 Thus, A = 47.98°
Angle D then equals: 180° - 110° - 47.98° = 22.02°
From the law of sines, d/sin D = b/sin B
So, d (the range) = (b sin D) / sin B =
8059 sin 22.02° / sin 110° = 3215 km

The loss calculations discussed in last month's column only
considered the line-of-sight loss. This month, we will deal with
the rest of the loss factors.

ATMOSPHERIC LOSS

Figure 3: Atmospheric loss in a satellite to ground link is a function of
frequency and satellite elevation angle.

* The distance from the satellite to the center of the Earth is
8,059 km (per Keppler's third law). Let's call this side b.
* The angle B from the satellite to the center of the Earth as
seen from the ground station is 110 degrees.
* Side d is the link distance from the ground station to the
satellite.
* Angle D is the geocentric angle between the ground station
and the satellite.

Antenna
Gain
Pattern
3 dB

XMTR

Figure 2 shows the atmospheric loss per kilometer for a signal
transmitted within the atmosphere. However, when a transmission is to or from a satellite, we can use the graph in Figure 3.
This is the loss through the whole atmosphere as a function of
frequency and the elevation angle of the path to the satellite
relative to the local horizon. For example, for a 5-MHz signal,
the atmospheric loss is negligible at 30 degrees elevation, but
about 2.2 dB at the horizon.

ANTENNA MISALIGNMENT

Where narrow-beam antennas are used in satellite links,
the alignment of the transmitting and/or receiving antenna
will cause a link loss because of a reduction in the effective
antenna gain, as shown in Figure 4. For small antenna misalignments, the gain reduction can be calculated from the formula:
∆G = 12 (θ / α) ²
Where: ∆G is reduction from boresight
gain in dB
	
α is 3 dB beamwidth (degrees)
	
θ is offset angle (degrees)
For example, if the transmitting
antenna has 5 degrees 3dB beam width and
Beam width ( )
is misaligned by 1 degree, but the receiving
antenna boresight is aimed directly at the
transmitting antenna, the received signal
strength will be reduced by the transmitBoresight
ting antenna gain reduction factor:
∆G = 12(1/5)2 = 0.48 dB

To
Receiver

Misalignment
Angle ( )
Figure 4: For small misalignment errors, the antenna gain is reduced by a function of the angular
error and the antenna 3 dB beam width.

WHATS NEXT
Next month, we will continue our
discussion of satellite link loss with
polarization mismatch and rain. attenuation. For your comments and suggestions, Dave Adamy can be reached at
dave@lynxpub.com. a

The Journal of Electronic Defense | October 2016

At a frequency of 5 GHz, the line-of-sight loss is: 32.44 + 20
log (3215) + 20 log (5000) = 32.44 + 70.14 + 73.98 = 176.56 dB

69



JED - October 2016

Table of Contents for the Digital Edition of JED - October 2016

The View From Here
Conferences Calendar
Courses Calendar
From the President
The Monitor
World Report
Bait in the Trap: Trainable Soft-Kill Systems Proliferate for ASMD
2017 EW/SIGINT Resource Guide
SIGINT History
EW 101
AOC News
Index to Advertisers
JED Quick Look
JED - October 2016 - cover1
JED - October 2016 - cover2
JED - October 2016 - 3
JED - October 2016 - 4
JED - October 2016 - 5
JED - October 2016 - The View From Here
JED - October 2016 - 7
JED - October 2016 - Conferences Calendar
JED - October 2016 - 9
JED - October 2016 - Courses Calendar
JED - October 2016 - 11
JED - October 2016 - From the President
JED - October 2016 - 13
JED - October 2016 - 14
JED - October 2016 - The Monitor
JED - October 2016 - insert1
JED - October 2016 - insert2
JED - October 2016 - 16
JED - October 2016 - 17
JED - October 2016 - 18
JED - October 2016 - 19
JED - October 2016 - 20
JED - October 2016 - 21
JED - October 2016 - World Report
JED - October 2016 - 23
JED - October 2016 - Bait in the Trap: Trainable Soft-Kill Systems Proliferate for ASMD
JED - October 2016 - 25
JED - October 2016 - 26
JED - October 2016 - 27
JED - October 2016 - 28
JED - October 2016 - 29
JED - October 2016 - 30
JED - October 2016 - 31
JED - October 2016 - 32
JED - October 2016 - 33
JED - October 2016 - 34
JED - October 2016 - 35
JED - October 2016 - 36
JED - October 2016 - 37
JED - October 2016 - 38
JED - October 2016 - 39
JED - October 2016 - 2017 EW/SIGINT Resource Guide
JED - October 2016 - 41
JED - October 2016 - 42
JED - October 2016 - 43
JED - October 2016 - 44
JED - October 2016 - 45
JED - October 2016 - 46
JED - October 2016 - 47
JED - October 2016 - 48
JED - October 2016 - 49
JED - October 2016 - 50
JED - October 2016 - 51
JED - October 2016 - 52
JED - October 2016 - 53
JED - October 2016 - 54
JED - October 2016 - 55
JED - October 2016 - 56
JED - October 2016 - 57
JED - October 2016 - 58
JED - October 2016 - 59
JED - October 2016 - 60
JED - October 2016 - 61
JED - October 2016 - 62
JED - October 2016 - 63
JED - October 2016 - 64
JED - October 2016 - SIGINT History
JED - October 2016 - 66
JED - October 2016 - 67
JED - October 2016 - EW 101
JED - October 2016 - 69
JED - October 2016 - AOC News
JED - October 2016 - 71
JED - October 2016 - Index to Advertisers
JED - October 2016 - 73
JED - October 2016 - JED Quick Look
JED - October 2016 - cover3
JED - October 2016 - cover4
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