# 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
strength will be reduced by the transmitBoresight
ting antenna gain reduction factor:
∆G = 12(1/5)2 = 0.48 dB

To

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
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

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
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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