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Design of a Two-Hop Microwave Link
76
3.4 Transmission Calculations
3.4.1 Antenna Height
The antenna height can be computed by the formula:
๐ป๐ด = ๐ท2
8+ 43.3 โ
๐ท
4๐
Where:
HA is the antenna height (ft)
d1 is the distance from a point to one end of the path (mi)
d2 is the distance from same point to the other end of the path (mi)
f is the operating frequency in GHz
D = d1 + d2
The following antenna heights are as follows:
Link Antenna D(mi) f(GHz) Height(ft) Height(m)
AR HA 12.427 12.813 40.62519 12.383
RA HR1 12.427 13.063 40.42018 12.32
RB HR2 12.427 12.938 40.52194 12.351
BR HB 12.427 13.188 40.31986 12.289
HA = 12.383 m
HR = 12.351 m
HB = 12.289 m
Design of a Two-Hop Microwave Link
77
Note: Choose the highest value for the antenna height of repeater to meet the clearance requirements for both
AR/RA and RB/BR links.
Antenna Height Computations:
๐ป๐ด = 12.4272
8+ 43.3 โ
12.427
4 โ 12.813= 40.62519 ft.
๐ป๐ 1 = 12.4272
8+ 43.3 โ
12.427
4 โ 13.063= 40.42018 ft.
๐ป๐ 2 = 12.42722
8+ 43.3 โ
12.4272
4 โ 12.938= 40.52194 ft.
๐ป๐ต = 12.42722
8+ 43.3 โ
12.4272
4 โ 13.188= 40.31986 ft.
3.4.2 Antenna Diameter
According to the Antenna Architecture below, for a frequency of 13 GHz, an
antenna with a diameter of 1.2 m should be used.
Design of a Two-Hop Microwave Link
78
Antenna Diameter Table
Link New Diameter (ft)
AR 4
RA 4
RB 4
BR 4
3.4.3 Antenna Gain
๐บ๐๐๐ก = 17.8 + 20 log(๐ท) + 20 log(๐)
where:
D is the diameter of the antenna (m)
f is the operating frequency (GHz)
Design of a Two-Hop Microwave Link
79
Link f (GHz) n D (m) GNEW (dB)
AR 12.813 0.55 1.2 41.537
RA 13.063 0.55 1.2 41.704
RB 12.938 0.55 1.2 41.621
BR 13.188 0.55 1.2 41.787
Calculations:
๐บ๐๐๐ก = 17.8 + 20 log(1.2) + 20 log(12.813) = 41.537 dB
๐บ๐๐๐ก = 17.8 + 20 log(1.2) + 20 log(13.063) = 41.704 dB
๐บ๐๐๐ก = 17.8 + 20 log(1.2) + 20 log(12.938) = 41.621 dB
๐บ๐๐๐ก = 17.8 + 20 log(1.2) + 20 log(13.188) = 41.787 dB
All of the calculated gain for each link are within the range of gain with 1.2 m
diameter of the chosen antenna (see data sheet in the Appendices. Therefore, this antenna
will be used in this design.
3.4.4 Losses
Total antenna losses can be determined from the values of the free space loss (FSL),
waveguide loss (WL), connector loss (CoL), Radome Loss (RL) and Circular Loss (CiL).
Design of a Two-Hop Microwave Link
80
3.4.4.1 Free Space Loss
The free space loss (FSL) can be computed by:
๐น๐๐ฟ = 92.4 + 20 log(๐๐บ๐ป๐ง) + 20log (๐ท๐๐)
where:
FSL is the free space loss (dB)
D is the distance between the two terminals (km)
f is the operating frequency (GHz)
Below are the computed FSL values for each link:
Channel Link f (GHz) D (km) FSL
f1 AR 12.813 20 140.574
f2 RA 13.063 20 140.741
f3 RB 12.938 20 140.658
f4 BR 13.188 20 140.824
FSL Calculations:
FSLf1 = 92.4 + 20log(12.813) + 20log(20) = 140.574
FSLf2 = 92.4 + 20log(13.063) + 20log(20) = 140.741
FSLf3 = 92.4 + 20log(12.938) + 20log(20) = 140.658
FSLf1 = 92.4 + 20log(13.188) + 20log(20) = 140.824
Design of a Two-Hop Microwave Link
81
3.4.4.2 Waveguide Loss
Waveguide Loss (WL) can be computed by:
๐๐ฟ = [๐ป๐๐๐โ๐ก๐๐๐๐๐ ๐๐๐ก๐ก๐๐(๐) + ๐ป๐๐๐โ๐ก๐ ๐๐๐๐๐ฃ๐๐(๐) + 2 โ ๐ฟ๐๐๐๐กโ๐๐๐ฃ๐๐๐ข๐๐๐] โ [๐ฟ๐๐ ๐ ๐๐๐ฃ๐๐๐ข๐๐๐
๐ฟ๐๐๐๐กโ๐๐๐ฃ๐๐๐ข๐๐๐
]
For the waveguide length, a common value of 6 meters will be used for
both transmitter and receiver ends. The chosen waveguide, E130 FLEXWELLยฎ
Standard Elliptical Waveguide), operates in the 10.7 to 13.25 GHz frequency band
which is suitable for our 12.75 to 13.25 operating band. The following values are
the attenuation in the waveguide per 100 m based on the data sheet:
Frequency (GHz) Attenuation (dB/100m)
12.8 11.24
12.9 11.21
13 11.19
13.1 11.16
13.2 11.14
13.25 11.13
The table below shows the values for WL for each link.
Link HT HR LT LR Atten/100m WL (dB)
AR 12.383 12.351 6 6 11.24 4.129
RA 12.351 12.383 6 6 11.16 4.1
RB 12.351 12.289 6 6 11.21 4.107
Design of a Two-Hop Microwave Link
82
BR 12.289 12.351 6 6 11.14 4.082
Waveguide Loss Calculations:
๐๐ฟ๐ด๐ = [12.383 + 12.351 + 2 โ 6] โ [11.24
100] = 4.129 ๐๐ต
๐๐ฟ๐ ๐ด = [12.351 + 12.383 + 2 โ 6] โ [11.16
100] = 4.1 ๐๐ต
๐๐ฟ๐ ๐ต = [12.351 + 12.289 + 2 โ 6] โ [11.21
100] = 4.107 ๐๐ต
๐๐ฟ๐ต๐ = [12.289 + 12.351 + 2 โ 6] โ [11.14
100] = 4.082 ๐๐ต
3.4.4.3 Radome Loss
Radome Loss (RL) is present for both receiver and transmitter so the loss
is twice per link. Based on the data sheet of the antenna, the radome loss is 1.3 dB
for 1.2 m diameter and 13 GHz frequency.
๐ ๐ฟ = 1.3 ๐๐ต โ 2
๐ ๐ฟ = 2.6 ๐๐ต
3.4.4.4 Connector Loss
Connector Loss (CoL) is present at both transmitter and receiver. There are
two connections per antenna, therefore, the loss will be multiplied by four. The CoL
can be computed by:
Design of a Two-Hop Microwave Link
83
๐ถ๐๐ฟ = 0.04 โ โ๐๐บ๐ป๐ง
Link CoL (dB)
AR 0.573
RA 0.578
RB 0.576
BR 0.581
Connector Loss Calculations:
๐ถ๐๐ฟ = 0.04 โ โ12.813 = 0.573 dB
๐ถ๐๐ฟ = 0.04 โ โ13.063 = 0.578 dB
๐ถ๐๐ฟ = 0.04 โ โ12.938 = 0.576 dB
๐ถ๐๐ฟ = 0.04 โ โ13.188 = 0.581dB
3.4.4.5 Circulator Loss
Circulator Loss (CiL) is present at both transmitter and receiver, therefore,
is twice per link. From the data sheet, the CiL is 0.5 dB.
๐ถ๐๐ฟ = 0.5 ๐๐ต โ 2
๐ถ๐๐ฟ = 1 ๐๐ต
The circulator will be used for all antennas therefore all links will have the
same Circulator Loss.
Design of a Two-Hop Microwave Link
84
3.4.4.6 Summary of Losses
The summary of losses was obtained by adding all the losses for each link.
Link FSL (dB) WL (dB) CoL (dB) RL (dB) CiL (dB) Total (dB)
AR 140.574 4.129 0.573 2.6 1 148.876
RA 140.741 4.1 0.578 2.6 1 149.019
RB 140.658 4.107 0.576 2.6 1 148.941
BR 140.824 4.082 0.581 2.6 1 149.087
Summary of Losses Calculations:
SOLAR = 140.574 + 4.129 + 0.573 + 2.6 + 1 = 148.876 dB
SOLRA = 140.741 + 4.1 + 0.578 + 2.6 + 1 = 149.019 dB
SOLRB = 140.658 + 4.107 + 0.576 + 2.6 + 1 = 148.941 dB
SOLBR = 140.824 + 4.082 + 0.581 + 2.6 + 1 = 149.087 dB
3.4.5 Received Signal Loss
The received signal loss (RSL) of the antenna can be computed by the formula:
๐ ๐๐ฟ = ๐๐ก + ๐บ๐ + ๐บ๐ โ ๐๐ฟ๐ฟ
where:
Pt is the output power (dBm), see data sheet
GT is the transmitter gain (dB)
GR is the receiver gain (dB)
Design of a Two-Hop Microwave Link
85
TLL is the total losses (dB)
Below are the computed values for RSL:
Link Pt (dBm) G (dB) Total Losses (dB) RSL (dBm)
AR 20 41.537 148.876 -45.635
RA 20 41.704 149.019 -45.778
RB 20 41.621 148.941 -45.533
BR 20 41.787 149.087 -45.679
Calculations:
๐ ๐๐ฟ๐๐ธ๐ = 20 + 41.537 + 41.704 โ 148.876 = โ45.635 ๐๐ต๐
๐ ๐๐ฟ๐๐ธ๐ = 20 + 41.704 + 41.537 โ 149.019 = โ45.778 ๐๐ต๐
๐ ๐๐ฟ๐๐ธ๐ = 20 + 41.621 + 41.787 โ 148.941 = โ45.533 ๐๐ต๐
๐ ๐๐ฟ๐๐ธ๐ = 20 + 41.787 + 41.621 โ 149.087 = โ45.679 ๐๐ต๐
3.4.6 Fade Margin
๐น๐ = ๐ ๐๐ฟ โ ๐ ๐กโ
where:
FM is the fade margin (dB)
RSL is the received signal loss (dBm)
Rth is the receiver threshold (dBm) = -87 dBm in data sheet
Design of a Two-Hop Microwave Link
86
Link RSL Rth FM(dBm)
AR -45.635 -87 41.365
RA -45.778 -87 41.222
RB -45.533 -87 41.467
BR -45.679 -87 41.321
Calculations:
๐น๐๐๐ธ๐ = โ45.635 โ (โ87) = 41.365 ๐๐ต๐
๐น๐๐๐ธ๐ = โ45.778 โ (โ87) = 41.222 ๐๐ต๐
๐น๐๐๐ธ๐ = โ45.533 โ (โ87) = 41.467 ๐๐ต๐
๐น๐๐๐ธ๐ = โ45.679 โ (โ87) = 41.321 ๐๐ต๐
The required reliability for this design is 99.99% which has its equivalent Fade
Margin (FM) shown in the table below:
Fade Margin (dB) Reliability (%)
18 99
28 99.9
38 99.99
48 99.999
58 99.999
Design of a Two-Hop Microwave Link
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By looking at the table above and with the computed values for FM, the values are
close. Therefore, the required reliability is met.
3.4.7 Reliability
UNDP
๐๐๐ท๐ = ๐ ๐ฅ ๐ ๐ฅ 2.5๐ฅ10โ6 ๐ฅ ๐ ๐ฅ ๐ท3 ๐ฅ 10โ๐น๐
10
where:
UNDP is the non-diversity outage probability
a is the terrain factor
b is the climate factor
f is the frequency of the transmit antenna (GHz)
D is the path length (mi)
a 4 for very smooth terrain including overwater
1 for average terrain with some roughness
0.25 for mountainous, very rough or very dry
b 0.5 Gulf coast or similar hot, humid areas
0.25 normal interior temperate or northern
0.125 mountainous or very dry
Link a b f (GHz) D (mi) FM(dBm) UDNP
AR 0.25 0.125 12.813 12.427 41.365 1.40294E-07
RA 0.25 0.125 13.063 12.427 41.222 1.4782E-07
Design of a Two-Hop Microwave Link
88
RB 0.25 0.125 12.938 12.427 41.467 1.38375E-07
BR 0.25 0.125 13.188 12.427 41.321 1.45871E-07
Calculations:
๐๐๐ท๐ = 0.25 ๐ฅ 0.125 ๐ฅ 2.5๐ฅ10โ6 ๐ฅ 12.813 ๐ฅ 12.4273 ๐ฅ 10โ41.365
10 = 1.40294E โ 07
๐๐๐ท๐ = 0.25 ๐ฅ 0.125 ๐ฅ 2.5๐ฅ10โ6 ๐ฅ 13.063 ๐ฅ 12.4273 ๐ฅ 10โ41.222
10 = 1.4782E โ 07
๐๐๐ท๐ = 0.25 ๐ฅ 0.125 ๐ฅ 2.5๐ฅ10โ6 ๐ฅ 12.938 ๐ฅ 12.4273 ๐ฅ 10โ41.467
10 = 1.38375E โ 07
๐๐๐ท๐ = 0.25 ๐ฅ 0.125 ๐ฅ 2.5๐ฅ10โ6 ๐ฅ 13.188 ๐ฅ 12.4273 ๐ฅ 10โ41.321
10 = 1.45871E โ 07
Reliability
%๐ = (1 โ ๐๐๐ท๐) ๐ฅ 100
Link UNDP %R
AR 1.40294E-07 99.99998597
RA 1.4782E-07 99.99998522
RB 1.38375E-07 99.99998616
BR 1.45871E-07 99.99998541
Calculations:
%๐ = (1 โ 1.40294E โ 07) ๐ฅ 100 = 99.99998597 %
%๐ = (1 โ 1.4782E โ 07) ๐ฅ 100 = 99.99998522 %
%๐ = (1 โ 1.38375E โ 07) ๐ฅ 100 = 99.99998616 %
%๐ = (1 โ 1.45871E โ 07) ๐ฅ 100 = 99.99998541 %
Design of a Two-Hop Microwave Link
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The computed values of reliability met the required 99.99%.
3.4.8 Tower Height
๐ป๐ = ๐ป๐ด +๐ท๐ด
2
Where:
HT is the height of the tower (m)
HA is the height of the antenna (m)
DA is the diameter of the antenna (m)
LOCATION HA (m) DA (m) HT (m)
A 12.383 1.2 12.983
R 12.351 1.2 12.951
B 12.289 1.2 12.889
Calculations:
๐ป๐ = 12.383 +1.2
2= 12.983 ๐
๐ป๐ = 12.351 +1.2
2= 12.951 ๐
๐ป๐ = 12.289 +1.2
2= 12.889 ๐
3.4.9 System Gain
The system gain can be computed by using the formula below:
Design of a Two-Hop Microwave Link
90
๐๐ฆ๐ ๐ก๐๐ ๐บ๐๐๐ = ๐๐๐ก๐๐ ๐ฟ๐๐ ๐ ๐๐ + ๐น๐ โ ๐บ๐ โ ๐บ๐
Link Total Losses (dB) FM(dBm) G (dB) System Gain (dB)
AR 148.876 41.365 41.537 107
RA 149.019 41.222 41.704 107
RB 148.941 41.467 41.621 107
BR 149.087 41.321 41.787 107
Calculations:
๐๐ฆ๐ ๐ก๐๐ ๐บ๐๐๐ = 148.876 + 41.365 โ 41.537 โ 41.704 = 107 dBm
๐๐ฆ๐ ๐ก๐๐ ๐บ๐๐๐ = 149.019 + 41.222 โ 41.537 โ 41.704 = 107 dBm
๐๐ฆ๐ ๐ก๐๐ ๐บ๐๐๐ = 148.941 + 41.467 โ 41.621 โ 41.787 = 107 dBm
๐๐ฆ๐ ๐ก๐๐ ๐บ๐๐๐ = 149.087 + 41.321 โ 41.621 โ 41.787 = 107 dBm
3.4.10 Effective Isotropic Radiated Power
๐ฌ๐ฐ๐น๐ท = ๐ท๐ป + ๐ฎ๐ป โ ๐ณ๐๐๐๐๐๐๐๐(๐ป๐ฟ)
Where:
PT is the transmitted power (see data sheet)
GT is the gain of the transmitter
LossTotal(TX) is the total losses in the transmitter (taken from specs)
Antenna
WL
(dB)
CoL
(dB)
RL
(dB)
CiL
(dB)
Total TX Losses
(dB)
Pt
(dBm) Gt
EIRP
(dBm)
A 5.662 0.573 1.3 0.5 8.035 20 41.537 53.502
Calculation:
Design of a Two-Hop Microwave Link
91
EIRP = 20 + 41.537 โ 8.035 = 53.502 dBm
3.4.11 Azimuth
For computing for the azimuth (referenced from True North), online software from
http://www.fcc.gov/encyclopedia/distance-and-azimuths-between-two-sets-coordinates
was used. Table below shows the tabulated Azimuth results.
Azimuth (wrt North)
A to Repeater 267.31ยฐ(wrt North)
Repeater to A 87.26ยฐ(wrt North)
Repeater to B 52.49ยฐ(wrt North)
B to Repeater 232.58ยฐ(wrt North)