Microwave Design

Design of a Two-Hop Microwave Link

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3.4 Transmission Calculations

3.4.1 Antenna Height

The antenna height can be computed by the formula:

𝐻𝐴 = 𝐷2

8+ 43.3 √

𝐷

4𝑓

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


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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:

𝐻𝐴 = 12.4272

8+ 43.3 √

12.427

4 ∗ 12.813= 40.62519 ft.

𝐻𝑅1 = 12.4272

8+ 43.3 √

12.427

4 ∗ 13.063= 40.42018 ft.

𝐻𝑅2 = 12.42722

8+ 43.3 √

12.4272

4 ∗ 12.938= 40.52194 ft.

𝐻𝐵 = 12.42722

8+ 43.3 √

12.4272

4 ∗ 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.


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Antenna Diameter Table

Link New Diameter (ft)

AR 4

RA 4

RB 4

BR 4

3.4.3 Antenna Gain

𝐺𝑎𝑛𝑡 = 17.8 + 20 log(𝐷) + 20 log(𝑓)

where:

D is the diameter of the antenna (m)

f is the operating frequency (GHz)


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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:

𝐺𝑎𝑛𝑡 = 17.8 + 20 log(1.2) + 20 log(12.813) = 41.537 dB

𝐺𝑎𝑛𝑡 = 17.8 + 20 log(1.2) + 20 log(13.063) = 41.704 dB

𝐺𝑎𝑛𝑡 = 17.8 + 20 log(1.2) + 20 log(12.938) = 41.621 dB

𝐺𝑎𝑛𝑡 = 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).


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3.4.4.1 Free Space Loss

The free space loss (FSL) can be computed by:

𝐹𝑆𝐿 = 92.4 + 20 log(𝑓𝐺𝐻𝑧) + 20log (𝐷𝑘𝑚)

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


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3.4.4.2 Waveguide Loss

Waveguide Loss (WL) can be computed by:

𝑊𝐿 = [𝐻𝑒𝑖𝑔ℎ𝑡𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑟(𝑚) + 𝐻𝑒𝑖𝑔ℎ𝑡𝑅𝑒𝑐𝑒𝑖𝑣𝑒𝑟(𝑚) + 2 ∗ 𝐿𝑒𝑛𝑔𝑡ℎ𝑊𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒] ∗ [𝐿𝑜𝑠𝑠𝑊𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒

𝐿𝑒𝑛𝑔𝑡ℎ𝑊𝑎𝑣𝑒𝑔𝑢𝑖𝑑𝑒

]

For the waveguide length, a common value of 6 meters will be used for

both transmitter and receiver ends. The chosen waveguide, E130 FLEXWELL®

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


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BR 12.289 12.351 6 6 11.14 4.082

Waveguide Loss Calculations:

𝑊𝐿𝐴𝑅 = [12.383 + 12.351 + 2 ∗ 6] ∗ [11.24

100] = 4.129 𝑑𝐵

𝑊𝐿𝑅𝐴 = [12.351 + 12.383 + 2 ∗ 6] ∗ [11.16

100] = 4.1 𝑑𝐵

𝑊𝐿𝑅𝐵 = [12.351 + 12.289 + 2 ∗ 6] ∗ [11.21

100] = 4.107 𝑑𝐵

𝑊𝐿𝐵𝑅 = [12.289 + 12.351 + 2 ∗ 6] ∗ [11.14

100] = 4.082 𝑑𝐵

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.

𝑅𝐿 = 1.3 𝑑𝐵 ∗ 2

𝑅𝐿 = 2.6 𝑑𝐵

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:


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𝐶𝑜𝐿 = 0.04 ∗ √𝑓𝐺𝐻𝑧

Link CoL (dB)

AR 0.573

RA 0.578

RB 0.576

BR 0.581

Connector Loss Calculations:

𝐶𝑜𝐿 = 0.04 ∗ √12.813 = 0.573 dB

𝐶𝑜𝐿 = 0.04 ∗ √13.063 = 0.578 dB

𝐶𝑜𝐿 = 0.04 ∗ √12.938 = 0.576 dB

𝐶𝑜𝐿 = 0.04 ∗ √13.188 = 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.

𝐶𝑖𝐿 = 0.5 𝑑𝐵 ∗ 2

𝐶𝑖𝐿 = 1 𝑑𝐵

The circulator will be used for all antennas therefore all links will have the

same Circulator Loss.


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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:

𝑅𝑆𝐿 = 𝑃𝑡 + 𝐺𝑇 + 𝐺𝑅 − 𝑇𝐿𝐿

where:

Pt is the output power (dBm), see data sheet

GT is the transmitter gain (dB)

GR is the receiver gain (dB)


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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:

𝑅𝑆𝐿𝑁𝐸𝑊 = 20 + 41.537 + 41.704 − 148.876 = −45.635 𝑑𝐵𝑚

𝑅𝑆𝐿𝑁𝐸𝑊 = 20 + 41.704 + 41.537 − 149.019 = −45.778 𝑑𝐵𝑚

𝑅𝑆𝐿𝑁𝐸𝑊 = 20 + 41.621 + 41.787 − 148.941 = −45.533 𝑑𝐵𝑚

𝑅𝑆𝐿𝑁𝐸𝑊 = 20 + 41.787 + 41.621 − 149.087 = −45.679 𝑑𝐵𝑚

3.4.6 Fade Margin

𝐹𝑀 = 𝑅𝑆𝐿 − 𝑅𝑡ℎ

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


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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:

𝐹𝑀𝑁𝐸𝑊 = −45.635 − (−87) = 41.365 𝑑𝐵𝑚

𝐹𝑀𝑁𝐸𝑊 = −45.778 − (−87) = 41.222 𝑑𝐵𝑚

𝐹𝑀𝑁𝐸𝑊 = −45.533 − (−87) = 41.467 𝑑𝐵𝑚

𝐹𝑀𝑁𝐸𝑊 = −45.679 − (−87) = 41.321 𝑑𝐵𝑚

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


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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

𝑈𝑁𝐷𝑃 = 𝑎 𝑥 𝑏 𝑥 2.5𝑥10−6 𝑥 𝑓 𝑥 𝐷3 𝑥 10−𝐹𝑀

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


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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:

𝑈𝑁𝐷𝑃 = 0.25 𝑥 0.125 𝑥 2.5𝑥10−6 𝑥 12.813 𝑥 12.4273 𝑥 10−41.365

10 = 1.40294E − 07

𝑈𝑁𝐷𝑃 = 0.25 𝑥 0.125 𝑥 2.5𝑥10−6 𝑥 13.063 𝑥 12.4273 𝑥 10−41.222

10 = 1.4782E − 07

𝑈𝑁𝐷𝑃 = 0.25 𝑥 0.125 𝑥 2.5𝑥10−6 𝑥 12.938 𝑥 12.4273 𝑥 10−41.467

10 = 1.38375E − 07

𝑈𝑁𝐷𝑃 = 0.25 𝑥 0.125 𝑥 2.5𝑥10−6 𝑥 13.188 𝑥 12.4273 𝑥 10−41.321

10 = 1.45871E − 07

Reliability

%𝑅 = (1 − 𝑈𝑁𝐷𝑃) 𝑥 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:

%𝑅 = (1 − 1.40294E − 07) 𝑥 100 = 99.99998597 %

%𝑅 = (1 − 1.4782E − 07) 𝑥 100 = 99.99998522 %

%𝑅 = (1 − 1.38375E − 07) 𝑥 100 = 99.99998616 %

%𝑅 = (1 − 1.45871E − 07) 𝑥 100 = 99.99998541 %


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The computed values of reliability met the required 99.99%.

3.4.8 Tower Height

𝐻𝑇 = 𝐻𝐴 +𝐷𝐴

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:

𝐻𝑇 = 12.383 +1.2

2= 12.983 𝑚

𝐻𝑇 = 12.351 +1.2

2= 12.951 𝑚

𝐻𝑇 = 12.289 +1.2

2= 12.889 𝑚

3.4.9 System Gain

The system gain can be computed by using the formula below:


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𝑆𝑦𝑠𝑡𝑒𝑚 𝐺𝑎𝑖𝑛 = 𝑇𝑜𝑡𝑎𝑙 𝐿𝑜𝑠𝑠𝑒𝑠 + 𝐹𝑀 − 𝐺𝑇 − 𝐺𝑅

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:

𝑆𝑦𝑠𝑡𝑒𝑚 𝐺𝑎𝑖𝑛 = 148.876 + 41.365 − 41.537 − 41.704 = 107 dBm

𝑆𝑦𝑠𝑡𝑒𝑚 𝐺𝑎𝑖𝑛 = 149.019 + 41.222 − 41.537 − 41.704 = 107 dBm

𝑆𝑦𝑠𝑡𝑒𝑚 𝐺𝑎𝑖𝑛 = 148.941 + 41.467 − 41.621 − 41.787 = 107 dBm

𝑆𝑦𝑠𝑡𝑒𝑚 𝐺𝑎𝑖𝑛 = 149.087 + 41.321 − 41.621 − 41.787 = 107 dBm

3.4.10 Effective Isotropic Radiated Power

𝑬𝑰𝑹𝑷 = 𝑷𝑻 + 𝑮𝑻 − 𝑳𝒐𝒔𝒔𝒕𝒐𝒕𝒂𝒍(𝑻𝑿)

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:


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EIRP = 20 + 41.537 – 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 267.31°(wrt North)

Repeater to A 87.26°(wrt North)

Repeater to B 52.49°(wrt North)

B to Repeater 232.58°(wrt North)

http://www.fcc.gov/encyclopedia/distance-and-azimuths-between-two-sets-coordinates

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