BUILDING MULTIPATH PROPAGATION LOSS
Losses due to multipath transmission because of buildings can be computed by the formula: Lmb = 20 Log ( f^MHZ ) Solution : Based on the table for 150% first freznel clearance, even if there are the 3 diffraction points crossing the 150% clutter clearance, none of these points are within the near field zone of both antennas. Computing for the near and far field distances:
In addition, the three building top diffraction at the point 26/27 Km from site A has already been computed with the diffraction loss. Alternative Solution : If you wish the omit the computation of clutter loses, increases the antenna height until they clear the 150% first freznel radius margin.
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ATMOSPHERIC LOSSES TO BE ADDED THE THERMAL FADE MARGIN
S tep 21 : Compute for Atmospheric Losses. OXYGEN ABSOPTION LOSS
Attenuation Attenuation is due to the absorption absorption of of radio frequency frequency energy by oxygen oxygen molecules molecules in the atmosphere is given by the formula : For Frequencies below 57 Ghz
Frequency f in Ghz. The Reason as that Ao is a constant set for frequencies between 57Ghz to 63 Ghz is the complex spectrum analysis of these frequencies which is dependent on the height of the transmitting and receiving antennas. The result however, would still around the area of 15 dB/Km. Solution : Computing for oxygen absorption loss at a path length of 30 Km:
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WATER VAPOR LOSS
Attenuation due to the absorption of radio frequency energy by water vapor in the atmosphere is given by the formula:
f in Ghz. a is Water Vapor Density in gm/m^3 should be below 12 gm/m^3
This formula applies for frequencies below 350 Ghz. Solution : Coputing for water vaporloss at a path length of 30 Km:
Step 22: Arrange all computed data into a systematic table.
The given and calculated data can then be arranged according to the fade margins they result into: 1. 2. 3. 4. 5.
Basic Thermal Fade Margin Thermal Fade Margin with Atmospheric Loss Considerations Dispersive Fade Margin Thermal Fade Margin with Rain Considerations (Rain Fade Margin) Thermal Fade Margin with Diffraction Considerations (Diffraction Fade Margin)
From these fade margins, a Flat Margin can then be calculated. The Flat fade Margin and Composite Fade Margin take into consideration all the fade margins calculated.
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Computation for Low Band Frequency – Tx = 12.62 Ghz PARAMETER
FUNCTION
VALUE
UNIT
Microwave Radio Output Power
Given
18.00
dB
Connector Loss
Subtracted
0.50
dB
Waveguide Loss
Subtracted
0.59
dB
Connector Loss
Subtracted
0.50
dB
47.00
dB
Antenna Gain
Added Subtracted
144.00
Atmospheric Losses (Oxygen Absorption)
Subtracted
0.23
dB
Atmospheric Losses (Water Vapor Absorption
Subtracted
0.58
dB
Antenna Misalignment Loss
Subtracted
0.50
dB
Antenna Gain
Subtracted
47.00
dB
Subtracted
0.50
dB
0.59
dB
Free Space Loss
Connector Loss Waveguide Loss
Added
dB
Connector Loss
Subtracted
0.50
dB
Power Input to Receiver (RSL)
Computed
-36.49
dB
Minimum Receiver Threshold
Given
-78.00
dB
THERMAL FADE MARGIN
COMPUTED
41.51
dB
VALUE
UNIT
18.00
dB
Computation for Low Band Frequency – Tx = 13.08 Gh PARAMETER
FUNCTION
Microwave Radio Output Power
Given
Connector Loss
Subtracted
0.50
dB
Waveguide Loss
Subtracted
0.59
dB
Connector Loss
Subtracted
0.50
dB
47.00
dB
Antenna Gain Free Space Loss
Added Subtracted
144.32
dB
Atmospheric Losses (Oxygen Absorption)
Subtracted
0.23
dB
Atmospheric Losses (Water Vapor Absorption
Subtracted
0.62
dB
Antenna Misalignment Loss
Subtracted
0.50
dB
Antenna Gain
Subtracted
47.00
dB
Subtracted
0.50
dB
0.59
dB
Connector Loss Waveguide Loss
Added
Connector Loss
Subtracted
0.50
dB
Power Input to Receiver (RSL)
Computed
-36.85
dB
Minimum Receiver Threshold
Given
-78.00
dB
THERMAL FADE MARGIN
COMPUTED
41.16
dB
Calculation of the Rain Fade Margin is the difference between the Thermal Fade Margin less Rain Losses. Calculation of the Diffraction Fade Margin is the difference between the Thermal Fade Margin less Diffraction & Clutter Losses. Rain Fade Margin is treated separately up to the calculation of reliability. Other Fade Margins may be given such as External Interference Fade Margin and Adjacent Channel Fade Margin. These are computed together along with the Thermal Fade Margin and Diffraction Fade Margin.
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FLAT MADE MARGIN S tep 23: Calculate Flat Fade Margin
Calculation for the Flat Fade Margin is given by the formula:
In cases when External Interference Fade Margin (FMint) and Adjacent Channel Fade Margin (FMadj.chan) is not given, then the terms which contains these values in the exponent are omitted. Solution : Computing for Flat Fade Margin:
Diffraction Fade Margin = Thermal Fade Margin – Diffraction Loss – Clutter Loss For 12.82 Ghz Diffraction Fade Margin (FM^DIFF) = 41.52 dB – 2.658 dB Diffraction Fade Margin (FM^DiFF) = 38.852 dB
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COMPOSITE FADE MARGIN S tep 24: Calculate the composite or effective Fade Margin using the following equation :
Where R^D is the Fade Occurrence Factor Solution : Considering a Dispersive Fade Margin of 40dB with an average fade occurrence factor (R^D = 3), we can compute for the Effective Fade Margin.
RELIABILITY CALCULATIONS S tep 25: Based on the Effective Fade Margin of the Link, the Link Reliability can be calculated. In calculating Reliability, Several Models can be used. 1. 2. 3. 4.
KQ Factor KQ Factor with Terrain Roughness Vigants Barnett CCIR Recommendations 530
Each method having a different calculation approach and different formula. TERRAIN ROUGHNESS FACTOR
In the Calculation of the reliability using the KQ factor with Terrain Roughness and Vigants-Barnett method, it is important to initially establish the roughness of the terrain. This is done by taking the standard deviation of regular increments of the path.
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n is the number of path length subdivisions between the 2 end stations. M is the average Elevations within the path S the standard deviation of the elevation within the path;
Notes: The end points of the path are not taken into consideration with the roughness terrain factor. The greater he value of n, the more accurate the terrain roughness factor value is calculated.
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Solution: Calculating the average terrain elevation. Since we are not to consider the elevation at the end, there are 29 segments at increments of 1 kilometer:
K-Q Reliability Calculation The Calculations for the fade probability in the K-Q method is given by the formula:
Where: K-Q – Regional K-Q Value f – Frequency in Ghz d – Path Length in Kilometres b, c – Regional Climatic Factor FM^EFF – Effective Fade Margin Page 28
To get the values of K-Q, b and c, use the following table:
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Using the same value for K-Q of 1 x 10^-9 , b = 1.2 and c = 3.5, the unavailability and reliability for link due to rain can be calculated. Rain Fade Margin = Effective Fade Margin – Rain Atenuation For 12.82 Ghz Rain Fade Margin = 33.002 dB -26.34 dB Rain Fade Margin = 6.68 dB For 13.08 Ghz Rain Fade Margin = 32.859 dB -25.44 dB Rain Fade Margin = 7.419 dB
K-Q Reliability with Terrain Roughness The calculation for the fade probability using the K-Q method and considering the roughness of the terrain is given by the fomula:
Where: K-Q – Regional K-Q Value f – Frequency in Ghz d – Path Length in Kilometres b, c – Regional Climatic Factor FM^EFF – Effective Fade Margin S – Standard Deviation of the Terrain Elevation (also called roughness Facotr) Using the same values of K-Q, b and c:
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And computing for the Rain Outage in the same manner: Rain Fade Margin = Effective Fade Margin – Rain Attenuation For 12.82 Ghz Rain Fade Margin = 33.002 dB -26.34 dB Rain Fade Margin = 6.68 dB For 13.08 Ghz Rain Fade Margin = 32.859 dB -25.44 dB Rain Fade Margin = 7.419 dB
Note the extreme difference, between both K-Q reliabilities with and without taking into consideration terrain Roughness.
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Vigants - Barnette Calculation C FACTOR
The C factor in the Vigants – Barnette method of solving for unavailability takes into consideration bot the terrain roughness and climatic conditions:
Where: C –C-Factor Value c^f - Climate factor S – Roughness Factor This formula is applicable if S is greater or equal to 6 meters but less than or equal to 42 meters. Values of S which are outside these limits may assume the minimum or maximum value. c^f – Climate factor may have the typical values : c^f = 0.5 Good Propagation Conditions, used for mountainous and dry conditions c^f = 1 Average Propagations Conditions, used for Average terrain and climatic conditions c^f = 2 Difficult Propagations Conditions, used for over water paths, gulf or coastal areas Solution. Using the Vigants-Barnette method, we can set the climatic factor to be 1 and the Roughness Factor to be 42.
Note the computed C factor value is for good propagation conditions as the typical Cfactor values are: C = 0.25
Good Propagation Condition
C=1
Average Propagation Conditions
C=4
Difficult Propagation Conditions
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The Vigants – Barnette unavailability formula is given as:
Where: C – C – Factor Value f – Frequency in Ghz d – Path Length in Kilometres
Solution: The computation for the unavailability using the Vigants-Barnette Method is:
Reliability can then be calculated:
Calculations for the unavailability due to rain is also done: Rain Fade Margin = Effective Fade Margin – Rain Attenuation For 12.82 Ghz Rain Fade Margin = 33.002 dB -26.34 dB Rain Fade Margin = 6.68 dB
For 13.08 Ghz Rain Fade Margin = 32.859 dB -25.44 dB Rain Fade Margin = 7.419 Db
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The Availability during rain:
CCIR Recc. 530 Calculation When using the CCIR Recc. 530 Unavailability calculation, it is important to determine 3 factors, the Path Inclination, the Average Grazing Angle and the Geoclimatic Factor. PATH INCLINATION
Path inclination is given by the formula :
Where : h1 and h2 – antenna height above MSL in meters d – Path Length in Kilometres
solution: Solving for the Path Inclination:
AVERAGE GRAZING ANGLE
The following are the necessary formula need to solve for the average grazing angle:
Where : h1 and h2 – antenna height above MSL in meters d – Path Length in Kilometres
solution: Solving for the factors needed to solve average grazing angle
Average Grazing Angle is given by the formula:
Where this time, h1 and h2 are expressed in meters above MSL and d in the kilometres. This will result in a value whose unit is in milliradians.
Solution: Solving for the average grazing angle
GEOCLIMATIC FACTOR
This is the percent of time when the refractivity gradiant of a specific place goes below 100 N units per Kilometre. This value changes from month to month. In path calculations, the worst fading month is taken. The variable P^L is used to solve for the geoclimatic factor K. P^L is taken from refractivity maps while K, being a factor of P^L is calculated by the use of the following formula:
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Solution : From the graph (August was chosen as it provided the worst month for the Philippines), we can solve for the value of K given the value of P to be 30. Choosing a Mountainous path :
K = 10^-6.0 x 30^1.5 K = 1.643 x 10^-14 CCIR Rec. 530 UNAVAILABILITY
Having established the particular factors, unavailability can now be computed:
Where : F – Frequency in Ghz D – Path Length in Kilometers Page 32
Solution : Solving for Unavailability using CCIR Recc. 530:
Solving got the corresponding availability
As seen here, the CCIR Recc. 530 gives the lowest unfaded reliability calculation so far.
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