rf path analysis

RE

V BYREVISION

FILE NAME REV

DATE 0

FJ.R. Lawrence Issued for general use. HOP NAME

August 7, 2000 SITE A to SITE B

0Your Name First Issue HOP TYPE

Date

BY CHKD APRVD

JRL

SIT

E A

GE

N

01 SITE NAME LOCATION TAG POINT CODE SITE "A" NAME

02 ADDRESS CITY COUNTY ST ZIP ADDRESS (If applicable) CITY COUNTY NAME ST Zip

03 LATITUDE / LONGITUDE DEG MIN SEC 32 29 52.0 NORTH LATITUDE 87 43 5.0 WEST LONGITUDE

04 OTHER INFO NAD 27

TO

WE

R 05 ELEVATION TOWER HEIGHT HEIGHT AGL 195 FT 59.4 METERS 360 FT 109.7 METERS 555 FT 169.2 METERS

06 MFR MODEL FCC TOWER # ROHN 80

07 OTHER INFO

AN

TE

NN

A /

CO

AX

08 MFR MODEL TYPE SIZE GAIN BEAM W. ANT. MFR. ANT. MODEL GRID DISH (or other) SIZE IN FEET 33.0 dBi 3.5 DEG

09 BEARING - A to B HEIGHT AGL OTHER 229.3 DEG 160 FT 48.8 METERS

10 COAX MFR TYPE SIZE COAX MFR. COAX TYPE COAX SIZE IN INCHES

11 COAX 1 LENGTH FREQ ATTENUATION 180 FT 54.9 METERS 2455.0 MHz 2.22 dB per 100 FT 4.0 dB LOSS


13 OTHER INFO

RA

DIO

14 MFR MODEL SERIAL CONFIG W-M LYNX 31250

15 XMIT FREQ XMIT GAIN XCEIVE SENS 2455.00000 MHz 27.0 dBm -94.0 dBm

16 OTHER INFO

MIS

C

17 POWER SUPPLY +/- 20 TO +/-63 Volts, < 45 W

18

19

20

SIT

E B

GE

N

21 SITE NAME LOCATION TAG POINT CODE SITE "B" NAME

22 ADDRESS CITY COUNTY ST ZIP

23 LATITUDE / LONGITUDE DEG MIN SEC 32 23 23.0 NORTH LATITUDE 87 52 1.0 WEST LONGITUDE

24 OTHER INFO NAD 27

TO

WE

R 25 ELEVATION TOWER HEIGHT HEIGHT AGL 310 FT 94.5 METERS 270 FT 82.3 METERS 580 FT 176.8 METERS

26 MFR MODEL FCC TOWER #

27 OTHER INFO

AN

TE

NN

A/C

OA

X

28 MFR MODEL TYPE SIZE GAIN BEAM W. 33.0 dBi DEG

29 BEARING - B to A HEIGHT AGL OTHER 49.3 DEG 250 FT 76.2 METERS

30 COAX MFR TYPE SIZE


32 COAX 2 LENGTH FREQ ATTENUATION 30 FT 9.1 METERS MHz 5.93 dB per 100 FT 1.8 dB LOSS

33 OTHER INFO

RA

DIO

34 MFR MODEL SERIAL CONFIG W-M LYNX 31250

35 XMIT FREQ XMIT GAIN XCEIVE SENS 2455.00000 MHz 27.0 dBm -94.0 dBm

36 OTHER INFO

MIS

C

37

38 POWER SUPPLY SAME AS ABOVE

39

40

CO

MM

ON

DA

TA 41 HOP DISTANCE HOP FACTORS 11.45 MILES 18.43 KM 0.50 (0.125 DRY to 0.500 HUMID) 1.00 (4.0 SMOOTH to 0.25 MOUNTAINS)

42 SYSTEM GAINS 27.0 dB XMIT 94.0 dB XCEIVE 33.0 dB "A" ANT 33.0 dB "B" ANT 187.0 TOT

43 SYSTEM LOSSES 131.1 dB PATH 5.8 dB COAX "A" 7.8 dB COAX B 7.8 dB OTHER 152.4 TOT

44 FADE MARGIN COMMENTS 34.6 dB

45 PATH AVAILABILITY PREDICTED DOWNTIME 99.999840% 50 SEC / YR or 0.84 MIN / YR or 0.01 HR / YR

NOTES

1 FADE MARGIN, AVAILABILITY AND DOWNTIME CALCULATIONS ARE FOR SITE "A" TO SITE "B".

2 SPIKE IN GROUND ELEVATION THROUGH FOLIAGE IN GRAPH IS AN EXAMPLE OF AN OBJECT, SUCH AS

A TOWER, IN OR NEAR THE LOS PATH.

© Copyright 2000, El Paso Energy

Unlicensed Radio HopData Sheet

0

100

200

300

400

500

600

60% Fresnel Clearance

document.xls 04/08/2023 Profile

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 220.00

100.00

200.00

300.00

400.00

500.00

600.00

Path Profile

LOS Path Fresnel Clearance 60% Fresnel Clearance Adjusted Elevation Foliage Elevation

Data Point

Ele

vatio

n (fe

et)

document.xls 04/08/2023 Topo Data

Rev Date Description

TOPO DATA CALCULATIONS

Path InformationData Distance Ground Distance LOS Fresnel 60% Fresnel Adjusted Foliage Earth PointPoint d1 (miles) Elevation d2 (miles) Path Clearance Clearance Elevation Elevation Curvature Adder Notes

1 0.00 195 11.45 355.00 355 355 195.00 195.00 02 0.55 200 10.91 364.76 332 345 202.97 242.97 2.973 1.09 190 10.36 374.52 329 347 195.65 235.65 5.654 1.64 200 9.82 384.29 330 352 208.03 248.03 8.035 2.18 200 9.27 394.05 333 357 210.11 250.11 10.116 2.73 212 8.73 403.81 337 364 223.90 263.90 11.907 3.27 190 8.18 413.57 343 371 203.39 243.39 13.398 3.82 250 7.64 423.33 350 379 264.58 304.58 14.589 4.36 250 7.09 433.10 357 388 265.47 305.47 15.47

10 4.91 200 6.55 442.86 366 397 216.06 256.06 16.0611 5.45 250 6.00 452.62 375 406 266.36 306.36 16.3612 6.00 292 5.45 462.38 385 416 408.36 348.36 16.36 100 Example of a structure in or near the path.13 6.55 250 4.91 472.14 395 426 266.06 306.06 16.0614 7.09 250 4.36 481.90 406 437 265.47 305.47 15.4715 7.64 200 3.82 491.67 418 448 214.58 254.58 14.5816 8.18 273 3.27 501.43 431 459 286.39 326.39 13.3917 8.73 200 2.73 511.19 445 471 211.90 251.90 11.9018 9.27 230 2.18 520.95 460 484 240.11 280.11 10.1119 9.82 150 1.64 530.71 476 498 158.03 198.03 8.0320 10.36 250 1.09 540.48 495 513 255.65 295.65 5.6521 10.91 200 0.55 550.24 517 530 202.97 242.97 2.9722 11.45 310 0.00 560.00 560 560 310.00 310.00 0

Frequency 2.455 GHz Notes:Path Length 11.45 miles 1) Columns in feet unless otherwise noted.

Curvature Height h = d1*d2 / 1.5k feet 2) The user input areas are un-shaded.k 1.33 4/3 (default)

Foliage Height 40 feetBeam elevation 0.00190155525546968 radians

document.xls 04/08/2023 B&D Calc


BEARING & DISTANCE CALCULATION

Definition of Variables

~ := Value Units Notes

A := 32.49778 deg Site "A" Latitude in decimal degrees. (Note 1)B := 32.38972 deg Site "B" Latitude in decimal degrees. (Note 1)La := 87.71806 deg Site "A" Longitude in decimal degrees. (Note 1)Lb := 87.86694 deg Site "B" Longitude in decimal degrees. (Note 1)L := -0.14889 deg Longitude of Site "A" minus the Longitude of Site "B"D := below degrees of arc Distance along path.C := below deg True bearing from North if sin L is positive.C' := below deg True bearing from North if sin L is negative, (360 - C).

Definition of Constants

:= Value Units Notes- := 0.017453293 rad/deg Note 2- := 111.2300 km/deg- := 0.62137119 mi/km Note 2- := 57.295779 deg/rad Note 2

Equations

1) cos D = sin A sin B + cos A cos B cos L2) cos C = (sin B - sin A cos D) / (cos A sin D)

Solution

Param. = Value Units Notessin A = 0.537266910 n/acos A = 0.843412276 n/asin B = 0.535675343 n/acos B = 0.844424021 n/asin L = -0.002598598 n/acos L = 0.999996624 n/acos D = 0.999995817 n/a From Equation 1 above

D = 0.002892403 radsin D = 0.002892399 n/acos C = -0.651498132 n/a From Equation 2 above

C = 2.280353827 radC = 229.345 deg Note 4C' = 49.345 deg Note 4D = 0.165722469 deg degrees of earth surface arc.D = 18.433 km Note 4D = 11.454 mi (statute) Note 4

Notes:

1) Value from user input on the Cover Sheet.2) From "Handbook of Chemistry & Physics", 59th Edition, CRC Press.3) There is no user input on this sheet.4) This value is shown on the Cover Sheet.

document.xls 04/08/2023 B&D Calc

document.xls 04/08/2023 Path Loss


PATH LOSS CALCULATION



f := 2.45500 GHz Operating Freq. Value from user input on the Cover Sheet.

D := 11.45393 mi (statute) From B&D Calc Sheet.:= calc below dB Free-space path loss.


:= Value Units NotesK := 102.07 dB Pseudo constant depends upon frequency.

Equation

1) Note 2

Solution

Param. = Value Units Noteslog f = 0.390051496 n/alog D = 1.058954445 n/a

= 131.051 dB This value is shown on the Cover Sheet.

Notes:

1) There is no user input on this sheet.2) Formula from the Adtran Tracer manual and from the Andrew Catalog. Values for K from

Cylink manual.

Lfs

Lfs := K + 20 log f + 20 log D

Lfs

document.xls 04/08/2023 Path Loss

document.xls 04/08/2023 Availability


AVAILABILITY CALCULATION



a := 1.00 n/a Terrain Roughness factor. User input from Cover Sheet.b := 0.50 n/a Climate factor. User input from Cover Sheet.f := 2.45500 GHz Frequency. User input from the Cover Sheet.d := 11.45393 mi (statute) Distance. Calculated value from the B&D Calc Sheet.

FM := 34.60062 dB Fade Margin. Calculated value from the Cover Sheet.


:= Value Units Notess := 31558149.504 sec/yr Seconds per mean solar year.

Equation

1)

Solution

Param. = Value Units NotesAv = 99.999840% Availabilitydt1 = 50 sec/yr Predicted downtime per year.dt2 = 0.84 min/yrdt3 = 0.014 hr/yr

Notes:

1) There is no user input on this sheet.2) Barnett's Model for outage or "unavailability". References:

"Engineering Considerations for Microwave Communications Systems", AG Communication

System, 4th Edition, 1991, pp. 68-69.

Availability (Av) = (1 - a * b * 10-5 * f/4 * d3 * 10-FM/10) * 100% (Note 2)

document.xls 04/08/2023 Availability

document.xls 04/08/2023 Other G & L


OTHER GAINS & LOSSES

LOSS

Description Qty Each Total Units BasisConnectors 8 0.10 0.800 dBCoax Cable Surge Suppressor 2 1.00 2.000 dBJumper 0.000 dBRadome 0.000 dBAttenuator 0.000 dBFilter 0.000 dBCable Degradation 1 1.00 1.000 dB Example of an estimated, temporary loss.Antenna/Feedline estimated mismatch 2 2.00 4.000 dB Example of an estimated, temporary loss.Other, Misc. 0.000 dB

0.000 dB0.000 dB0.000 dB0.000 dB

7.800 dB

GAIN

Description Qty Each Total Units BasisAmplifier 0.000 dB

0.000 dB0.000 dB

0.000 dB

NET LOSS = 7.800 dB

Notes:

1)

document.xls 04/08/2023 Documentation


Spreadsheet Documentation

1.0 Purpose and Scope

2.0 General

3.0 User Input

The purpose of this "Program" is to provide data-sheet style documentation for an unlicensed radio path, (hop), and to provide calculations to support the viability of the hop. Although the calculations used herein are generally applicable to several VHF, UHF, and microwave bands, the intended scope of application is the 902-928 MHz, the 2.4-2.483 GHz, and the 5.7 GHz unlicensed spread spectrum, (ISM), bands. This program is not intended to replace commercial programs - it is intended to provide a more readily available tool for individuals involved in path analysis. It was created for use by Communications Engineers and Technicians and should not be used by those not familiar with path analysis.

Note: This spreadsheet is not suitable for microwave system design; a more sophisticated analysis is required.

The Program is an Excel Workbook consisting of several spreadsheets including: Cover; Profile; Topo Data; B&D Calc (Bearing & Distance); Path Loss; Availability; and Other G&L (Gains & Losses). Calculations and input/output data span the various spreadsheets. The user should be certain he is using the latest Program version. See the Version information in the Summary paragraph for information. Contact the author for the latest version.

User input is allowed only on the following sheets; Cover, Topo Data, and Other G&L. Space for user notes is allowed on the Path Loss and Availability sheets. The various spreadsheets are protected so that the user cannot inadvertently overwrite a formula or a reference. The spreadsheet contains sample data for instructional purposes. The user should overwrite sample data during data entry and delete all other sample data in non-required spreadsheet cells.

Cover Sheet:User input areas are generally un-shaded. The revision and hop nomenclature areas at the top contain sample input data and should be overwritten with site specific data. Ensure that the data are entered using the units of measure indicated. In several cases, conversions are calculated for the user's viewing pleasure.

Topo Data:User data input is limited to several areas. These are; the twenty (20) elevation points, the average foliage height, the point adder column, and the notes.

With regard to the elevation or data points, the elevation data would normally be read from a topographic map such as a USGS 7.5 minute type. For program simplicity, the number of data points requested by the spreadsheet was fixed at twenty, (20), and the distance between the data points is automatically calculated as equidistant based on the total distance between the subject sites. It is recommended that the user select twenty equidistant points along a straight line drawn on the topo map(s) between the two subject sites. Note that the subject site locations are not to be included in the count of the twenty selected data points. The elevation for any particular datum point may be selected "off-center" to accentuate a ridge, peak, or valley.

Note: If the path was previously engineered or is known to be good empirically, this step may be bypassed. If bypassed, it is recommended that "dummy" data be entered and a notation be made on the cover sheet.




4.0 Calculations and Output

5.0 Summary & References

References:

Conversion Factors "Handbook of Chemistry & Physics", 59th Edition, CRC Press.

Path Loss Formula Various Supplier catalogs and Radio Manufacturer support documentation.

For adjustments to elevations based upon man-made objects in or near the path, there is a column for "Point Adder". An example of this is given. See point #12 on the Topo Data sheet and note the effect of this "adder" on the graph.

Average foliage height may be adjusted as required; this number is set at 40 feet for a default value. The foliage height will appear as a green trace on the path profile graph.

Other Gains & Losses:The "Other G&L" worksheet provides space for estimating additional factors which will affect the Fade Margin, (or Received Signal Level). Note that although an amplifier is listed under "Gains", in most cases, an amplifier would not be acceptable due to the power restrictions imposed on the intentional radiator, (the antenna), by the FCC for the subject ISM bands.

The Program provides a path analysis from Site A to Site B. Because of the intended use of this program with regard to service, (ISM), transmitting and receiving equipment at each end will normally be identical with regard to make, model, and performance. If there is a significant difference between power outputs and antenna types between the sites, the user may elect to do the calculation twice, (e.g. "B" to "A"), or use the worst case scenario at Site A.

Formulae and reference information is included on the various sheets. Additional reference information is given in Paragraph 4 below. Of most interest to the User is the calculated output data given on the Cover Sheet Line 41 (distance between the sites), Line 44 (Fade Margin), and Line 45 (estimated Availability). Also refer to Lines 9 and 29 for the bearing or azimuth angle from North for the purpose of antenna aiming. The topo data entered provides a full page Profile and a summary profile on the Cover Sheet.

This spreadsheet is intended to document unlicensed spread spectrum hops in the ISM bands. The results obtained will be in close agreement with commercial and vendor supplied programs using the same data although the calculations herein may be slightly more conservative. It is not the purpose of this documentation to teach path analysis - this Program should only be used by qualified personnel with an understanding of radio path analysis. Any suggestions, recommendations, or corrections are welcomed.

Availability Formula(Barnett's Model)

"Engineering Considerations for Microwave Communications Systems", AG Communication System, 4th Edition, 1991, pp. 68-69.

Note: Other calculations are based on simple algebra and spherical trigonometry. Some suggested inputs are based upon the author's experience. Standard spreadsheet functions have been applied, and all formulae are within printable sheet boundaries and in plain view.

rf path analysis

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