# Wireless Calculators

### A Wireless System (more or less!) Key: Green is good, Red is bad.

1. Power Budget - total power of your system in dBm.
2. Free Space Loss - power loss over distance.
3. System Performance - How far will it go, will it get there or what is my Operating Margin?
4. Fresnel Zones - How much more than LOS or how high should my antenna be?
5. Power Conversion - dBm to milliWatts and milliWatts to dBm

Power Budget

Use this calculator to walk through all the factors that make up your Power Budget. The 'Power Budget' is the the total power being output from the wireless system and is the sum of:

• PLUS Radio Transmit Power (A above)
• MINUS cables and connectors losses (B above)
• PLUS antenna gain (C above).

Enter one parameter in each column (or leave blank) depending on what you know and the calculator will supply the appropriate conversions automatically. Up to 2 decimal places may be entered as 0.xx or .xx.

Note: Connector loss is generally small UNLESS you've got lots of 'em in which case you are probably in trouble anyway, or your cable is VERY short. Just leave the line blank if you are feeling lazy.

Calculations and equations used.
 Radio and Antenna Transmit Power Antenna Gain Power mWOR  dBm dB(i) dB Cable Loss Cable Properties (per 100 ft or m) Cable Length dB (100 ft) OR  dB (100 m) feet OR  meters dB Connector Loss Frequency in MHz No. of Connectors MHz. No. dB Budget dB

Free Space Loss

Loss of power over distance (assuming no FRESNEL Effect and nothing in the way). This a very idealised calculation and in practice everything interferes with the signal but it will give you a reasonable approximation of the actual loss over distance.

Enter the system Frequency in MHz and the distance in either Kilometers (Km) or Miles below and then click the 'Calculate' button. 1 GHz = 1000 MHz e.g. 2400 = 2.4 GHz.

Calculations and equations used.
 Frequency Distance Result MHz KmOR  Miles dB

Fresnel Zones

Defines how much clearance you need (yes you need more than simple Line-of-Sight) and for longer links > 3 Km (2 miles) whether you may have a ground clearance problem from our friendly planet.

Enter the Total link distance (in Miles or Kilometers), if you do not enter an Obstacle distance (in Miles or Kilometers) the calculator will use the mid-point for all calculations (Note: assumes antennas at same height). Finally enter the system Frequency in MHz and then click the 'Calculate' button. 1 GHz = 1000 MHz e.g. 2400 = 2.4 GHz.

The calculator will generate the radius of the 1st Fresnel zone only (at the obstable point or the mid-point), the 60% (no obstacle) radius and the height of the effective earth curvature at the mid-point of the Total link distance using the effective earth radius.

Calculations and equations used.
 Total Link Obstacle Distance 1st Fresnel Zone Radius KmOR  Miles KmOR  Miles mat  Km ftat  Miles Frequency 60% No Obstacle Radius MHz m ft Earth Height (mid-point) m ft

System Performance

This calculator will give you one of three answers:

1. If you leave distance blank it will apply the defined SAD factor (or default to 30%) to the Operating Margin and supply the max. distance (in Km and Miles) at which the Margin operates.
2. If you enter the distance it will calculate the Operating Margin and the SAD factor.
3. If you enter distance but leave RX or TX antenna gain (or both) blank it will apply the chosen SAD factor (or default it to 30% if none supplied) and generate the required antenna power. If both are left blank it will calculate a symmetrical antenna gain.

To RESET any parameter just set it to BLANK before clicking 'Calculate'

Notes: RX Sensitivity is ALWAYS expressed as a negative dBm (- dBm) and is the lowest power of signal your radio can handle. Its buried somewhere in your radio spec and will be typically in the range of -70 to -110 dBm. Don't guess or 'fudge' this number.

Note: If you solve for TX antenna (you leave it blank) and define a specific SAD factor it is applied to the TX budget and any TX antenna value will include this factor. If you then click Calculate again without changing anything, the SAD factor will be calculated to include the supplied TX antenna value and thus may show a lower value than the original one.

Calculations and equations used.
 Frequency Distance FS Loss MHz KmOR  Miles dB TX Power TX Cable TX Antenna Total TX dBmOR  mW dBm dB dB RX Sensitivity RX Cable RX Antenna Total RX dBm dB dB dB Margin RX Power SAD Factor Theoretical dBm % dB

milliWatts to dBm (and vice versa)

Power in milliWatts to dBm (and vice versa) . Enter the 'Transmit Power' (A or G above) in milliWatts OR the 'Power Ratio' in dBm and click the appropriate 'Calculate' button. 1 Watt = 1000 milliWatts.

Calculations and equations used.
 Transmit Power Result mW dBm Power Ratio Result dBm mW

## Power Budget Calculations

1. mW to dBm = 10Log10(mW)

2. feet to meters = .3048

3. meters to feet = 3.28

4. Calculator normalises all distances to kilometers and meters

5. Connectors loss = 0.10 * square root (frequency in GHz)

## Free Space Calculations

1. Free space loss = 36.56 + 20Log10(Frequency) + 20Log10(Distance in miles)

2. Calculator normalises all distances to miles

3. Miles to Kilometers = 1.609

4. Kilometers to miles = 0.621

## Fresnel Zone Calculations

1. Calculator normalises all distances to kilometers and meters

2. Miles to Kilometers = 1.609

3. Kilometers to miles = 0.621

4. feet to meters = .3048

5. meters to feet = 3.28

6. 1st Fresnel Zone radius (Km) = 17.3 x Sqr root ((Obstacle Distance x (Total Link - Obstacle Distance)) / (Frequency in GHz x Total Link))

7. 1st Fresnel Zone radius (miles) = 72.6 x Sqr root ((Obstacle Distance x (Total Link - Obstacle Distance)) / (Frequency in GHz x Total Link))

9. Radius of nth Fresnel zone (meter) = sqr root ( (n x wave length x Obstacle distance x (Total Link - Obstacle Distance)) / Total Link )

10. wave length (meters) = speed of light (299,792,458 m/s) / frequency in Hz

11. Earth curvature calculation = (Total Link) 2 /(8 * effective earth radius)

13. Earth radius = 3963 miles, 6378 Km

## System Performance Calculations

1. Calculator normalises all distances to miles and feet during calculations.

2. Free space loss = 36.56 + 20Log10(Frequency) + 20Log10(Dist in miles)

3. mW to dBm = 10Log10(mW)

4. dBm to mW = 10(dBm/10)

5. RX Power = Margin - RX sensitivity

6. Theoretical margin = TX power budget + RX power budget - free space loss

7. SAD factor = Theoretical margin/TX power budget * 100 and shows the percentage of spare power on transmission.

## dBm to milliWatts Calculations

1. mW to dBm = 10Log10(mW)

2. dBm to mW = 10(dBm/10)