## Author's Contact Information

### Introduction

• Transmitter power
• Cable and connector losses
• Antenna gain and efficiency (Tx and Rx)
• Free space and Flat Earth propagation
• Height of Tx and Rx
• Obstruction loss
• Multipath loss

The spreadsheet will be upgraded in the future to include new features and increased sophistication of existing features. These will include:

• Connector loss information
• Calculation of multipath loss from scattering models
• Calculation of loss from propagation medium (humidity, conductivity, permittivity, human/animal tissue, foliage, etc.)

This application note briefly describes the major assumptions about the propagation path, some of the mathematics behind those assumptions, and then provides instructions for using the spreadsheet.

### Propagation Path Loss

The two fundamental propagation paths in the spreadsheet are the Free Space path and the Flat Earth path. There are additional entries to account for multipath, obstruction, and penetration losses, which are common inside buildings or on urban streets. Analog's ISM-RF products are used in parking lots, streets, open areas, and buildings where the radio height above ground is small. This means that the Flat Earth path model is usually best suited for estimating the link budget. In applications where both Tx and Rx are located on towers or rooftops, and the antenna beams are narrow, the Free Space model would be more relevant.

A radio signal that transmits very close to the ground relative to the desired distance of the horizontal path consists of two components: the direct, Line-Of-Sight (LOS) signal and the signal that is reflected from the ground. The phase of the ground bounce electric field, with few exceptions, is always opposite the phase of the line-of-sight electric field. In free-space propagation, there is no ground reflection.

PR = PTGTGRλ2/(4πR)2

where PR is the received power, PT is the transmitted power, GT is the transmitter antenna gain, GR is the receive antenna gain, R is the range, and λ is the wavelength.

The path loss formula for flat-earth propagation is

PR = ½PTGTGRλ2/(4πR)2 (1 + a2 - 2acos(2πΔR/λ))

where ΔR is the difference in length of the direct path and the ground reflection path and "a" (≤ 1) is the relative strength of the ground bounce path.

ΔR = √(R2 + (h2 + h1)2) - √(R2 + (h2 - h1)2)

Notice that the result in Equation 2 is the product of the free space loss in Equation 1 and a ground bounce loss factor shown below.

LGB = ½(1 + a2 - 2acos(2πΔR/λ))

At close range, where the path loss difference, ΔR, is greater than or equal to about half a wavelength, LGB varies rapidly with R, and the received power fluctuates significantly. At longer ranges (usually 30m or more in handheld applications), LGB exhibits an R-2 variation, so that the received power in a flat-earth environment (Equation 2) decreases as the 4th power of R.

Both formulas for the propagation loss are calculated in the spreadsheet. You can choose which one to use to determine link margin.

### User Tabs Descriptions

There are five tabs in the spreadsheet that perform calculations or have information to guide the user in making entries:

• Ground Multipath
• Cable Loss
• Obstructions

Of these tabs, only the Link Budget and Ground Multipath tabs require inputs from the user. The Cable Loss tab contains insertion loss specifications from commonly-used coaxial cables and connectors. The Obstructions tab contains estimated losses for walls and windows inside buildings, and for forests, vegetation, and structures outside. These numbers can be used to determine the entries in the Link Budget tables for cable and obstruction loss. Connector losses are usually less than 1dB and can be entered without the use of an additional tab. The Link Plot tab depicts the radio link loss contributions from the hardware and the channel (propagation path) from start to finish.

The Ground Multipath tab requires user inputs for the transmitter and receiver height, and contains a useful plot of path loss vs. distance, including (in some scenarios) the deep transmission fades associated with terrestrial radio links.

The entries in the spreadsheet are color-coded to identify their source.

Black: Direct entry from the user
Dark Red: A constant, e.g. the speed of light
Blue: Calculated number
Green: Values obtained from another tab

Open the Link Budget tab of the spreadsheet. A screen shot of this tab is shown at the end of the instructions.

1. Enter the carrier frequency of the radio in megahertz. The spreadsheet will calculate the wavelength.
2. Enter the PA power of the transmitter. This is the power level estimated or measured as close to the PA output pin of the transmitter circuit as possible.
3. Enter the Tx match loss (if any). Most transmitters need a few passive components to transform the antenna impedance to the optimum impedance for the transmitter.
4. Enter any significant connector and cable losses between the transmitter circuit and the antenna. At this point, the spreadsheet shows the power at the Tx antenna input.
5. Enter the Tx antenna gain. This includes the efficiency of the antenna, losses in any additional impedance transformation networks, and allowance for variation in the directional pattern of the antenna. Antennas whose dimensions are less than 0.1 wavelength will have a loss rather than a gain.
6. Enter the distance in meters that you wish to cover with the radio link.
7. Enter the loss from the medium, if applicable. Examples are propagation through media other than air or propagation at higher frequencies (> 2GHz) where moisture or molecular absorption may occur.
8. Go to the Ground Multipath tab on the spreadsheet and enter the height of the transmitter antenna and receiver antenna.
9. Return to the Link Budget tab. At this point, the spreadsheet calculates the path loss for both Free Space and Flat Earth at the distance you have chosen.
10. The received power at the antenna for Free Space Loss appears a few rows above the received power for Flat Earth Path Loss. If the link is a free space link, the Free Space Loss is used and there is no need to calculate the Flat Earth Loss.
11. Enter the anticipated Multipath Loss (from reflecting and scattering objects in the path). This is usually at least 20dB, unless the path is flat and empty (an open field or a deserted parking lot, for example).
12. Enter the anticipated Obstruction Loss (from walls or buildings).
13. The received power at the antenna for Flat Earth Loss appears a few rows below the Free Space Path Loss.
14. Enter the Rx antenna gain. The same rules for efficiency apply as for Tx antenna gain.
15. Enter any significant connector and cable losses between the antenna and the receiver circuit. The final Rx power at the receiver input is shown for both Free Space path loss and Flat Earth path loss.
16. The entry immediately to the right of the Rx power is the sensitivity of the receiver. This is the minimum signal level at which the receiver will process information correctly from the radio link. When the received signal level for the path of interest (Free Space or Flat Earth) is equal to the sensitivity, the distance entered is the maximum achievable range of the radio link. Adjust the range as needed to match the received signal level with the sensitivity.
17. To determine the proper sensitivity number to enter in the cell, use the Receiver Sensitivity Calculations section of the Link Budget tab or select a value from the Analog RX table on the Link Plot tab. The three numbers to enter for calculating the sensitivity and SNR of the receiver are the noise figure, the receive bandwidth, and the operating temperatures.

### Example 1: Remote Keyless Entry (RKE) Control Link

Figure 1 is a screen shot of the Link Budget tab filled out for an RKE control link at 315MHz. Figures 2 and 3 show the Ground Multipath tab with entries for Tx and Rx height and the path loss vs. distance from the radio link. Discussion of the results appears after the screen shots.

#### RKE Example Observations and Analysis

Entries in the Link Budget spreadsheet are characteristic of RKE applications, which have very low antenna gains of -15dB for the Tx and Rx and transmitter power levels of +10dBm or lower. The size of the key fob antenna is usually no more than 1in × 1in (40mm × 40mm), which is tiny compared to the 950mm wavelength, so the antenna is very inefficient. The receive antenna can be larger, but allowance needs to be made for shadowing and blockage inside the car or behind the dashboard. The transmitter power at the IC is typically +10dBm to minimize drain on the battery and to keep the peak radiated power from the antenna below the allowable FCC limit. This maximum value is given in terms of the peak field strength 3 meters away from the transmitter. This can be as high as 60mV/m (equivalent to +0.4dBm radiated power from the antenna) if the duty cycle of the transmitter is kept low enough.

The entries that are needed in the Ground Multipath tab are the height of the transmitter and the height of the receiver. These determine the effect of the ground bounce. In the example, the height of both transmitter and receiver are 1m, which is typical for the person holding the key fob and for the location of the receiver in the vehicle.

Under the conditions entered in the spreadsheet, including the -114dBm sensitivity of the receiver, the maximum range in an open area is approximately 175m. This result was found by changing the value of the Distance entry in the Link Budget tab, until the received signal power equaled (within a few tenths of 1dB) the sensitivity.

### Example 2: Home Automation Sensor and Keypad

Figure 4 is a screen shot of the Link Budget tab filled out for a home automation link at 433.92MHz. Figures 5 and 6 show the Ground Multipath tab with entries for Tx and Rx height and the path loss vs. distance from the radio link. This link could be between an occupancy detector and wall-mounted keypad in a home security system, a remote thermostat control, and a thermostat in another room, or a remote dimming control and a lighting fixture. In this example, unlike the RKE Control Link, there are obstructions and multipath losses, which add to the path loss and therefore reduce the range. Contrastingly, the antenna efficiency is higher (antenna is a larger fraction of a wavelength), and the radios are placed at slightly greater heights above the ground, which increase the range. The net result in this example is a reduction in range.

#### Home Automation Example Observations and Analysis

Entries in the Link Budget spreadsheet that are characteristic of a home automation application are low antenna gains of -10dB for the Tx and -5dB for the Rx, and the transmitter power of +10dBm. The size of the remote Tx antenna depends on the package constraints of the sensor (occupancy detector, thermostat mount, etc.), but it is usually larger than the antenna in a key fob. In addition, the wavelength is smaller at 433MHz than it is at 315MHz. For these reasons, the antenna gain in this application is higher than it is in an RKE application, but the antenna is still very inefficient. The receiver antenna can be larger, because the receiver enclosure (usually mounted on a wall) has more room, but it is not likely to be as large as one-fourth of a wavelength (17.5cm, or 7in). Therefore, the receiver antenna gain is still less than 0dB. The transmitter power is typically +10dBm to minimize drain on the battery (some home automation transmitters may be able to use "house power") and to keep the peak transmitted power below the allowable FCC limit. Again, this maximum value, which is higher at 433MHz than at 315MHz, is given in terms of the peak field strength 3 meters away from the transmitter. This level can be up to 110mV/m if the duty cycle of the transmitter is kept low enough. The power needed to produce this field strength is +5.6dBm. In both this example and the previous RKE example, the transmitted power entered into the spreadsheet is not at the FCC limit, because the antennas are small and inefficient. If a larger antenna can be deployed, you can easily improve the range.

The entries that are needed in the Ground Multipath tab are the height of the transmitter and the height of the receiver. These determine the effect of the ground bounce. In the example, the height of both the transmitter and receiver is 1.5m. Even the small added height, compared to the RKE example (1.5m vs. 1.0m), will improve the range. This is because the ground bounce approximation for path loss improves as the square of the height of each antenna. Depending on the particular home automation application, each height may vary. For instance, an occupancy sensor may be mounted on the ceiling, which would increase its height in the spreadsheet.

The indoor environment adds loss from multipath (reflections and scattering from objects in a house or building) and blockage (walls and ceilings). The multipath loss is estimated at 25dB and allowance for 3 walls (10.2dB blockage loss) has been made through the entries in this spreadsheet.

Under the conditions entered in the spreadsheet, including the -114dBm sensitivity of the receiver, the maximum range in an indoor area is approximately 80m. This result was found by changing the value of the "Distance" entry in the Link Budget tab until the received signal power equaled (within a few tenths of a dB) the sensitivity. This example shows how the multipath and blockage losses associated with the inside of a building dramatically reduces the range of indoor radio links.