**Comparing Wave Propagation of 900 MHz and 2.4 GHz Frequencies**

To demonstrate the basic difference in wave propagation of 900 MHz and 2.4 GHz waves, a quick look at path loss is provided. As waves propagate out from the transmitter, some attenuation of the signal takes place due to properties of the medium (air in most cases). Path loss describes this attenuation as a function of the wavelength of the operating frequency and the distance between the transmitter and receiver. The path loss is derived from the Friis transmission equation and is defined as:

Path Loss = 20 log(4*p*r/?) dB

where r is the distance between the transmitter and receiver, and ? is the wavelength . The table below shows how path loss differs between 900 MHz transmitters (?=0.33 meters) and the 2.4 GHz transmitters (?=0.125 meters).

NOTE: Path loss analysis does not account for effects such as differing TX power outputs and RX sensitivities. See the "Range of 9XStream (900 MHz) and 24XStream (2.4GHz) Modules" section for more detailed range information.

Frequency | r = 10 Meters | r = 100 Meters | r = 1000 Meters |
---|---|---|---|

900 MHz | 51.527 dB | 71.527 dB | 91.527 dB |

2.4 GHz | 60.046 dB | 80.046 dB | 100.046 dB |

Thus, the path loss is +8.519dB more over a given range for the 2.4 GHz modules. Since the range doubles with every 6 dB of reduced path loss, the 900 MHz modules have 2.67 times as much range as the 2.4 GHz modules [2^(8.519/6) = 2.67].

**Range of 9XStream (900 MHz) and 24XStream (2.4 GHz) Modules**

A link budget analysis can mathematically predict the system range based on the power output, receiver sensitivity, antenna gains, path loss, and fading margin. The path loss equation represents path loss (signal attenuation) as a function of distance between the receiver and transmitter and the wavelength of the operating frequency. This equation is derived from the Friis transmission equation and is given by:

Path Loss = 20* log(4*p*r/?) dB (Eq. 1), where

r = distance between transmitter and receiver

? = wavelength

The Friis transmission equation can be used to represent the path loss as the sum of the other system factors leading to the following equation:

Path Loss = P(t) + G(t) + G(r) - R(s) - F(s) dB (Eq. 2), where

P(t) = transmitted power

G(t) = gain of transmit antenna

G(r) = gain of receive antenna

R(s) = sensitivity of receiver

F(s) = fading margin, (experimentally determined to be 22dBm)

These two equations can be used to compare the maximum range of the 9XStream and 24XStream modules.

- Consider the range of the 9XStream module:
= 0.33 meters (for f=900 MHz)

(Eq. 1) Path Loss = 113 dB = 20 * log(4*p*r/?)

(Eq. 2) Path Loss = 21dBm + 2dB + 2dB - (-110dBm) - 22dBm= 113 dBBy setting these equal to each other, a little computation reveals that r=11848 meters, or a little over 7 miles.

- Now consider the 24XStream module:
= 0.125 meters (for f=2.4 GHz)

(Eq. 1) Path Loss = 105 dB = 20 * log(4*p*r/?)

(Eq. 2) Link Budget = 18dBm + 2dB + 2dB - (-105dBm) - 22dBm = 105 dBOnce again, setting these equations equal leads to r=1768 meters, or just over 1 mile.

From this example, it is shown that operating at 900 MHz exhibits a significantly longer range than is possible at 2.4 GHz.