The transmitter radiates power uniformly in all directions (assuming the antenna is isotropic as discussed above), forming a sphere. Consequently, at a distance r from the antenna, the power density (or "flux") decreases by an amount proportional to 1/r
2 as it spreads out in a sphere of increasing surface area. The actual equation that determines the Flux density (F) at a distance r from the transmitter is:
F = (Pout . Gant_TX)/( 4 . π . r2) [W/m2]
The received power at the receiver is:
Prec = (Pout_TX . Gant_TX . Gant_RX)/Path_loss
Where Path_loss = (4 . π . r/ λ )2
In other words, both range and transmission frequency determines the Path_loss. For the receiver to demodulate, the received power must be equal to, or larger than the sensitivity limit (see Figure 1). In ideal conditions, a 6dB (fourfold) increase in output power (or receiver sensitivity) corresponds to a doubling of the effective range.
Headroom decreases with range, and as headroom is reduced, the probability of communication loss due to environmental obstacles increases. For example, if the headroom of a 2.4GHz link is less than 15dB at 10 meters in ideal conditions, then attenuation due to obstacles exceeding 15dB will cause loss of communication.
Signal fading can also happen because of multipath interference. This is caused when signals travel along different paths from transmitter to receiver (see Figure 4). Multipath interference is caused by reflection, diffraction, and scattering. Reflection occurs when the transmitted energy reflects off the surface of an object that is large compared to the carrier wavelength (for example, walls, buildings or the ground). Diffraction describes the "wave-bending" around sharp irregular edges of an object in the transmission path. Scattering describes energy dispersion, caused by objects that are small compared to the wavelength of the propagating wave.
Figure 4: Signals arriving at the receiver after travelling along paths of different length can cause signal fading.
A designer must be prepared for the loss caused by obstacles such as floors, walls, buildings and windows. The loss depends heavily on the physical characteristics of the object. For example,
reinforced concrete walls introduce higher losses than wooden or plaster walls. Metal tinted windows are high loss barriers compared to un-tinted windows (see Table 1).
Table 1: Attenuation due to common building materials
As different paths have different lengths, the combined signals typically arrive at the receiver out of phase, attenuating the power and causing "smearing" of the received signal in the time-domain. This smearing causes inter-symbol interference (a phenomenon whereby the energy of the previous symbol or bit affects the next bit, increasing BER).
As the wavelength at 2.4GHz is 12.5 centimeters, fading may fluctuate on a short-term basis if one or both radio units are mobile. Fading may also occur due to moving objects such as people, furniture, or machinery in the area even if the radio units are stationary.
Consider a 2.4GHz system with +10dBm output power, antenna efficiency (gain) of -20dB and -105dBm sensitivity. This system may have a theoretical range of more than 40 meters, but in a typical application the effective range may drop to just 5 to 10 meters. This is why the designer should treat a manufacturer's "free-line-of-sight" range with caution.
Part 2 focuses on key specifications, avoiding interference, and navigating data sheets.
About the Author
Jay Tyzzer is a senior applications engineer with Nordic Semiconductor based on the US West Coast. This feature is based on a white paper by Frank Karlsen, an RF Designer with Nordic Semiconductor entitled "Guidelines to low cost wireless system design". The white paper can be downloaded from www.nordicsemi.com
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