When we consider unguided wireless communications, we must understand the signal attenuation that occurs between transmit and receive antennas. Understanding the amount of signal attenuation enables us to determine how much transmit signal power is required to effectively communicate with the receiving system.
The information, or message, that we wish to transmit, is modulated onto a frequency carrier, which is then emitted from a transmit antenna in the form of an electromagnetic (EM) wave. This EM wave propagates through free space, and is then collected by the receive antenna. The receive antenna then converts the EM wave into an electrical signal which can then be demodulated back into the original message. However, the signal power (watts) received by the antenna is much less than the transmitted power due to attenuation loss. The Friis equation (also known as the Free Space Loss, FSL equation) describes this attenuation loss.
First, let's consider what attenuation is. Attenuation, as treated in the Friis equation, is the spreading of power over an ever increasing surface area as it propagates away from the transmit antenna. Imagine an ideal, but unrealistic, antenna that is a single point (termed isotropic antenna). Power is transmitted from the isotropic antenna in the shape of a sphere. At the antenna the power you transmit is all located in a single point. As the EM wave propagates outwardly in a sphere, the power is stretched over an ever increasing sphere surface. It is useful to measure power density (watts per meter squared) since the receive antenna will only be able to collect a portion of the power transmitted from the ideal isotropic antenna. We can measure how much power resides in a 1 meter2 area as a function of distance from the isotropic antenna.
Power Density, Pd = Pt/(4πd2)
In the above power density equation, Pt is the power transmitted from the antenna and d is the distance from the transmitting antenna (note: d is typically the distance between the transmit and receive antennas).
Although deriving Friis' equation is beyond this tech note, we can see similarities between the power density and FSL equations.
FSL=(4πd)2/l2, where l is the wavelength of the carrier
We can also place the above equation into decibel format:
FSLdB = [FSL] = 20log10(4πd/l) = 20log10(4π) + 20log10(d) - 20log10(l)
Now let's look at two isotropic antennas, one transmitting and the other receiving. We would like to understand how much FSL has impacted our signal (i.e., know how much of the transmit power will be received by the receive antenna). Therefore, we can use the following equation to determine how much receive power we will have.
Pr = Pt ¸ FSL = Pt ¸ ((4πd)/l)2 = (Pt*l2)/(4πd)2, where Pr is the power received by the receive antenna
By converting to decibels, it is easier for us to see how the link equation works.
[Pr] = [Ps] - [FSL] = 10log10Ps - 20log10(4πd/l), brackets denote decibel values
The above equations tells us that the power received by the antenna in decibels, is simply the power transmitted minus FSL in decibels.
In some transmission systems, especially those that operate at high frequencies (i.e., GHz ranges) where direct line-of-sight between antennas becomes more critical, we'll want to shape our antennas so that we concentrate transmit power in the direction of the receive antenna. Doing this maximizes power density in a single direction towards the receive antenna vice in the shape of a sphere. The directivity of an antenna therefore provides an antenna gain (G) in a desired direction over that of an isotropic antenna. This gain enables the EM signal to travel further distances using the same transmit power.
If using directional antennas for both transmit and receive, we will also have antenna gains associated with both, denoted as GT and GR for transmit and receive antenna gains respectively. The link equation then becomes:
Pr = (Pt*GT*GR) ¸ FSL = (Pt*GT*GR) ¸ ((4πd)/l)2 = (Pt*GT*GR*l2)/(4πd)2
In terms of decibels, the equation becomes:
[Pr] = [Pt*GT*GR] - [FSL] = 10log10Ps + 10log10GT + 10log10GR - 20log10(4πd/l)
On the transmit side, we typically term the combination of Pt and GT as the Effective Isotropic Radiated Power (EIRP).
EIRP = Pt * GT, or in decibels, [EIRP]=[Pt] + [GT]
Substituting EIRP into our equation, we get,
[Pr] = [EIRP] + [GR] - [FSL]
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