We've all heard the following at some point, "5 GHz has more attenuation than 2.4 GHz". You may have even heard "FSPL (free space path loss) proves it". I'm going to talk about this in depth, why this is wrong, and why the FSPL formula may have frequency in it, but that doesn't mean that FSPL is dependent on frequency. And then we will discuss the reason frequency is part of the FSPL formula, Antenna aperture in more depth.
Let's start by looking at the FSPL formula and calculating two examples, with all things equal except for the frequency. You may see multiple versions of the FSPL, but this one is my favorite.
FSPL = 20*LOG10(d)+20*LOG10(f)+20*LOG10(4*π/c)-Gt-Gr
d = Distance between transmitter and receiver in meters
f = Frequency in Hz
c = speed of light in Meters/second
Gt = Gain of transmitting antenna
Gr = Gain of receiving antenna
So let's plug in some numbers. Our examples will use 50 meters as our distance, and the same antenna gains of 6 dBi for transmitter, and 2.15 dBi for the receiver.
FSPL = 20*LOG10(50)+20*LOG10(2400000000)+20*LOG10(4*π/300000000)-6-2.15 = 65.87 dBm
FSPL = 20*LOG10(50)+20*LOG10(5180000000)+20*LOG10(4*π/300000000)-6-2.15 = 72.55 dBm
You can see that with a 5 GHz channel we lose approximately 6.7 dBm more signal strength. But make no mistake, this doesn't prove that a higher frequency signal suffers more attenuation. Instead what we are seeing, is that the FSPL formula takes antenna aperture into consideration.
Let's get into the meat of this post. Antenna aperture is the area around a antenna in which we can receive RF energy. For most antenna types, the physical size of the antenna is directly related to wavelength, and a physically larger antenna is exposed to more RF energy. This includes the popular omni-directional dipole antenna. Antennas are generally either full wavelength or a fractional wave length. So what does this mean? First we must calculate the wavelength of 2.4 GHz and 5 GHz.
λ = Wavelength = (c/f)
c = speed of light in MPH = 186,282 MPH
f = Frequency in Hz
λ = 186,282 / 2400000000 = 4.92 Inches
λ = 186,282 / 5180000000 = 2.27 Inches
This simply means dipole antennas for a 5 GHz network will be shorter, and therefore will be exposed to less RF energy. You may wonder why the antenna must be shorter for 5 GHz signal reception. The answer is resonance. You may have heard of this at some point. You can think of resonance in physical terms, as an opera singer shattering a glass with their voice alone. Resonance is the natural frequency something wants to vibrate in the physical world. Of course this is physical resonance and not electrical resonance. Electrical resonance defines when capacitive reactance and inductive reactance cancel eachother out. Both capacitive and inductive reactance are the equivalent to resistance from a DC circuit, but are only seen in a AC circuit, and are created from the changing flow of electricity inherent in a AC circuit. Meaning current is able to flow with the least resistance, which equals more power being radiated when the antenna is the appropriate size, this is why a power cable doesn't radiate much EMR, because the cable generally isn't resonant with the frequency running through it, which in the US would be 60 Hz, which would require a rather large power cable to achieve resonance. You can achieve resonance with an antenna that is a fraction of the wavelength in size, such as 1/2 and 1/4 wavelength dipole antennas. Just know that a lower frequency = larger antenna = exposure to more RF energy = more signal received. These are generalities, because there are many variables involved here.
We can further break this down by actually calculating the area around the antenna in which we can receive energy.
Antenna aperture = λ^2*Gr/4*π
λ = Wavelength
Gr = Antenna gain of receiving antenna. Must be a linear value, and not logarithmic
π = Pi
Antenna aperture for 2.4 GHz = 4.92^2*1.99/4*π = 3.83 Inches^2
Antenna aperture for 5.18 GHz = 2.27^2*1.99/4*π = .816 Inches^2
Notice that the Antenna aperture for 2.4 GHz is approximately 4.7 times the size of the 5.18 GHz antenna. This matches our FSPL difference. Example below
20 dBm = 100 mW
26.7 dBm = 468 mW
468 / 4.7 = 99.6 mW
If we wanted to change the gain of an omnidirectional antenna, we have two options. Active gain, achievable through the use of an amplifier. Or passive gain, using for example a collinear array.
A collinear array, would be multiple omnidirectional structures arranged in a serial connection. This gives you the same pattern in the azimuth plane, but a more focused beam in the elevation plane. If you want to see what this may look like, this article from Cisco has some great images that we will use. Figure 4, shows a regular dipole antennas radiation pattern in azimuth and elevation planes at 2.2 dBi . Figure 5, shows a dipole antenna that is a collinear array at 5.8 dBi. Notice that in the elevation plane the radiation pattern has become flatter and more disk like. This means that when the dipole antenna in Figure 5 transmits, the energy will be more concentrated in the elevation plane. No additional energy is being added. You may be wondering how this could be possible, essentially each separate element in the collinear array is transmitting the same pattern from FIgure 4. But we are leveraging the fact that we will create nulls, these nulls come from the fact that each element in the array are 180° phase shifted from the previous element. You end up with antenna patterns similar to this image. If you want a visual of what this looks like in action, this video, can help you visualize it, I've already linked it at the point you should start watching. It's a very similar concept to the way a phased array works for beamforming. Antenna reciprocity applies to this as well. We can use the Antenna aperture formula to see the affects of changing antenna gain.
Our examples will use a 2.4 GHz signal. With a receiving antenna that has a gain of 3 dB and 6 dB. First example will be 3 dB.
Antenna aperture = 4.92^2*1.99/4*π = 3.83 Inches^2
Next is antenna gain of 6 dB
Antenna aperture =4.92^2*3.98/4*π = 7.67 Inches^2
We just doubled our Antenna aperture. But don't be fooled, remember antenna reciprocity. Since we are increasing gain passively at the antenna, we aren't adding any energy, we are just concentrating it. Thus we have proven that passive antenna gain also affects reception, and not just transmission of signals.
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