There is less of a power diffrent than you expect. If you look at the number you find that typically the transmission power per channel is around 20 W compared to the up to 2W for a cellphone.
But total output power is not what is important it is the output in the direction of the receiver. The antennas on the cell towers are directed.
You have typical 3 channels that each cover 120 degrees around the tower so only 1/3 of the horizontal area is covered by a channel. They are also limited vertically so they cover the ground area below where cellphones typically are.
Cellphones do not have directional antennas like that, you really do not know in what direction the tower is so you send it in all directions.
So the power in the relevant direction is a lot more than the total difference in transmission power
Directional antennas are not just important when you send data, a directional antenna results in a stronger signal when you receive a single too if it comes from the right direction. An example of this is the satellite dishes.
The size of the antenna also has an effect on the received signal, a larger antenna receives more of the signal than a small antenna. Cell towers have larger antennas the cellphones
So the tower can receive a weaker signal from a phone because of larger directional antennas.
You can compare it to a light bulb. Use the light bulb by itself and try to illuminate something a distance away. Then put the same lightbulb in a spotlight that reflects light in a single direction and you can illuminate objects in one direction a lot more.
When receiving signals is is more like if you use a telescope or binoculars, The larger the diameter they have the more light they can collect.
So the explanation is direction tower versus omnidirectional phone antennas both to send and receive data. You also have large vs small antennas. This will do more than the small difference in transmission power
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