Do cell-phone base station antennas emit the same power of waves as from a cell phone?
I would assume so because both waves need to travel the same distance, right?
In principle, this is symmetric, correct.
In practice, the tower will control both its and the connected phones' transmit power to get a working configuration, and the tower will also use beamforming techniques to direct power only in specific directions.
For reception to work, the tower needs to receive all connected phones at roughly similar levels, because the analog amplifier behind the antenna is shared for all connections, and division is made later, on digital data, which has a limited dynamic range, so the actual transmit power in phones is mostly dependent on distance and transmission properties to the base station it is connected to.
The transmit power at the tower depends on the reception capabilities of the phones the transmission needs to reach, largely how much gain is available in their RF amplifiers, and whether there are other transmissions that further limit the available gain.
For example, if I have one LTE modem downloading lots of data, and use my phone in the same room, the phone's antenna will also pick up the LTE traffic from the modem to the tower at a fairly high level, so it needs to reduce its receive amplifier gain to not overload the mixer stage. It will notify the tower of this, and the tower will then increase the transmit power to this phone to make up for this reduction in receive gain.
In short, how much is actually radiated depends on a lot of factors. In general, everyone will try to use the smallest possible setting, this will be considerably lower when base stations are placed closer together.
The same order of magnitude - somewhat yes
The same exactly - not really.
The radio signal propagation is pretty much symmetrical between the base station and the cellphone antenna. This is independent on factors like beamforming, cell sectors, antenna gain and likes. But, their design constraints and their use cases are pretty much different.
The base station has cheap and abundant power available so it can simply use more power if this could improve the connection. The phone has its finite-capacity battery, its SAR limits and its transmitter cooling limits that constrain this approach. Phones do vary their radio transmission power, but within their own limits.
The base station also could use more sensitive (but bulky and power-hungry) receiving circuity so it can hear the weaker phone signal so it can negotiate with the phone lower transmission power on the phone side.
The base station serves multiple (hundreds or thousands) phones at once. It has to beam the downstream data for all of the phones and the phones have to beam only their own upstream data.
While voice connections are generally symmetric (upstream and downstream data rates are equal), data connections (e.g. used for browsing the web) are pretty much downstream dominated with down/up rates of 5-50. This translates to the base station having to beam as much more data packets on average, compared to the phone.
The usual radio noise distribution favors the base station (it is usually away from radio noise sources other than its own gear). The phone, on the other hand, is usually near home, office and industrial equipment so the base station has to use more power in order to overcome the noise around the phone.
All this can be summed up to:
Phone radiates at most 1 watt (3G or above) or 2 watt (2G) pulses that average at few hundreds of miliwatts. In a good coverage conditions this goes as low as few miliwatts for the typical use case. If there is no data traffic and the phone is not moved, it does not transmit anything for as long as hours. This is how non-smart phones run for a week off an 2-4 Wh battery.
The base station can radiate as little as under 1 watt (for micro cells) or hundreds of watts (for the usual cells) on average. Some special base stations go well into kilowatt-range radio power.
If you happen to be the single user of a base station, the phone and the base station happen to be of the same technology generation, the distance is moderate and you only do a single voice call (no web browsing, etc...), chances are that the phone and the cell tower radiate the same amount of radio power. But this is usually pretty much not the case.
Yes, approximately. As discovered with a simple Google search:
Note, though, that a cell phone tower handles many calls, each using that level of power, so the total power from the cell phone tower is much higher than that value. A cellphone handles a single call.
The cell tower emits much more power than the "user equipment" (UE -- the phone in your pocket.)
The important thing to carry information is the power spectral density, which is a measure of how much power there is over a given frequency range. As the frequency range increases, more power is required to overcome the noise over a wider spectrum. Greater power spectral density results in greater signal/noise ratio which, for 4G and 5G, means more bits per symbol and so higher data rates.
The UE needs to transmit enough power to provide a useful uplink. The base station needs to transmit enough power to provide useful downlinks for all the UEs that are using the base station.
In practice, one of those antennas you see at the top of a mast is emitting tens of watts of RF. The mobile in your pocket is emitting tens or hundreds of milliwatts.