dB Am I doing this right???

[KM4FER]

My understanding of dB is a little weak and my math skills are rusty, so am I doing this right?

By definition:

1.        dB = 10 log (P1/P2)

dBm is when the power is referenced to 1mW so we replace P2 with 1mW.

2.        dBm = 10 log (PW/1mW)

My cell phone tells me that received signal strength is -100dBm, so plugging that into equation 2

3.       -100dBm  = 10 log (PW/1mW)
          -10 = log (PW/1mW)
           PW/1mW = 10^-10
           PW = 10^-10  X  1mW  =  10^-10  X  10^-3W  =  10^-13W = 0.1pW

Now I expected to see a small number but one tenth of a picoWatt seems impossibly small.

Have I made a mistake or are cell phones that incredibly sensitive?

Thanks...
earl...

[djacobow]

Regarding power, do this little thought experiment:

 - imaging that a cell phone tower transmits with 10W
 - imagine that you are 3 miles from the tower
 - imagine that it broadcasts isotropically (in a spherical pattern). It doesn't, but for simplicity...

The area of that sphere is 4*pi*r^2. The flux density in W/cm^2 at 3 miles is... Now, how much power could even theoretically pass through an object the size of a cell phone?

[ludzinc]

Yep, 1 picoWatt is correct!

[miguelvp]

Yep, 1 picoWatt is correct!

you mean 0.1 pico Watt is correct, right?

[coppice]

Regarding power, do this little thought experiment:

 - imaging that a cell phone tower transmits with 10W
 - imagine that you are 3 miles from the tower
 - imagine that it broadcasts isotropically (in a spherical pattern). It doesn't, but for simplicity...

The area of that sphere is 4*pi*r^2. The flux density in W/cm^2 at 3 miles is... Now, how much power could even theoretically pass through an object the size of a cell phone?

Fleshing that out a little.....

Let's say a cell tower transmits 10W and you are a nice close 1km away looking directly at the tower. Where you are the energy from an isotropic antenna has spread out to be 10/4*pi*1000*1000 W/m^2 or about 8*10^-11 W/cm^2, or 80pW/cm^2. In practice the antenna would have a doughnut pattern, and you might be 10dB up on that power, or 800pW/cm^2.

Now step into the entrance area of any building and you are down at least 10 or 20dB. Let's say its only 10dB, so we are back to 80pW/cm^2 as a very optimistic figure. Further into the building you will be down another 20dB at least, so we down to 0.8 pW/cm^2. If we were 5km from the tower, we would be another factor of 25 down, or at about 0.03pW/cm^2. Now we in the ballpark of your 0.1pW sensitivity level. How many cm^2 of effective energy gathering area do you think you get from the tiny antenna in a phone?

[German_EE]

Now we are beginning to get a new appreciation of how wonderful radio really is. If I hear a low power ham radio station buried in the noise he could be at -120dB or 10^-15 watts or 1 femto watt, yet I can still exchange a signal report.

[lapm]

Newer occurred me to take a look how low power radios really work... Just blows my mind how small power levels you need and are still able to receive... 

[GreyWoolfe]

Some years back I participated in a Boy Scout JOTA event.  I was running a digital station-Compaq laptop, Small Wonder Lab's PSK20 transceiver kit running at 2.5 watts and a resonant dipole antenna.  I had a 599 contact with a station in Queensland, Australia from south Florida. The kids enjoyed it as they didn't have to touch a microphone.  I also had the furthest contact of the event, beating out a 20 Meter phone station using an amplifier and a 2 element quad beam mounted on a mobile tower.  Very satisfying to let the air out of the kilowatt station.  You have to love the "magic" of radio

[KM4FER]

Whew !!!   I guess I am getting a little understanding of this stuff afterall.

Before this little exercise I would have guessed that to obtain reliable communication with only 1pW you would need to cool with liquid nitrogen to get the noise floor down.   You people who design these things must be some kind of geniuses.

Thanks again...
earl...

[ConKbot]

Newer occurred me to take a look how low power radios really work... Just blows my mind how small power levels you need and are still able to receive... 

GPS comes down to earth at -130 dBm, and some receivers have sensitivity extending down to -160 dBm

Now for the real mind bender.  Thermal noise for an amp 2 MHz wide, with a noise temperature of 10 Kelvin ( below anything commercially available that's non cryogenic, AFAIK ) the thermal noise power is -125.6 dbm. So your SNR is negative.