Ok lets talk a little about using the Decibel as it pertains to Radio Frequency energy power measurements. We use it for audio (sound) measurements too, but I will try to make this logical RF power both from transmitters and as it pertains to received signal strengths in our radio receivers.
The decibel scale is a logarithmic scale. It would be helpful of you could remember some some simple reference points. If we double our RF (Radio Frequency energy) power like say going from 1 watt of power to 2 watts of power we have increased our power by 3db. It we quadruple our power, like going from 1 watt to 4 watts we have increased power by 6db. If we multiple our power by x10 we have increased our power 10 db. so a 1 watt starting power and we go to 10 watts, that is 10db of gain, and if we go from 10 watts to 100 watts that is another 10db of gain, and it follows that if we go from 1 watt to 100 watts we have a 20db of gain.. If we can just remember these things. we can calculate most things pretty close in our heads.
So now for some examples. Stay with me here. If we say that an amplifier has 23 db of gain, in other words we stick a certain power, lets say 1 watt of power on its input port, how much power will come out of the output port?. We know from the above statements, that the 20 db is multiplipling by 10 and them by 10 again and then the 3 db is a doubling of power. So 1 watt x 10 =10 watts and x10 again =100 watts and then a doubling that power for the 3db is now 200 watts coming out of this amplifier. I hope this made some sense.
Now these ways of calculating power work for antennas that have gain or loss, and for coax cable that only has loss, and for free space path loss and loss in air path's.
OK lets look at some examples of loss in coaxial cable. A given length of coaxial cable often rated in 100 foot lengths, may have a loss lets say of 3 db per hundred for a given frequency. Now remember as the frequency of the RF energy goes up so does the loss per hundred foot.
So if the above coax has 3 db of loss per hundred foot and we stick 10 watts of power in one end of it how much can we expect to get out at the far end into the load? We can expect a halving of the power so we could expect 5 watts to come out of the far end of the coax. The remaining 5 watts are lost in heat energy inside the coax. Now for those of you just chomping at the bit to talk about conjugate impedance matching and reflection mechanics... remember this is a simple discussion of the db scale and power measurement, and we have a ways to go to get there.
So on that 10 watt transmitter and that 3db of loss piece of coax, lets now include hooking up the far end of that coax to an antenna with 10db of forward gain. This might typically be a yagi type of antenna. How much Effective radiated power would we expect coming off of that yagi antenna in the forward direction it is pointed in? So 5 watts going into the antenna x 10db of antenna gain yeilds a 50 watt Effective radiated power coming off of the end of the yagi.. so far so good?
Now lets talk a little bit about receivers. Receivers deal with very small amounts of RF energy. We can set a baseline of the Milliwatt which if you know your prefix is a milliwatt is 1/1000 of a watt of power. And lets set that 1/1000 of a watt or the milliwatt as the 0db reference level as 0dbm. So 0db as referenced to a milliwatt of power. NOW that would be one heck of a strong signal in the input of a receiver, but we need to set a reference somewhere, and this is where we did it. Our typical signal strengths are much much much less than a milliwatt or 0dbm so we normally talk about negative numbers here.
So a signal strength of -10dbm is 1/10 of a 0dbm level. So if a milliwatt is 0dbm, what is a microwatt? Well a microwatt (again we are using those scientific notation prefixis) is 1 millionth of a watt or 1/1,000,000 of a watt or another way of saying it is 1/1000 of a milliwatt. So if we start at the 0dbm and divide by 10 then divide by 10 then divide by 10 we come to -30dbm is a microwatt. So figuring out these super small divisions is getting tedious so we usually just refer to a -dbm number to express these signal levels.
A fairly good receiver would be able to detect and process signals at a -120dbm level. Some may do better, some less. There are many factors that contribute to this including the ambient noise floor in the area you are operating the receiver in and so forth.
Lets now try a system gain/loss scenario from a cell tower to the inside of your radio(phone) in your hand.
Lets make some assumptions. Transmitter power of cell tower 100 milliwatts, Coax loss 3db Total, Transmit antenna gain 13db, Path distance 10 miles, reciever antenna gain 0db, no coax loss inside the receiver. What is the signal level in dbm in our receiver?
Ok lets start by converting all units to dbm. so 100 milliwatt transmitter is +20dbm, the coax loss is 3db so we have 17dbm now into the antenna but we have 13 db gain from the antenna so we squirt out the antenna at +30dbm. Now we go to the
path loss calculator and see that the path loss at our 1.9Ghz frequecny for our 10 miles is about 112 db. And so +30dbm-112db = -82dbm of signal into our radio receiver.
This is a pretty decent signal and as much as 40db over the possible noise floor. Of course that would depend on your specific noise floor.
I hope this rambling dissertation helped a bit in understanding the db scale and how we figure loss and gain in systems.
(be careful for what you wish for)
