# Comparing RF Power

We’ve briefly mentioned a few RF basics in past articles. When discussing RF spectrum bands we were were speaking of frequency which is how often the wave occurs within a given timeframe (cycle) and is often measured in Hertz. Wavelength is closely related in that it is the physical distance that a wave travels over in a complete cycle. What we are going to dive into next is amplitude, or the height of the waveform (top peak to bottom peak). This strength of an RF signal is commonly measured by its power in Watts.

When power is measured in Watts, we call this absolute power. It is the actual amount of energy which exists in the RF signal. Sometimes though we need to compare two power signals. Either comparing two transmitters or comparing power before and after a potential change. Now this is where things get a little complicated because we normally take this next part for granted. Lets take an unrelated example, car speeds. If we have one car, a Mustang, traveling at 50mph and we have a second car, a Corvette, traveling at 100mph how do we compare their speeds? We could say that the Corvette is traveling 50mph faster, or we could say that it is traveling twice as fast as the Mustang. We never think about it, but how we describe the speed comparison depends on the mathematical method that we used to compare them. Did we subtract their speeds to get the difference ( 100mph – 50mph = 50mph difference)? Or did we divide their speeds (100mph / 50 mph = 2)? This may not seem like a big deal at first but when we start talking about transmit power, the absolute power values can differ greatly. Think about comparing your running speed to the speed of a bullet fired from a gun. It is not a linear range, but they grow exponentially. To help us deal with this, we use a logarithmic function called the decibel (dB). When each absolute power value (in W) have been converted to decibel (dB) then we can more easily compare the two values.

The decibel (dB) is an actual mathematical function. However this is not a math blog. What we need to know are just a few dB Laws so that we can do mental math. These laws are needed to be able to quickly compare power values in wireless certification exams. These laws include the Law of Zero, the Law of 3s, and the Law of 10s. A dB value of 0 means that the two absolute power values are equal. A dB value of 3 means that the absolute value being compared is double, and a dB value of 10 means the absolute value being compared is 10 times larger.

 Power Change dB Value = 0 dB x 2 +3 dB / 2 -3 dB x 10 + 10 dB / 10 -10 dB

To put this in practice let’s look at two quick examples. First, we have one transmitter at 5mW and another at 10mW. To get from 5 to 10, we have to multiply by two (5 x 2 = 10). Therefore according to the Law of 3s, the second transmitter is +3 dB greater.

A more complicated example would be comparing one transmitter at 5mW and another transmitter at 100mW. To get from 5 to 100 using our laws we have to make a few jumps:
5 x 2 = 10
10 x 10 = 100
So if we look at the changes we made, first we multiplied by two (x2 = +3 dB) and then we multiplied by 10 (x10 = +10 dB). So if we combine those operations (+3 dB) + (+ 10 dB) then we can say that the second transmitter is +13dB greater.