# RF Power – dB vs dBm vs dBi vs dBd

In my last post we discussed comparing RF power between 2 transmitters. In that comparison we used a logarithmic function called the decibel (dB) to compare two absolute power values. When we compare two absolute values one is considered the source of interest and one is called the reference or the source of comparison. This works simply enough if we just want to compare transmitter A to transmitter B, but what if we need to see the bigger picture? When working with wireless networks we always have a transmitter and a receiver, as well as the path in between. To ensure that the receiver has enough signal strength we could just compare the absolute transmit power to the absolute receive power to find the total loss. However if we need to make a change to this signal path we may want to change transmit power, or we may want to make a change to the path in between. To really see the big picture we need to know what the change is at each point on the signal path.

### The dBm

To find the change at each point along the signal path it would be easiest to compare them all against a common reference so that the values could be added or subtracted along the path. In wireless networks the reference power level is usually 1mW which is where we get dBm (dB-milliwatt). Instead of comparing the absolute power of each end of the path, we compare each end to a common value so that we can see the change which is occurring.

To expound on this further, we’ve always discussed transmitter and receiver as though they were a single unit. However in reality we know that there exists the transmitter, the antenna, and usually the antenna cable. When we connect an antenna to a transmitter it provides a certain amount of gain, or amplification. However when we remove the antenna it does not generate any power by itself. That is to say that the antenna itself does not generate any amount of absolute power, and therefore we cannot measure its gain in milliwatts or dBm.

### The dBi

Since we can’t compare millitwatts for an antenna what can we compare it to? We could compare it to another antenna, and to keep everything equal we should always use the same antenna as a comparison. This is where the isotropic antenna was created, or at least the idea of it. The isotropic antenna does not actually exist because it is the perfect antenna. It is a tiny point which sends RF power out equally in all directions. It is basically a concept which can be worked out mathematically. So when we compare our actual antenna to this ideal isotropic antenna we get a value in decibel-isotropic (dBi).

### EIRP

An important concept to note here is Effective Isotropic Radiated Power (EIRP). EIRP is the combination of the transmitter absolute power value, the loss from the antenna cable, and the gain from the antenna. This is the first point where the dBm makes itself useful. When measuring EIRP we are not comparing two transmitters, we want to add up the gain and loss for the components of a single transmitter so we have to rely on a common reference point. We measure the transmitter power in dBm, the antenna gain in dBi, and the antenna cable manufactures give us the cable loss  in dB per foot of cable. We can then start with the transmitter’s dBm value, subtract the dB loss of the cable, and add the dBi value of the antenna gain to give us the EIRP. The EIRP value is important because it is regulated by the government bodies such as the FCC.

### The dBd

We can’t leave well enough alone, can we? The dBi was a comparison of our actual antenna to the conceptualized isotropic antenna. However sometimes antenna gain is measured against a real antenna. This value is called the decibel-dipole (dBd) since the comparison is between our actual antenna and a simple dipole antenna. The dipole antenna has a gain itself of 2.14 dBi. So when we describe our antenna gain in dBd we are comparing it to the dipole antenna. However we can’t add up the EIRP values using dBd because we have to take into consideration the gain of the dipole antenna it was originally compared against.

In other words,  when calculating EIRP or the total signal path, we always have to convert dBd to dBi (by adding 2.14 dBi).

All of these measurements can be confusing, but if you take the time to slow down and consider what you are comparing then it will begin to make sense. And remember when we are adding things up we need to make sure that we are adding values that are all compared to the same reference value. In other words, we can only add/subtract with dB, dBm, and dBi. If we introduce dBd we have to take into account it’s own gain.

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# 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.

Why don’t you try a few more and leave a comment with your answers:

1. 3mW vs 12mW
2. 5mW vs 50mW
3. 5mW vs 200mW
4. 60mW vs 3mW
5. 500mW vs 5mW