All right, so let's talk about mathematical operations. A significant aspect of being a wireless engineer involves converting between milliwatts (mW) and decibels (dBm). First and foremost, we need to understand what exactly decibels measure. If I say 10 dBm, what does that even mean? Furthermore, how do I begin to perform the mathematical operations? If I want to increase the wireless signal by 3 dBm, how much does that wireless signal increase from a milliwatt perspective?
Fortunately, there are concrete
methodologies for accomplishing this, and we're going to explore them to ensure
we can perform these mathematical operations. The first thing we need to
understand about the decibel is that it is a relative unit of measurement.
It's somewhat like when we're
counting; if we think about it, numbers are also relative, but they're relative
to zero. When I say I have two oranges, you know exactly how many I have
because you understand I'm talking about two more than zero.
In the same way, if I said, 'I
have three more oranges than you,' and you can count your oranges, let's say
you have one orange. Now you understand that I'm not saying I have three
oranges; I'm saying I have three more than you, which means I have four
oranges.
What's important here is that we
have a frame of reference, whether it's relating to zero oranges or how many
oranges you have. This frame of reference is either explicitly stated or
implied. So, we need to understand what our decibels are relative to.
Well, in wireless communications,
the decibel is relative to milliwatts. As we've discussed, we typically operate
in the milliwatt range for the power levels used in Wi-Fi transmissions.
Decibels are agnostic to the specific application; in fact, we can use decibels
to measure various quantities, as we mentioned, including audio.
To explicitly state that we are
measuring in milliwatts, we use the unit dBm. The 'm' in dBm stands for
milliwatts, providing us with a clear reference point. So, when we say we have
zero dBm, we are referencing one milliwatt, not zero milliwatts. Therefore,
having zero decibels from a milliwatt perspective means you have one milliwatt.
This foundational concept remains unaltered when using dBm.
Now, how do we utilize dBm to
measure other milliwatt values? Suppose we are measuring 10 milliwatts. This
essentially means 10 to the power of one milliwatt (101), or simply
10 milliwatts. Our focus here is on the exponential value, which is the essence
of logarithmic measurement. dBm serves as a measure of this value.
Here's an interesting point:
while we call it a decibel (which signifies one-tenth of a bel ‘1/10’), this
number represents a whole bel. We could hypothetically call it Bm, bel relative
to the milliwatt. However, we prefer to measure things in decibels, as we will
see when we perform mathematical operations.
Instead of saying that 10
milliwatts are equal to 1Bm, we prefer to state that it's equal to 10 dBm.
Recall that a decibel is one-tenth of a bel. So, if we have one bel, we have 10
decibels. Therefore, 10 milliwatts is equal to 10 dBm.
However, it's important to note
that this alignment between milliwatts and dBm is coincidental. If 100
milliwatts were equal to 100 dBm, we wouldn't need to use decibels at all.
Let's perform this mathematical operation again: 100 milliwatts is 10 to the
power of two milliwatts (102), resulting in two bels (2Bm). To
convert to decibels, we multiply by 10, making it 20 dBm. So, it amounts to 20
dBm. Therefore, 100 milliwatts is equivalent to 20 dBm.
We have very concrete methods for
quickly performing this conversion. If you were paying attention, when we
multiplied my milliwatt value by 10, it resulted in a 10x increase in the dBm
value. This is essentially an addition of 10 from a dBm perspective.
So, if I increase my dBms by 10,
it leads to a 10x increase in milliwatts. I can extrapolate this further.
Without performing all the calculations, I can tell you that 1,000 milliwatts,
which is equal to one watt, represents another 10x increase. Consequently, from
a dBm perspective, this also corresponds to a plus 10 increase. Indeed, it is.
Therefore, 1,000 milliwatts is equal to 30 dBm.
As we chart this out, we begin
with 0 dBm, which is equal to 1 milliwatt. Then we have 10 dBm, which
translates to 10 milliwatts. We can continue with 20 dBm, equaling 100
milliwatts.
Another important point to note is that if we were to decrease by 10, representing a minus 10 change, going from 20 to 10, we observe a 1/10 reduction. In this case, we are not multiplying by 10; rather, we are multiplying by 1/10.
|
Rule of thumb |
|
0 dBm = 1 mW |
|
+10 = x10 power |
|
-10 = 1/10 power |
|
+3 = x2 power |
|
-3 = /2 power |
|
1dBm = +10 -3 -3 -3 |
|
2 dBm = +3 +3 +3 +3 -10 |
|
3 dBm = +3 |
|
4 dBm = +10 -3 -3 |
|
5 dBm = +10 +10 -3 -3 -3
-3 -3 |
|
6 dBm = +3 +3 |
|
7 dBm = +10 -3 |
|
8 dBm = +10 +10 -3 -3 -3
-3 |
|
9 dBm = +3 +3 +3 |
|
10 dBm = +10 |
This is our first rule. But we
also have another cool rule: a 3 dBm increase is equal to a doubling of the
value. In our case, 3 dBm is equal to 2 milliwatts. So, another thing to note
is that plus or minus 3 dBm is equal to a 2x change.
If I add another 3 and I'm at 6
dBm, I've just doubled it again. Now I'm at four milliwatts. We can take this
further. For example, if I have 13 dBm, which might seem like an odd number, I
can start by knowing that 10 dBm is 10 milliwatts and then add my 3 to it. I
can see that it's a 2x increase. So, 13 dBm is equal to 20 milliwatts.
In many cases, Wi-Fi devices tend
to align with these 10s and 3s. For instance, if you have a 250-milliwatt
transmission and increase it by 6 dBm, what is the total power after the math
operation? Well, adding 3 and 3 means I'm going to double this value twice,
which multiplies it by 4. So, 250 becomes 500 milliwatts, and when I double it
again, it becomes 1,000 milliwatts, or one watt in that case.
These two types of math operations serve as the guide for quickly and effectively performing dBm and milliwatt calculations.
Happy Learning!!
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