In radio transmission. 1
We use a new unit, which is the decibel. 2
You're going to tell me: why? 3
a new unit? 4
The decibel has many advantages, which we will see in the next few slide and will makes your life 5
much easier when we will study a specific use case. 6
The first idea is to have a clear value of the relationship between two powers. 7
If we take an example of a transmission with power Pₜ, Pₜ stands for transmitted power. 8
This signal will spread over the air and arrives at the receiver 9
with the power Pᵣ. 10
. 11
Pᵣ stands for receive power. 12
If Pₜ is equal to Pᵣ, then we said of the gain is zero dB. 13
If Pᵣ is equal to two Pₜ, it means that there was a multiplication by two, it's a gain of three decibels. 14
And finally, if Pᵣ is equal to ten times Pₜ, so a gain of ten times the power transmitted, we 15
say that the gain was ten decibels. 16
I know it sounds a little bit weird, but where does the decibel come from? 17
In reality, it comes from a formula that may seem a little bit complicated, which is that the gain 18
in decibels is equal to ten times the log of Pᵣ over Pₜ. 19
If we do this calculation, we find here ten, three and zero. 20
Now, what's interesting is that we have a received power, which is the power transmitted divided by 21
two. 22
We have minus three dB. 23
And finally, if the received power is the transmitted power divided by ten. 24
We have minus ten dB. 25
Here, we have the first advantage of using decibels. 26
Thanks to decibel calculation in the form of a multiplication and division will be treated with additions 27
and subtractions. 28
Let's have a look at a small example right away. 29
In this example, we use the same representation for Pₜ for the transmitted power and Pᵣ for the 30
received power. 31
And we assume that the received power is 1 billion time lower 32
than the transmitted power, that is very common for short run wireless transmission. 33
This means that Pₜ is equal to 10 power 9 so 1 billion time Pᵣ. So how do we transform this 1 billion 34
power ratio into DB? 35
1 billion is ten power nine. 36
I can represent it with a sequence of zero. 37
So it's actually ten by ten, by ten by ten, nine times. 38
And each time we multiply it by ten, there is an addition of ten dB, ten plus ten plus ten and so on. 39
That gives 90 dB. 40
We can therefore set two things. 41
Pₜ has been attenuated by 90 dB and because it seamlessly work the other way around. 42
You can also say that Pₜ has been amplified by -90 dB. 43
In wireless transmission we use very large values, tens of billions of billions and also very small 44
values. 45
It will be much easier to use numbers that goes from 100 150 dB or -100 -150 dB 46
than these large numbers of billions that have no meaning for us. In the next video will see the use 47
of decibels for power.