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