 We'll just recap on what we've learned briefly about decibels Because we're going to need that in this topic or the next topic on transmission media and in subsequent topics We'll see DB come up a lot So it's important to understand what decibels or a decibel is And last week towards the end we got to the point that well to calculate DB is 10 times log base 10 of two power levels DB is used to measure a ratio or a factor That is if we have two power levels Then the ratio between them one divided by the other Gives us some some Multiplying factor we can convert that to decibels. So the general equation here that we've used in a few examples The examples we used We use one with a audio amplifier We said that there's some input power to the amplifier. There's some output power and We can talk about that amplifier having a gain Which is the output divided by the input saying The gain means that if we have some value coming in the game means we multiply that value to determine what will come out So this amplifier we calculated had a gain of a factor of 100 The output is 100 times larger than the input DB is just another way to express that that factor 100 is the same as 20 decibels So it's a little bit confusing for some people because they see DB and think that's a unit, but it's not a unit This is just a factor or a ratio It's not a unit like seconds watts bytes It's just a different way to express a factor or a ratio in this case 100 We also introduce the concept of loss We have a communication system We transmit some signal with some power level in our example 8 watts At the receiver we receive at 1 watt in Absolute factors the loss is a factor of 8 The received signal is 8 times smaller than the transmitted signal We can convert that to DB 10 times log base 10 of the factor of 8 gives us 9 DB So we can say the loss is 9 decibels But also we talk about the gain is the inverse of the loss if we lose by a factor of 8 That means we gain by a factor of 0.125 the inverse The received power is 8 times less than the transmit power or the other way The received power is point one two five times the transmit power And again if we convert to DB it becomes a nice negative 9 DB So gain and loss in the absolute values are the inverses in DB the the Invert the the negative of the other value and we got to the last example of doing a calculation It turns out that we can when we have a system made up of components with different gains and losses To talk about the overall gain of the system. We can just add up the components So the example we went through said there are three components one had a gain of 5 DB a loss of 10 DB and A gain of 2 DB so overall we can say that there's a gain of the system of minus 3 DB just the sum of those values or in the other way a system loss of 3 DB a Gain of minus 3 is the same as a loss of plus 3 and We did a calculation as to what the transmit power would need to be Any questions on DB before we move on? Easy 10 log base 10 of some factor Let's give one or a couple more examples on DB Often in communication systems we'll talk about we transmit a signal with some power level So I say PTX the transmit power level And it's often measured in watts or milliwatts. Let's say 16 as an example Let's make up some transmit power of 16 watts We can often we also see in communication systems that power levels are Also expressed relative to decibels and this is a bit confusing so far DB is indicating a ratio or a factor Sometimes some factor larger than something else or smaller than something else It's relative between two different values, but we can express a power level also relative to DB Let's show you how Remember our general equation for DB 10 log base 10 of two power levels Generally P1 divided by P2 depending on what we're talking about signal to noise ratio P1 would be the signal P2 the noise if we're talking about gain of a system Then P1 would be the output power and P2 the input and the loss the inverse So it depends upon the system we're talking about but in general the ratio between two power levels let's Take as a reference point And let's set P2 to some some value a reference value Let's set P2 to be one watt one is a nice reference point and We'll use that to express our transmit power relative to this fixed reference point so if P2 is one watt and Now we ask our transmit power of 16 watts Can we express that relative to the rest reference point of one watt? well 10 log base 10 of Our power level 16 watts Divided by the reference power level of one watt and someone will calculate that for me What's the answer? log base 10 of 16 so the watts will cancel out we left with 16 someone use it 1.2 So times by 10 is 12 is that right so log of 16 is 1.2 times by 10 is about 12 DB Sorry, not DBW DB That is 16 relative to the reference point is 12 DB now How do we use that we can say 16 watts is the same as 12 DB relative to one watt And we write that as DBW This is a different thing now we're using decibels in measuring a single power level not a ratio between two Where that single one is relative to a reference point? so the The notation DBW means decibels Relative to one watt the W means one watt Which means the lower the the denominator in the factor is one watt We'll often see power levels expressed in DB watts And a few and others will see in a moment. That is if my transmit power is 16 watts It also means my transmit power is 12 DBW decibels relative to one watt So remember DB on its own is a ratio between two values DBW means it's a ratio between two values where the second value the bottom one is one watt So the W means that P2 is one So DB says it's a ratio a logarithmic ratio ratio and the W This is the new part says that the bottom part is fixed at one watt make sure people understand that what about What does 30 DBW equal? Try and calculate. What is 30 DBW now when we talk about DBW? We're talking about a power level not a ratio anymore, so what's What's the power level in this case? You need to go backwards with your decibels equation 1000 1000 no 1000 something What? 1000 watts, okay? Let's calculate remember our general equation 10 log 10 log base 10 of P1 divided by P2 When we write DBW, we know that P2 is One watt So we know that the equation would be 10 log base 10 of Some power level P the one we're looking for divided by one watt That's what the W here means that the denominator in the ratio is one watt So now we just need to solve for P. So divided by 10 we get 3 Equals log base 10 of P divided by one watt So that means that P divided by one watt Equals 1000 Because log base 10 of 1000 equals 3 that is P the power level equals 1000 watts Now we're using DB for something different a power level of 1000 watts is Identical to 30 DBW any questions Why did I use one watt because that's the common reference point that's used in many systems? Yes? It's fixed when we write DBW. It means one watt as a denominator We don't have to use it. There's a few other values which are common. We'll see one other The other common value is instead of having one watt here is to have one milliwatt That is the reference point the reference value That is P2 and our general equation is one milliwatt so What do we have before? we had our Transmit power of 16 watts find out what That value is relative to one milliwatt What is 16 watts relative to one milliwatt and then convert it to DB? There are the two common reference reference points we'll see in at least in our studies relative to one watt or Relative to one milliwatt. Well, you just use the DB equation and 10 log base 10 of our power of 16 watts relative to one milliwatt which equals 10 log base 10 of What 16 watts divided by one milliwatt is 16,000 be careful of the unit there 16 watts is 16,000 times larger than our reference point and then take the logarithm times by 10 What do you get? 42 42 DB relative to one milliwatt Here we have a new notation 16 watts relative to one milliwatt. It's 16,000 times larger or In DB it's 42 DB relative to one milliwatt. So we write it as 42 DB MW But we're often lazy and we remove the W and just write DB M so In summary what we've seen in the first example is that 16 watts is the same as 12 DBW Which is the same as 42 DB milliwatts, which we commonly just write as DB M But that can be confusing. It's not meters. It's sure for milliwatts All the same value, but just expressed in different ways Think of it as like a prefix everything's measuring a power level But in different scales in the last two we're using logarithmic scales It's DB MW, but we often don't write the W We just write DB M It doesn't mean DB meters. It means DB milliwatts decibels relative to one milliwatt 12 DBW is 12 decibels relative to one watt You can write you can write MW But in other literature in my questions, you'll often just see DB M. So we recognize that DB M The M means milliwatt There are other reference points that are used But these are the two that we'll see in the most common I think that you'll come across so we'll not cover others. Micro is sometimes used decibels relative to one micro watt Make sure everyone's clear We've had two examples. We said 1000 watts was 30 DB W 1000 watts is how many DB M 1000 watts relative to one milliwatt What's the the ratio and then convert it to DB answer? Calculator someone You don't need a calculator for this one The beauty of decibels start to come into play at this point So 1000 watts relative to one milliwatt 1000 watts divided by one milliwatt is How much? One million So we take log base 10 of one million gives us six Six zeros in one million times by 10 gives us 60 DB M 1000 watts is the same as 30 DB W, which is the same as 60 DB M You may notice the difference between DB W and DB M is 30 Because one is relative to one watt the other is relative to one milliwatt Which is a factor of 1000 which is equivalent to 30 DB You don't need to remember that but you'll maybe if you use these Decibels a lot you'll start to see some of those common Relationships for now just know that when you see DB W it really means a power level And you should be able to convert it back by just remembering the general decibels equation 10 log base 10 of One power divided by another If it's DB W that other the denominator is one watt if it was DB M the denominator is one milliwatt Then you solve for the power level So we'll see decibels used for two purposes in this case to measure a power level and What we covered last week was to measure a ratio between two power levels. So DB watts DB M Let's finish with one last example We have a transmit power Into a some system which has a gain G again Then a component has a loss. I think we did this example before and again and Then we receive what do we have as values before? This is this I'm very close to the same example. We had last week. I think you may have it in the picture I try to remember the numbers If the gain of the first component is five decibels the loss of the second component is 10 DB and the gain of the third component is 2 DB and Let's say we do something different. We transmit with a power of Let's say 20 DB M The transmit power is 20 DB M We could convert that back to watts or milliwatts 20 DB M. So Divided by 10 we get true. So I think you'll find it's a hundred milliwatts You can check The nice thing about everything expressed relative to in the logarithmic scale in decibels is that to find well What is the receive power in this case? Well, we have a transmit power. We have some gain Normally with a gain we amplify we multiply and a loss we divide But when we're using DB the gain is we plus We add and the losses we subtract So what is the receive power? the receive power is We start with the transmit power of 20 DB M We add five DB The first component we subtract 10 DB The loss and then add on to DB and we get left over What? 17 DB M We start with a power level. We amplify it We increase it here with a gain then it's reduced According to this loss then increased again and what do we receive? When we're doing everything in DB Then we can just add up the values Where loss is negative and the result is we receive at a level of 17 DB M If we wanted to we could convert that back to milliwatts or watts Which is the same as anyone have a calculator 10 to the power of 1.7 milliwatts Someone will solve that for me 50 About 50 milliwatts 10 to the power of 1.7 why 17 equals 10 log 10 of Some number divide by 10 we get 1.7 The opposite of log is raised to the power so 10 to the power of 1.7 is about 50 milliwatts What was the transmit power the transmit power? if we convert 20 DB M is 10 to the power of 2 milliwatts 100 milliwatts if we have a hundred milliwatts relative to 1 milliwatts is a factor of 100 and In log in decibels a factor of 100 is equal to 20 DB So 20 DB M is the same as 100 milliwatts We transmit at a power of 100 milliwatts We have some gain some loss some gain and we receive at a power of 50 milliwatts This one tries to demonstrate the fact that when everything's in DB Calculating the answer is usually much faster than doing Multiplications and division when everything's using the absolute factor. We will not do it I'll leave it as a homework task for you to do Convert the gains and losses into their absolute values So convert this to an absolute value and think okay We start with 100 milliwatts the gain in the absolute value is a multiplier. So we increase The loss is a divider we reduce and then the second gain we increase again And you should end up with 50 milliwatts at the end That's an exercise for you to solve questions Before we move on at least for now no decibels used to measure ratio or a factor Commonly used to talk about the gain of a system the loss of a system signal to noise ratio But we also have DBW where do we go up the top DBW and DBM? Meaning relative to one watt or one milliwatt to measure absolute power levels Questions before we start the next topic Transmission media I'm sure we have another An impromptu quiz Okay We'll have a quiz soon Sometimes we may have a quiz during lectures instead of online just to make sure people are following Let's move on to transmission media