Hey friends, welcome to the YouTube channel ALL ABOUT ELECTRONICS. so in this
video we are going to learn about the decibel scale which is commonly used in
electronics and communication system and we will also see the different decibel
scales like dBm, dBW and dBV. Now I am sure many of you are already knowing
about this decibel scale and how it is being used
in electronics and communication systems. In fact, in the earlier videos of filter
design we have also used this decibel scale right !! But sometimes we are getting
confused with this decibel scale. particularly when we are representing
the voltage and power gain in terms of this decibel. so let us clear all this
confusion in this video. so this decibel scale is basically a
logarithmic scale which defines the ratio of two quantity and particularly
in electronics it is being used to represent the voltage or power gain of
particular amplifier system or electronic system. And if we talk about
the communication system, in communication system this decibel scale
is used to represent the attenuation that is being provided by particular
channel and this decibel scale is also used to represent the voltage and power
as well. Now whenever this decibel scale is used to represent the power gain or
power then you will see that the factor of 10 is being multiplied with this
logarithmic scale and likewise whenever it is being used to represent the
amplitude or voltage then you will see the factor of 20 that is being
multiplied with this logarithmic scale. so whenever it is being used with the
voltage then the factor of 20 is getting multiplied with this logarithmic scale
and whenever it is being used with the power then factor of 10 is being
multiplied with this logarithmic scale. Now the reason is that this power is
proportional to the square of the voltage so that is the reason whenever
you are representing any voltage or voltage gain then it is being multiplied
by the factor of 20 with this logarithmic scale. So first of all now
let us talk about the power gain and let us see how this power gain can be
represented in a decimal form. so let us say we have an amplifier which is
providing a power gain off 10. That means whenever you are applying the
input of 1 watt then at the output you will get an output power of 10 watt.
So in decibel it can be represented as 10 log of capital G, where G represents
the gain of this amplifier that means 10 log of 10, which will be equal to 10 dB.
And whenever the gain of the amplifier is 1 that means output is equal to input
at that time if you see, the gain in decibel will be equal to 10 log of 1
that is equal to zero dB. So in this way we can represent the different gains in
a decibel. so when the gain is zero it reverses the 0 dB. Whenever a gain is 10
it represents the 10 dB. Likewise, we can represent the different gains in decibel.
So as you can see here, every time whenever the gain is being multiplied by
the factor of 10, you will see the increase in gain by a 10 dB. Now the
advantage of representing this gain in decibel is that the larger quantities
like 10 to the power 8 10 to the power 9 can be easily represented in just 2 or 3
digits. And it is particularly useful when you have multiple amplifiers in
your system. So let us say here we have a two amplifiers which are being cascaded.
so let's say if first amplifier is having a gain of A1 and the second
amplifier is having gain of A2 then the overall gain will be equal to A1 into A2.
now let's say if A1 is equal to 10 to the power 4 and A2 is equal to 10 to
the power 5 then the overall gain will be equal to 10 to the power 9. But if we
represent this gain in decibel then the A1 will be equal to 10 log of 10 to the
power 4, which is nothing but 40 dB and likewise this gain A2 will be equal to
10 log of 10 to the power 5, which will be equal to 50 dB and the overall gain
will be the summation of these 2 gain that is 40 plus 50, that is 90 dB. So
whenever you have a multiple amplifiers in your system then if you represent
them in decibel then it is easy to find the overall gain of that system and the
larger gain can be easily represented in this decibel
form. So now if your system is having a gain of 2 then in decibel it can be
represented as 10 log of 2, which will be approximately equal to 3 dB.
So, let's say if I have one amplifier which provides me the gain of A1 dB and
if I add the another amplifier which simply multiplies the gain by a factor
of 2 then I can say that the overall gain will be equal to A1 plus 3 dB. So
in this way in any system whenever the input is being multiplied by the factor
of 2 then we can say that the gain that is being added to the system is 3 dB
Similarly, let us say we have one particular system which provides you the
attenuation. So whenever you are providing the input of 1 watt then at
the output you are getting a 0.1W. So we can say that the gain of the
system is 0.1. So, in decibel if we represent it then it can be represented
as 10 log of 0.1, that is equal to minus 10 dB. Similarly let us say if the
system is providing me the gain of 0.5 then in decibel I can write it as a
10 log of 0.5 and if you calculate it you will get it as a minus 3 dB
so we can say that whenever the output is getting 0.5 times the input then the
gain that is being provided by the system is minus 3 dB or in another way
we can say that the attenuation that is being provided by the system is 3 dB. So
now so far we have seen about the power gain, now let us talk about the voltage
gain. so let us say we have a amplifier which provides me the voltage gain of
let's say 100. That means whenever I am applying a input of let's say 1 volt
then at the output I am getting a hundred volt. So the gain in the decibel
can be represented as 20 log of 100 so now here if you calculate the
in decibel will be equal to 40 dB. likewise let's say if I have a gain of
thousand then in decibel it will be equal to 60 dB
similarly let us say if the system is providing the gain of 2 then in decimal
it can be represented as 20 log of 2 and if you calculate it it will come out as
a 6 dB. So every time when the input voltage is being multiplied by the
factor of 2 then we can say that the gain that is being added to the system
is by 6 dB. Similarly let us say if the system is providing the gain of 0.5 then
in decibel it will be equal to 20 log of 0.5, which will come out as a minus 6 dB
so every time whenever the output voltage is 1/2 then the input voltage
then we can say that the gain that is provided by the system is minus 6 dB or
the attenuation that is being provided is 6 dB. So here is the representation of
different voltage gain and corresponding gain in a decibels. so as you can see
here whenever the voltage gain is being multiplied by the factor of 2 then you
will see the increase in the gain by a 6 dB and likewise whenever the gain is
being multiplied by the factor of 0.5 then you will see the reduction in the
gain by a 6 dB and similarly whenever the gain is being multiplied by the
factor of 10 then you will see the increase in the gain by a 20 dB and same
is true for the attenuation that means if the attenuation that is provided by the
factor of 10 then you will see the reduction in the gain by a minus 20 dB
so this is all about the representation of voltage and power gain in decibels
now let us see what do we mean by this dBW, dBm and dBV. So now, so far we have
represented this voltage and power gain in terms of the decibel but what if I
want to represent this power and voltage itself in a decibel scale. So of course
we can represent this voltage and power in decibel scale but as this decibel scale
is the unitless quantity so you need to represent this voltage and power in
terms of the some reference. So let us say when we are representing this power
in dBW form that means we are representing this power with the
reference of one watt. similarly whenever we are representing this voltage in
decibel form, it means that we are representing this voltage with respect
to 1 volt. So let us say if I want to represent this 10W of power in
decibel form then it will be equal to 10 log of P1 with respect to 1 watt. so it
will come out as a 10 dB. Now here as we are representing this power with respect
to 1 watt so after dB you will find the term that
is equal to W. Similarly, let us say if I want to represent this voltage V 1 of
100 volt in decibel then it will be equal to 20 log of V 1 with respect to 1
volt of voltage. And it will come out as a 40 dB, and as we are representing this
voltage with respect to 1 volt of power so after dB you will see the term that
is equal to V, that is a unit of the reference voltage. So here is the
different voltages which are represented in a dBV form. So now let us talk about
this dBm. So whenever we are representing this any power P with respect to 1
milliwatt of reference power then it corresponds to dBm. So now let us say if
I have a hundred milli watt of power and if I want to represent it in a decimal
form with respect to 1 milli watt of power then it can be represented as 10
log of hundred milli watt with respect to 1 milli watt and that will be equal
to 20 dBm. Similarly now let us say if I want to represent thousand million of
power or let's say 1 watt of power in dBm form then it will be equal to 10 log
of thousand milliwatt with respect to 1 milli watt and that will be come out as
a 30 dBm, but at the same time suppose if I represent this power in a dBW form
then it will be equal to 10 log of 1 watt divide by 1
watt. And it will come out as a zero dBW. so as you can see here if the same power
if I represent it in a dBm form then it will be equal to 30 dBm, while if I
represent it in a dBW form, it will be equal to 0 dBW. so now let us say if
I have some power of X dBW and if I want to represent it in a dBm form then
simply I need to add a 30 in that particular value. so here as we have seen
if we have a zero dBW of power and if you want to represent it in a dBm form
then it will be equal to 0 plus 30 dBm, that is equal to 30 dBm. And same is true
if we have a power in dBm and if we want to represent it in a dBW form then
simply we need to subtract it by a minus 30 dBW. So I hope this conversion
between dBW and dBm is clear to you. So here is the list of some powers and
corresponding powers in a dBm format. Now before I end up this video here is the
question for you. Let us say if I have a power P1 that is equal to 10 dBm and
power P2 that is equal to 5 dBm then what will be the total power P that is
equal to P 1 plus P 2 .so do let me know in the comment section below. so I hope
in this video you understood the different decibel scales which are
commonly used in electronics and communication system. so if you have any
question or suggestion do let me know in the comment section below, if you like
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