00:00:01
we in this video we're going to try to
00:00:02
answer the question what is dbm or DB mu
00:00:07
or
00:00:08
dbmv and uh why do we use these various
00:00:11
units on a spectrum
00:00:14
analyzer now of course to answer that
00:00:17
question uh the first uh question we
00:00:19
need to address ourselves with is what
00:00:21
is a
00:00:22
DB a DB or a decibel is a logarithmic
00:00:27
expression of the ratio of two power
00:00:29
power levels and uh the general equation
00:00:33
is just like this it's 10 * the log base
00:00:37
10 of the ratio between two power levels
00:00:40
we'll call them P1 and P2 it's important
00:00:43
to note that it's the logarithm base 10
00:00:46
not the natural log which on your
00:00:48
calculator is typically Ln it's usually
00:00:51
spelled out the capital letters l g for
00:00:54
the uh log base
00:00:56
10 so we're going to answer the question
00:00:59
what is a DB
00:01:01
and uh why do we use them and how can
00:01:03
you relate them to things like volts and
00:01:06
watts and things like that that you're
00:01:08
used to looking at or dealing with with
00:01:10
an oscilloscope in electronics the
00:01:14
definition for a decibel or a DB is a 10
00:01:17
* the log of the ratio of two power
00:01:20
levels not voltage levels but power
00:01:22
levels so um we can kind of look at it
00:01:25
this way as a couple of examples so
00:01:28
let's say P1 is a quantity of one say
00:01:31
one watt P2 is one watt the ratio
00:01:34
between them is one if you punch that
00:01:36
into your calculator the log of the
00:01:39
value one gives you 0 so 0 * 10 is 0
00:01:44
let's say that the P P1 was twice the
00:01:47
value of P2 the ratio would then be two
00:01:50
that would be 3 DB if you do that in
00:01:52
your
00:01:54
calculator if P1 was 10 times the value
00:01:57
of P2 the ratio would be 10 and that
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would be 10
00:02:01
DB now here's a if let's say the that P1
00:02:05
was 1/2 the value of uh
00:02:09
P2 then the ratio would be 1/2 and that
00:02:12
would be minus 3db so what you can see
00:02:15
here is that a factor of two increase
00:02:17
was a plus 3db a factor of two decrease
00:02:21
or
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1/2 uh was minus
00:02:25
3db so just take some odd Bowl numbers
00:02:28
like 7.2 for P1
00:02:30
1.6 for P2 the ratio is 4.5 and if you
00:02:35
punch that into your calculator you get
00:02:37
6.5 DB is is the ratio between these two
00:02:41
power levels so a couple of other
00:02:44
interesting things is if you take a look
00:02:46
at say let's say that P1 was 100 * P2
00:02:50
that would be 20 DB a th000 times that's
00:02:53
30 DB so you can see for these three
00:02:56
cases say from 10 to 100 to 1,000 we
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multiply by 10 10 10 so we go from 1 to
00:03:03
10 to 100 to 1,000 each of those is
00:03:05
multiplying by 10 but the DB values
00:03:08
increase linearly by 10 so 10 20 and 30
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so uh one way to think about that is
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that logarithms will turn multiplication
00:03:18
and division into an addition and
00:03:21
subtraction that's kind of the reason
00:03:23
why we use logarithms years and years
00:03:24
ago before we had calculators okay the
00:03:28
other convenient thing about this is
00:03:30
that logarithms can be used uh so to
00:03:33
express or to view large variations in
00:03:36
ratios and to be able to see them on a
00:03:38
reasonable scale uh we can uh we can see
00:03:41
for example that we have a ratio of 10:1
00:03:44
or 100 to1 we to view them on the same
00:03:46
scale is just going from you know 0 to
00:03:49
10 to 20 to 30 um so even if we had a th
00:03:52
to1 ratio and we wanted to look also at
00:03:55
another quantity that had 100 to1 ratio
00:03:57
we could see them on the same scale very
00:03:59
very easily and we'll see if we try to
00:04:01
look at things linearly without using
00:04:04
this logarithm
00:04:05
expression that um that would be very
00:04:08
tough to see we're going to look at the
00:04:09
uh the scope in a little while and
00:04:11
you'll see a really good example of
00:04:14
that so here's a quick example of how
00:04:17
these large variations and ratios can be
00:04:20
expressed on a reasonable
00:04:22
scale uh on
00:04:23
anoscope the vertical axis or the the
00:04:27
displayed voltage is linear so I've got
00:04:29
a sine wave here and if I reduce its
00:04:32
amplitude by 10 DB we can see that uh
00:04:36
how small that signal got if I reduce it
00:04:38
by another 10
00:04:40
DB okay now I can still see it if I
00:04:42
reduce it by another 10 DB so that's 30
00:04:46
DB lower and I can just barely see it if
00:04:49
I go to say 40 DB I can't even see that
00:04:52
change on this same scale okay so you I
00:04:56
can really get you know typically about
00:04:58
30 DB maybe a little bit uh a little bit
00:05:01
more on a scope screen to be able to see
00:05:03
that on the same scale let's move the
00:05:06
signal over to the Spectrum analyzer
00:05:09
I'll turn the Spectrum analyzer on and
00:05:11
turn the uh time domain off so there's
00:05:15
that signal represented in the frequency
00:05:16
domain on a spectrum analyzer if I cut
00:05:19
its amplitude by 10 DB all right I can
00:05:22
still see it very easily 20 DB 30 DB
00:05:27
even 40 DB very easy to
00:05:30
see uh that signal still on the screen
00:05:34
so even if I go 50 DB 60 DB or even 70
00:05:38
DB 70 DB is starting to be way down in
00:05:41
the noise there but that is now 70 DB is
00:05:45
a factor of 10 million okay so I've made
00:05:49
that signal 10 million times lower in
00:05:51
power and I can still see it there would
00:05:54
be no way to see that on an oscilloscope
00:05:56
screen so this is why DBS are used when
00:06:02
looking on a spectrum analyzer because
00:06:04
it allows us to view maybe large signals
00:06:07
in the presence of or excuse me be able
00:06:10
to simultaneously view large signals and
00:06:13
small signals on the same scale even if
00:06:15
the power of those signals varies by uh
00:06:19
tremendous amount so we can see if this
00:06:21
signal is sitting up here at full power
00:06:24
if I had another signal that was sitting
00:06:25
down here 60 DB down I'd be able to see
00:06:28
that which would be very very difficult
00:06:30
or impossible to do if the scale was
00:06:33
linear so that's why we use DB so let's
00:06:36
look at a couple of examples of how we
00:06:39
use them and where some of these other
00:06:41
units come from like dbm and DBU and and
00:06:44
that kind of
00:06:46
thing now we stated earlier that uh
00:06:49
since a DB is a ratio it's not an
00:06:52
absolute quantity like a watt or a volt
00:06:55
so for example we can say that hey this
00:06:58
signal that we're looking at at is 3db
00:07:01
greater than that one okay because
00:07:03
that's a ratio but we cannot say that
00:07:05
this signal is 3db that doesn't make any
00:07:07
sense because DB isn't a unit or isn't
00:07:10
an absolute value DB is always a ratio
00:07:14
so how do we use it to measure absolute
00:07:16
quantities so in order to measure an
00:07:18
absolute quantity we must specify or
00:07:21
imply a reference like we did here
00:07:23
saying 3D be greater than some value all
00:07:27
right so in example we can always say
00:07:29
that hey this signal is twice as big as
00:07:31
X or this signal is half the size of Y
00:07:35
all right knowing the reference okay the
00:07:38
ratio then becomes an absolute value
00:07:41
because if we know what this value is if
00:07:43
this signal is twice as big of it we
00:07:45
know how big that signal is so once we
00:07:48
know the reference or we imply a
00:07:50
reference okay then we can turn a DB
00:07:54
into essentially an absolute value and
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uh this is where the suffix comes comes
00:07:59
in on uh the DBS so when you see say dbm
00:08:04
that's implying that the reference is a
00:08:07
mwatt when you see DBU it's implying the
00:08:11
reference is a microwatt and typically
00:08:13
the W is omitted if the you know with
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that being omitted the uh the assumption
00:08:19
is and uh the convention is is that
00:08:22
we're talking about power so that would
00:08:24
be Watts if you see you know typically
00:08:27
if you're not going to be specifying a
00:08:28
reference as a power level in Watts but
00:08:30
you're going to express it in volts then
00:08:32
that typically would show up here so
00:08:35
dbmv the reference is a molt so we're
00:08:38
going to say that this signal is x times
00:08:40
larger than a molt or x times smaller
00:08:43
than a microwatt or x times larger or
00:08:45
smaller than a milliwatt so um the
00:08:49
suffix then can turn a DB into an
00:08:52
absolute quantity like dbm so dbm is an
00:08:55
absolute quantity that says we're going
00:08:58
this power level is is x times larger or
00:09:01
smaller than a millatt so we can
00:09:03
calculate that that out to a specific
00:09:05
quantity so that's where these
00:09:07
particular values come in so let's run
00:09:09
some examples on the instrument and uh
00:09:12
show you what we're talking
00:09:15
about okay let's use this example that
00:09:17
we have on the screen this is a 10 mahz
00:09:21
signal that's uh measuring just about
00:09:24
950 M volts Peak to
00:09:27
Peak so if we run that calculation that
00:09:30
10 MHz uh signal at 950 Ms Peak to Peak
00:09:34
it is being terminated into uh 50
00:09:37
ohms and that's kind of an important
00:09:39
thing too and we're going to be
00:09:40
measuring and comparing power levels
00:09:43
they all have to be with respect to the
00:09:45
same load so in this case we're going to
00:09:47
consider 50 ohms so if the peak-to peak
00:09:49
voltage is 950 molts we need to
00:09:52
calculate the RMS voltage in order to
00:09:54
calculate power so that's simply the
00:09:56
peak to Peak voltage divided by two *
00:09:59
the < TK of 2 so if we do that
00:10:01
calculation the RMS voltage is 336 MTS
00:10:06
therefore the power in the 50 ohm load
00:10:08
is equal to the RMS voltage squared
00:10:10
divided by the load resistance so that's
00:10:13
336 squar divided 50 or 2256
00:10:18
M so to express this value in dbm the
00:10:22
reference is a mwatt so we basically say
00:10:26
the value in dbm is equal to 10 * the
00:10:28
log
00:10:29
of 2256 M divided by a millatt that's
00:10:33
our reference and that gives us
00:10:36
3.53 dbm so let's see if that that's
00:10:40
what we have we'll move the signal over
00:10:42
to the Spectrum analyzer input and turn
00:10:45
the Spectrum analyzer on we'll turn off
00:10:48
the analog trace and uh so there's the
00:10:51
uh the signal we're seeing on the scope
00:10:53
we take a look at the measurement there
00:10:55
it is right at uh 3.5 dbm that's pretty
00:10:58
dark and close 03 dbm different but uh
00:11:02
so that uh is basically what our answer
00:11:05
is if we want to express that value in
00:11:09
DBU or DB relative to a microwatt then
00:11:12
we would just run the calculation here
00:11:14
to say it's 10 * the log of 2.25 6 * 10-
00:11:18
3 that's mwatts divided by a microwatt
00:11:22
which is 1 * 10 - 6 and that would give
00:11:25
us
00:11:27
33.538325 we hit the amplitude key here
00:11:31
change the vertical units I'll use the
00:11:33
uh knob here to change that to DB
00:11:37
microwatts or DBU if we take a look
00:11:40
there we are
00:11:42
33.5 and we expected
00:11:44
3353 that's basically the same number so
00:11:48
now you can see how those numbers relate
00:11:50
to the voltage that we measured on the
00:11:54
scope so what about comparing voltage
00:11:57
ratios can we use use DBS for that well
00:12:00
a DB like I said by
00:12:02
definition uh relates to power so we
00:12:06
have to calculate it against power but
00:12:08
uh we can still kind of do this so
00:12:09
here's how it works so if we're going to
00:12:12
compare power levels we're going to
00:12:14
basically take the voltages of interest
00:12:16
and compute the power so uh the power
00:12:18
from voltage number one is v1^2 / R the
00:12:23
power of our reference value is v2^2 / R
00:12:26
and we're going to assume an equal r
00:12:29
uh for this for this video which is
00:12:32
almost always the case so let's simplify
00:12:34
this equation so when you have a
00:12:37
fraction over a fraction you can invert
00:12:39
and multiply so that's the same as 10 *
00:12:41
the log of v1^2 R * R over v2^ 2 the RS
00:12:46
cancel out so you're left with 10 * the
00:12:49
log of v1^2 over v2^
00:12:52
2 uh that's the same as 10 * the log of
00:12:55
V1 over V2 that whole quantity squared
00:12:59
now you may remember from your high
00:13:01
school algebra that uh when you have the
00:13:03
logarithm of a quantity that has an
00:13:05
exponent the exponent can come outside
00:13:08
and multiply against the front so that
00:13:11
would be the same as having 2 * 10 * log
00:13:14
of V1 over V2 and that's why we wind up
00:13:17
seeing the expression when we're
00:13:19
Computing uh Logs with respect to
00:13:22
voltages where it's 20 * the log when
00:13:25
you're comparing a voltage ratio it's 10
00:13:27
* the log when you do a Power ratio 20 *
00:13:31
the log doing a voltage ratio and again
00:13:33
this is all assuming an equal load
00:13:35
impedance okay the equal R all right now
00:13:39
in our case we have this 950 molt Peak
00:13:42
to Peak signal uh and that can be
00:13:44
expressed say in DB relative to a molt
00:13:47
or
00:13:48
dbmv we have to compute the you know use
00:13:51
the RMS value that we computed on the
00:13:53
previous uh page so we say the dbmv is
00:13:57
20 * the log of the r RMS value of that
00:13:59
which is 336 molts divided by a molt and
00:14:03
that gives us
00:14:05
50.2
00:14:06
dbmv so let's take a look let's change
00:14:09
the unit here uh we were looking at uh
00:14:12
about 3.5 dbm before Let's uh move this
00:14:15
unit down to
00:14:18
dbmv and uh we're looking at uh
00:14:21
50.5 DV MV and that's basically what we
00:14:26
calculated so you may ask what about DBC
00:14:30
you know I uh I always see DBC when
00:14:33
we're talking about Spectrum analyzers
00:14:34
what does that mean what's the reference
00:14:36
there um well
00:14:38
DBC basically means that it's decb
00:14:41
relative to some carrier power level now
00:14:44
this is very very common in RF
00:14:46
applications because what this might do
00:14:48
is to say how how large is a distortion
00:14:51
component with respect to my main signal
00:14:54
okay so we often we'll call that DBC or
00:14:56
DB relative to a carrier level let's
00:14:59
take a look at how we might use that on
00:15:00
this analyzer here so I've got this
00:15:03
signal coming in here that's at uh you
00:15:05
know 10 MHz about 3 and 1/2
00:15:08
dbm and uh let's change the span I'm
00:15:11
going to change my stop frequency here
00:15:13
out to 30 MHz and uh in doing that what
00:15:17
I can see now is I see the my
00:15:20
fundamental signal here okay 10 MHz uh
00:15:24
plus 3.5 dbm and I also see if I look
00:15:28
carefully here I can see there's a uh
00:15:31
another tone down here it's actually the
00:15:33
second harmonic coming out of my signal
00:15:34
generator and that guy is down at uh oh
00:15:38
- 53 - 53 - 54 dbm or so so that's the
00:15:43
absolute power level of it but what
00:15:45
might what might be important to me is
00:15:47
how far down is that with respect to my
00:15:50
carrier uh we can set the markers up
00:15:52
here to be relative reading markers so
00:15:55
if I set that to be an a relative or
00:15:57
Delta reading marker what that will do
00:15:59
is I'll take this measurement here okay
00:16:03
as my reference level and now when I go
00:16:05
to make the other measurement here it
00:16:07
shows it Me shows it to me as
00:16:10
DBC uh DBC means it's decb relative to
00:16:14
the carrier which is my uh reference
00:16:17
point over here so it tells me that the
00:16:19
second harmonic is in this case about 57
00:16:22
DB down from the carrier and that's
00:16:25
typically what we'll need to know we'll
00:16:27
typically use the absolute value for the
00:16:29
carrier measurement and then use
00:16:31
relative values or DBC values to look at
00:16:35
other components with respect to our
00:16:37
carrier level so that's what DBC means
00:16:40
it's looking at other power levels with
00:16:42
respect to some other level that you
00:16:44
might be looking at as your reference on
00:16:48
screen so I hope this video gave you a
00:16:51
little bit of an idea of what the
00:16:53
various
00:16:54
amplitude uh units are that you'll find
00:16:57
on a spectrum analyzer
00:16:59
and why we use decb in the first place
00:17:02
or a logarithmic exp uh representation
00:17:05
of amplitude on a spectrum analyzer you
00:17:08
know the spum analyzer gives us so much
00:17:10
dynamic range makes it easy to see
00:17:12
signals that are a million times or 10
00:17:15
million times lower in power um than
00:17:18
another signal for example that would be
00:17:20
impossible to see on the linear display
00:17:23
that you get on an oscilloscope screen
00:17:26
so um we use uh this log rythmic
00:17:29
representation of the power level uh to
00:17:32
make it easy to visualize these things
00:17:34
with respect to each other anyway thanks
00:17:36
again for watching and I'll so
00:17:39
later
