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Episode: 4382
Title: HPR4382: Understanding Antenna Gain and the Decibel scale
Source: https://hub.hackerpublicradio.org/ccdn.php?filename=/eps/hpr4382/hpr4382.mp3
Transcribed: 2025-10-26 00:01:55
---
This is Hacker Public Radio episode 4382,
produced at the 20th of May 2025.
Today's show is entitled,
Understanding in 10 Again and the Decable Scale,
is part of the series HAM Radio.
It is hosted by Paul J and is about 8 minutes long.
It carries a clean flag.
The summary is,
the use of decibels can be a bit confusing.
So in this episode, Paul will enlighten you.
Good day, everyone.
This is Paul J and I'd like to give you a quick show about decibels and antenna gain.
So, why am I doing this?
I'm working towards getting my full licence for amateur radio in the UK.
I decided it would be a good idea to review the training material available for the foundation,
intermediate and full licence.
Even though I had the foundation licence already,
I wanted to go back and really confirm my understanding.
Now, one aspect that I find,
I kind of understand,
but never really properly understood, is decibels.
So, when you read the book about decibels,
it doesn't really go into much detail about
how they calculated or how to use them.
It just says,
well, you need to know that
three decibels is double-layer gain
and ten decibels is ten times the gain.
So as part of this activity,
I've actually now gone into the maths behind it to understand
and really clarify my own head how it works.
The formula for power in decibels
is ten times log to the base of ten of P,
where P is the power in watts.
Now, the base reference is one watt.
So, one watt is actually zero decibels.
When we look at antenna gain,
we look at the amount of power output relative to this one watt.
So, if we start with two watts,
then the power in decibels will be ten times log ten of two.
This is a fraction over three.
So, if you go back to my original comment
about three being double the power,
so two watts is double-one watt
and ten the log ten of two is three.
And similarly, if you were to take log ten of ten,
then it's one, so ten times one would be ten.
So, this is how we have ten times.
So, this is really straightforward.
Now, the next unit that you will see
in amateur radio is dBm,
or decibels relative to a milli watt.
So, it's the same formula again.
Except this time, we take one milli watt as zero decibels.
And we can then reference the power to this one milli watt.
So, one watt is equal to one thousand milli watts.
Log to the base ten of a thousand times ten
would be thirty dBm.
So, this is another figure you often see.
Thirty dBm is equal to zero dB.
The next unit that you will see is dBm,
which is decibels relative to an isotropic antenna.
Now, the gain of an isotropic antenna is one.
And therefore, gain of ten dB would be again of ten dBm.
The next unit of reference is dBd,
which is decibels of gain relative to a standard half wave dipole antenna.
Now, the gain of a half wave dipole antenna is 2.15 dBm.
So, 2.15 decibels relative to an isotropic antenna.
So, 2.15 dBm is equal to zero dBd.
So, an antenna with a gain of ten dBm is equal to ten dB,
and is therefore equal to seven point eight five dBd.
Because the decibel scale is logarithmic,
it means that you can add the decibel values together
to understand the gain or losses through a full circuit.
You haven't got to multiply the numbers together.
So, to get from dB to dBd,
you can simply subtract 2.15.
So, ten dBm is equal to seven point eight five dBd.
Okay, so now I like to talk about effective radiated power.
So, if we check the page in Wikipedia, it says this.
Effective radiated power is the standard definition of direct...
of directional radio frequency power,
such as that emitted by a radio transmitter.
It is the total power in watts that would have to be radiated by a half wave dipole antenna
to give the same radiation intensity as the actual source antenna
at a distant receiver located in the direction of the antenna's strongest beam.
If we use an isotropic antenna instead of a dipole,
then we get the value of ERP,
which is the effective isotropic radiated power.
You'll not be surprised to hear that the relationship between ERP and ERP
is fairly easily calculated.
So, if we use decibels,
then ERP is equal to the ERP plus 2.15 decibels.
So, 2.15 decibels reflects the gain of a dipole antenna.
If we take watts, ERP and watts is equal to ERP and watts multiplied by 1.64,
which is the power gain of the dipole antenna.
Let us look at a practical application of these values.
My KX3 transmitter has a maximum power of 15 watts.
This is 11.77 dB when I put the numbers through the formula we discussed at the beginning.
I now connect my transmitter to a Yagi Uda antenna with a gain of 10 dB.
So, this is 10 times the gain of a half wave dipole.
We can now add those two numbers together.
So, 11.77 plus 10 would give us 21.77 dB.
And if we then look at the conversing that back to watts,
this will give us 150.3 watts of ERP.
So, what does that mean?
So, that means that if I had a dipole antenna to achieve the same signal strength in the direction that I am pointing my antenna,
I would have to input 150 watts into that antenna.
So, clearly from my 15 watt KX3, that is quite a good result.
Now, if I want to calculate that number as ERP,
then this would be adding the 2.15 value.
So, another of the 21.77 would give us 23.918.
And if we convert this back to watts,
then this would give us 246 watts of ERP.
So, in other words, we would have to feed 246 watts into an isotropic antenna
in order to get the same signal strength in the direction I am pointing my antenna in.
Now, clearly the isotropic antenna is a theoretical thing,
dipole isn't, but it just goes to show that you can achieve a lot more with antennas in terms of power outputs
than you can just by increasing the power on the transmitter alone.
So, I hope that's been a useful round tour of decibels and how to use decibels and look at antenna performance.
If your mind works like mine,
I really recommend you get a calculator out and use the formula
and just calculate back and forth from decibels to watts or millawatts
and just try and understand how the numbers feel.
This helped me understand more clearly how this all fits together.
If you consider studying to become a radiometer,
I strongly recommend it, it's not difficult to do.
Particularly, if I take the UK example at foundation level,
the coursework is fairly straightforward
and the exam is a multiple choice.
So, you can work to get through this and if you have a local radio club,
I definitely recommend you go and join them.
But to be fair, I did it during lockdown when that option wasn't available.
So, yeah, become a radiometer, you'll find it good fun
and it might be useful and expand your interests in other areas as well.
So, that concludes this particular episode of Hacker Public Radio.
If I've got anything wrong, I will come back and make another show to correct it.
But I think now I have actually got everything in this show correct.
Even though I did have to go back and record the EIRP and EIRP section again
because I had made some mistakes.
I think it just goes to show that if you really want to understand something,
try to explain it to somebody else.
Anyway, I look forward to seeing your comments in the show notes
and I look forward to making another episode at some point in the future.
So, this is Paul J signing off for Hacker Public Radio.
You have been listening to Hacker Public Radio at Hacker Public Radio does work.
Today's show was contributed by a HBR listener like yourself.
If you ever thought of recording a podcast,
then click on our contribute link to find out how easy it really is.
Hosting for HBR has been kindly provided by
an onesthost.com,
the Internet Archive and R-Sync.net.
On the Sadois status, today's show is released on our Creative Commons
Attribution 4.0 International License.