Why Is Y Considered 1 in Antenna Power Gain Calculations?

[amgc63]

TL;DR Summary

Question;
Given that a dipole antenna has directional gain of 2, calculate the power gain in Dbi?

Answer;
Power gain = 10 log (x/y), where y =1
Power gain = 10 log (2/1) = 3dbi

My question is….how come y = 1??

Thanks in advance

Question;
Given that a dipole antenna has directional gain of 2, calculate the power gain in Dbi?

Answer;
Power gain = 10 log (x/y), where y =1
Power gain = 10 log (2/1) = 3dbi

My question is….how come y = 1??

Thanks in advance

 

[berkeman]

Welcome to PF.

dB gain will be with respect to some reference. So the antenna gain in this case is with respect to a unity gain (isotropic) antenna.

Other common dB gains are dBm (dB above 1mW into 50 Ohms) and dBuV (dB above a microvolt).

 

[Baluncore]

My question is….how come y = 1??

Because dB is always the log( abs( ratio ). In this case, the directivity of 2 is being compared with the isotropic antenna, which is defined as having a directivity of 1.

Question;
Given that a dipole antenna has directional gain of 2, calculate the power gain in Dbi?

It is unusual to mix antenna directivity with power gain without considering ohmic losses in the antenna. A half wave dipole has a directivity gain of 2.15 dBi .
https://en.wikipedia.org/wiki/Antenna_(radio)#Gain
https://en.wikipedia.org/wiki/Antenna_gain

 

[amgc63]

Because dB is always the log( abs( ratio ). In this case, the directivity of 2 is being compared with the isotropic antenna, which is defined as having a directivity of 1.It is unusual to mix antenna directivity with power gain without considering ohmic losses in the antenna. A half wave dipole has a directivity gain of 2.15 dBi .
https://en.wikipedia.org/wiki/Antenna_(radio)#Gain
https://en.wikipedia.org/wiki/Antenna_gain

Thanks.

What if the question ask a directivity gain of 4?
What is the power gain in dbi??

10log(x/y)
10log (4/?)

Still can’t get the “y” into my head. :(

 

[Baluncore]

Are you aware that multiplying numbers in the real domain is equivalent to adding their logs ?

A gain of 2 is 10 * Log( 2 ) dB = 3.0103 dB
A gain of 4 is a gain of 2 twice, 2*2 = 4. That is 2 * 3.0103 dB = 6.0206 dB
10 * Log( 4 ) = 6.0206
10^{( 6.0206 / 10 )} = 4.0000

 

[amgc63]

Are you aware that multiplying numbers in the real domain is equivalent to adding their logs ?

A gain of 2 is 10 * Log( 2 ) dB = 3.0103 dB
A gain of 4 is a gain of 2 twice, 2*2 = 4. That is 2 * 3.0103 dB = 6.0206 dB
10 * Log( 4 ) = 6.0206
10^{( 6.0206 / 10 )} = 4.0000

Thank you.
Yes, but I just don’t understand y=1

Was given a question previously,
Question;
Given that a dipole antenna has directional gain of 2, calculate the power gain in Dbi?

Answer;
Power gain = 10 log (x/y), where y =1
Power gain = 10 log (2/1) = 3dbi

I just don’t understand why y =1
Is it becoz isotopic? “Y” always 1?

 

[Baluncore]

Because dB is always the log( abs( ratio ). In this case, the directivity of 2 is being compared with the isotropic antenna, which is defined as having a directivity of 1.

I just don’t understand why y =1
Is it becoz isotopic? “Y” always 1?

Yes. An isotropic antenna is a virtual antenna that has a directivity of 1.
If you want gain in dBi you use y = 1.
If you want gain in dBd you use y = 1.64

You should read the wikipedia section on Antenna Gain where it is fully explained;
https://en.wikipedia.org/wiki/Antenna_(radio)#Gain

 

[Tom.G]

Yes, but I just don’t understand y=1

Gain is defined as a RATIO between what the improvement is and some standard.

For instance you mentioned a power gain of 4. OK, that makes the power 4 times greater than 'something.' Looking at it this way, the 'something' is the standard and you are getting 4 times as much of it.

Now the number '4' can also we written as '4/1', with the '1' representing what you started with.

That's why the '1' in the denominator.

In this case the 'something' is the broadcast power of the simplest omni-directional antenna.

Here is another, made-up example that wouldn't actually be used:

If you had a 2HP motor and replaced it with an 8HP motor. You can say that you are now using a motor that is 4 times stronger than the original, or a power increase of 6dBH (H for horsepower).

Hope this helps!

Cheers,
Tom

 

[amgc63]

Yes. An isotropic antenna is a virtual antenna that has a directivity of 1.
If you want gain in dBi you use y = 1.
If you want gain in dBd you use y = 1.64

You should read the wikipedia section on Antenna Gain where it is fully explained;
https://en.wikipedia.org/wiki/Antenna_(radio)#Gain

Thank u so much. Now the “y” get into my head.

 

[sophiecentaur]

What if the question ask a directivity gain of 4?
What is the power gain in dbi??

Yes. An isotropic antenna is a virtual antenna that has a directivity of 1.

All this assumes that all the power that's put into the feed point of the antenna gets radiated. It's got nowhere else to go but into space and an isotropic antenna will radiate equal power densities in all directions (hence the "1")
It's easy to want (intuitively) to consider practicalities like the effect of plugging a different antenna into the same transmitter / feed arrangement but the theoretical antenna gain ignores this. The design Engineer doesn't because higher gain antennae tend to have higher currents flowing in places (like the ground) which introduces loss and another 'dB factor' to be added in.

 

[Baluncore]

It is unusual to mix antenna directivity with power gain without considering ohmic losses in the antenna.

The OP persists in computing the “power gain” directly from the directivity.

The problem here is that directivity specified in dB is not "power gain" even though it uses 10 * Log10( ratio ).

 

[sophiecentaur]

The OP persists in computing the “power gain” directly from the directivity.

It's a pretty common 'error'. The geometrical gain talks much more than the 'signal gain' in the mind and often in practice. Moreover, when considering a receiving antenna, the important performance criterion is very often to do with rejection of interference off-beam and less to do with receiver noise.

We're getting into more complex matters here and perhaps the OP would see that factors, other than just antenna are very relevant in real radio communications.