Discussion Forum

Khalid,

In my understanding of it, you have a "gain" of -3dB in the plane of your polar plot in comparison to an isotropic radiator.

Cheers
Edgar

Hi Edgar, you are allways present.

You mean it is dBi ( reffered to isotropic antenna)?

Another point, In far field, i can plot Efar or Efar in dB. I could not find any relation between them.

What do you think>

Thanks alot Edgar

Khalid,

yes I think it is dBi. The normdBEfar must some way be normalized. My tests show that S11 is also taken into account. The gain decreases in case there is an impedance mismatch.

I think this deviates from standard antenna gain definitions. The dBi values generally compare the directivity of an antenna regardsless of impedance match.

So far I didn't find in the documentation how the normdBEfar is calculated exactly. Maybe someone else knows?

Cheers
Edgar

Hello Edgar,

I tried to understand if it relates to dBi or not. However, when i change the lumped port voltages( 1,2,3, etc), I get different values. in other words, when the voltage increases, the dB value increase !!!!

I sent an email to COMSOL support and waiting for their explanasion.

Any comment?

regards,
Khalid

Unfortunately, Comsol's software does not offer the option to scale its antenna pattern plots to show the gain in dBi. For 3D problems in Comsol 3.5a, you can compute Gain in dBi on a sphere (which may be physically separated from the rest of the problem) via the following formula: G(dBi)=20*log10(normEfar/sqrt(60*P_in)) where P_in is the input power to the antenna. You need to separately calculate P_in before using this expression. In many cases, at least for Port boundary conditions, P_in may be equal to 1 W, but not always. Often, you need to create an integration coupling variable to find P_in. I believe a similar situation occurs in Comsol 4.2 . In either version, be sure to use a relatively fine mesh when representing the source, so that P_in will be computed properly.

Hello Robert Koslover,

Thanks for your post. Actually I have some questions please:

First, regarding P_in, i am using a lumped port to drive the dipole antenna. Is the formula (P_in=(V0^2)/(2*Zref)) correct? If not how can i calculate P_in.

Second, You have said "Often, you need to create an integration coupling variable to find P_in". Do you mean the formula or something else?

Finally, regarding the meshing , is it ok to use normal meshing for the whole model? or can i use more aqurate meshing for the lumped port alone?

Thanks for your help.

Regards
Khalid

Update: I tried the equations and got fixed value for different Vin.

Some people have asked me about where the factor of 60 comes from in the formula that I posted for the far-field gain. The answer is that it arises due to the somewhat non-traditional way Comsol chose to define the "far-field pattern." As noted in the help system, Comsol states that the "far field" pattern (as they define it) is given by the square of the computed radiated far-field electric field. But to understand directivity (aka, directive gain), we must put this in terms of power densities instead. Consider a point at a far-field distance R (the value of which is large, but in the end will be immaterial). The average power density that an idealized isotropic source radiating P_in would produce at a distance R would be simply S_iso=P_in/(4*pi*R^2). Now, suppose we look at the peak power density from an antenna, also at point R, and call that S_p. Then the peak directivity G = S_p/S_iso, by definition. But S_p can also be written in terms of the magnitude of the electric field E at point R, as: S_p = E^2/(2*eta), where eta = impedance of free space, which is very nearly given by the following simple expression: eta = 120*pi.

Put all these all together, and you get G = S_p/S_iso = [E^2/(2*120*pi)]/[P_in/(4*pi*R^2)] = R^2*E^2/(60*pi*P_in). The R^2 disappears from the equation however, since Comsol's programmers effectively define it as equal to unity (after all, they didn't want their computed "far-field" electric field value to go to zero, which it necessarily would in all problems, if R went to infinity, so who can blame them?).

This then yields the computed numerical value of the directivity G = E^2/(60*pi*P_in). We prefer to express G in terms of dB relative to isotropic (aka, "dBi") however, and thus (if we write G(dBi) in terms of Comsol 3.5a variable names) this becomes (among other ways to write it):

G(dBi)=20*log10(normEfar/sqrt(60*P_in)).

Now, you should note that the above formula is actually for the directive gain (aka, directivity). But (and this is more subtle) even though the above formula is already scaled properly to the "true" input power, it overestimates the textbook "gain" definition if the antenna is impedance-mismatched. This is because P_in (true input power) will be less than what the RF source is capable of, if there is any mismatch. And people usually include this mismatch loss in what they call "gain" of the antenna. Specifically, let's suppose we are driving the antenna with a port boundary, and it is port # 1. In that case, the true "gain," accounting for the mismatch at port 1, can now be written as:

Gain(dBi) = 20*log10(normEfar/sqrt(60*P_in))+10*log10(1-abs(S11_rfw)^2)

Note: The notation has to be changed slightly to account for variable name differences if you use version 4.2

Best regards,
Dr. Robert A. Koslover
SARA, Inc.

Hi Robert

Thanks for a detailed explanation, it will be very useful for my next RF study. With all this "multiphysics", there are many underlying assumptions one must catch ;)

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Good luck
Ivar

Hi Robert,

this is indeed a remarkable piece of work. One of the rare cases to print a thread and put it to the 'valuable' folder. Thanky a lot for sharing it!

Just wondering whether the final formula has been validated by the Comsol folks?

And do I understand properly that although the formula comprises S11 it is the traditional directivity related gain, i.e. a geometrical property? So S11 is just present because of some interesting way Comsol implemented the far field normalization, but actually the formula would yield the same result regardless of mismatch? This is the way I understand directive gain.

Best regards
Edgar

Edgar, thanks for the kind remarks.

1. I don't know of any specific work on this by the official Comsol folks, but I have "validated" the formula with my own models of standard gain horns and it works well. That said, there remain *many* ways in which it can be improperly implemented, so you need to be careful! Common pitfalls include improperly defining a surface for the aperture integration, failure to properly account for factors of 2 that can arise if using symmetry planes (in problems with symmetry), inadequately-fine meshes, and even misinterpreting angle values from the output plots.

2. Terminology in the antenna community is somewhat imperfect, but I'll tell you what I use (which i believe corresponds to the modern, most-common usage). The "directivity" is a geometric property of the antenna and has NO dependence on S11. The "directive gain" is the same as the "directivity." But the "gain" (if used without other qualifiers) is supposed to include mismatch loss, hence the S11 term is needed there. I confess that I sometimes use these terms a bit loosely myself and apologize for any confusion.