Antenna gain reciprocity violation of conservation of energy?

[davenn]

http://www.radio-electronics.com/info/antennas/yagi/yagi-antenna-gain.php

something along the lines of your comments ...

Yagi gain vs number of elements
Although there is variation between different designs and the way Yagi-Uda antennas are constructed, it is possible to place some very approximate figures for anticipated gain against the number of elements in the design.Approximate Yagi-Uda antenna Gain levels
Number of elements Approx anticipated gain dB over dipole
2 ...... 5
3 ...... 7.5
4 ...... 8.5
5 ...... 9.5
6 ....... 10.5
7 ....... 11.5
It should be noted that these figures are only very approximate.

As an additional rule of thumb, once there are around four or five directors, each additional director adds around an extra
1dB of gain for directors up to about 15 or so directors. The figure falls with the increasing number of directors.D

 

[Baluncore]

not sure that adding elements affects the gain in the way that you are stating ... I have NEVER seen it referenced like that ... if you have a solid reference please share

No reference, but plenty of head scratching back in the 1980's. It was based on the reasoning that; because neither the near field diffraction around the forward elements of a Yagi, nor the propagation along the director structure, are 100% efficient, the aperture and so upper gain limit of a real Yagi must be less than the gain of a broadside array with lossless feeds.

The early modelling of Yagis by amateurs used the method of moments without consideration of resistive losses. Very high gain single frequency resonant models could be simulated that could never be built with real materials in a real world. The real antenna was often sold with claims of those artificial simulated gains.
The 2.15 dBd + 3 * Log2(n) is a guide for the maximum gain. If the computer simulation says it is better than that you should question the computer simulation.

A similar gain overestimate occurred with LPDAs as the analysis was based on the concept of a 3 element Yagi. But when the currents in a real wide-band LPDA are analysed it turns out that only two elements are actually ever playing a significant role. That is why the gain of real LPDAs were also often over-estimated.

 

[davenn]

But when the currents in a real wide-band LPDA are analysed it turns out that only two elements are actually ever playing a significant role

that's an interesting comment ... I have always known it as 3 elements, as in, you take one of the elements as the driven one
at a given freq within the range of the LPY and you have a director and reflector for it ... which makes sense

Dave

 

[Quandry]

procity assumption and obviously not conservation of energy assumption. Any thoughts to help me

Simple answer is that the gain is relative to an isotropic radiator. So the transmit gain is never more (or even as much) as the available power and the receive gain is also relative to that received by an isotropic receive aerial.

 

[tech99]

Simple answer is that the gain is relative to an isotropic radiator. So the transmit gain is never more (or even as much) as the available power and the receive gain is also relative to that received by an isotropic receive aerial.

Antenna gain can be specified relative to any sort of antenna you want, such as an isotropic or a dipole, but it is only a relative measurement, so the reference must always be stated e.g. dBi or dBd. The formula for spreading loss comes in a number of disguises, but is always based on a particular type of antenna. For microwave work, using aperture antennas, it is usual to employ an isotropic antenna as the reference, for VHF work it may be more convenient to use a dipole, whilst for MF and low frequency work it is common to use a monopole as the reference. You can convert the path loss from one case to another by allowing for the relative gains of the reference antennas.
Notice also that "gain" includes both the focusing of the energy by confining the energy to a beam (properly called the directivity), and the Ohmic losses of the antenna.

 

[Merlin3189]

Simple answer is that the gain is relative to an isotropic radiator. So the transmit gain is never more (or even as much) as the available power and the receive gain is also relative to that received by an isotropic receive aerial.

I don't see how this is the "simple answer"!
I think we are all agreed that conservation of energy is not at fault! And I hope we all agree that reciprocity is founded on solid physics. So the OP question becomes, why does the Friis equation not work here. That has nothing to do with the units you use to measure gain - doesn't even have to be in any sort of decibels - so long as you know what you are doing and convert to isotropic levels for the values you put in the equation.

As far as I can see, several people have now explained the approximations and assumptions in the Friis equation, which IMO boil down to, the antennae must be much further apart. Neither the Free Space Loss nor the calculated antenna gain will be realistic at short range. And the range at which the Friis equation works, increases with the gain of the antennae.

For an antenna, it is not the units of gain nor what it is relative to that is at fault. It is the concept of an antenna having a definite gain which is fixed from here to eternity and unaffected by its surroundings (I have in mind here that the other antenna is part of the surroundings and has a diminishing influence as it moves further away.)

 

[Quandry]

I don't see how this is the "simple answer"

My answer was to the original question asked by and4bj which was to do with conservation of energy. S(he) had specifically endeavoured to take near field effects out of the equation.
Harald Friis developed his equation using gains relative to isotropic antennas. The equation undergoes many transformations when applied to specific situations but specifically requires the distance between antennas to be a large number of wavelengths so in ande4bj's question the simple answer is that the Friis equation works. But the real simple answer remains that gain is relative to a standard antenna.

 

[Baluncore]

But the real simple answer remains that gain is relative to a standard antenna.

True.
Antenna “gain” is not power amplification. It is the effective aperture or capture cross-section, expressed in dB to make computation of the energy budget easier. Since dB is a Log(ratio), the effective aperture must be referenced to something, usually the aperture of either an isotropic radiator, dBi, or a dipole element, dBd.

Antenna gain is only specified in the far field where the spherical wavefronts can be treated as being flat. It is not surprising that something will break if the far field cross-section is misapplied, in the near field, as power amplification.