Prof Grimes,
Thank you for your clarification. We have two different analyses of the
bandwidth of small antennas, both presumably correct mathematically, and the
difference must lie in the initial formulation of the problem, particularly
the exact definition of stored energy in the definition of Q.
I was interested in your comment that Collin never investigated what happens
when the wave is modulated, which is a true statement, but it is commonly
held to be sufficient to make impedance measurements in which the frequency
is incremented in slow time, each measurement being made under steady-state
conditions, and the assumption is that any changes within the rf cycle
resulting from modulation are so slow as to be negligible. I agree that is
an assumption, but few would think it is a fundamental error in my opinion.
Therefore it is assumed that if an impedance measurement is made using a
slowly swept frequency to establish the bandwidth, then the same bandwidth
applies to the frequency-spectrum of a modulated wave under dynamic
conditions. I am not aware of any measurements to the contrary, and if it
is true the stored energy under fixed frequency and power conditions is
significant.
I understand that for single small antennas your results and Collin's are in
agreement, and that the differences appear when there are TE and TM modes
present, generated by a magnetic and an electric dipole together. For the
input impedance of one element to depend on the drive current in the other,
some mutual coupling is required, yet it is difficult to see how two such
antennas would couple: an x-directed loop does not couple to an x-directed
dipole because the wires as mutually orthogonal, while an x-directed loop
does not couple to a y-directed dipole because the loop's E field must be
zero along the dipole, by symmetry. In other words, an x-directed loop
produces Ex=0 along the x axis and Ey=0 along the y axis, so neither dipole
couples to the loop. However the figures in your MOT Letters paper October
2000 shows the dipole asymmetrically placed relative to the loop, and some
coupling might be possible in this case, and enough data is given in the
paper to allow the NEC modelling to be repeated by anyone interested.
I hope this is constructive and not too much of a ramble.
Kind regards,
Alan Boswell
-----Original Message-----
From: Dale M Grimes [mailto:dmg6_at_psu.edu]
Sent: 23 January 2003 01:49
To: alan.boswell_at_baesystems.com
Cc: Craig Grimes; dhw_at_psu.edu
Subject: Small antennas
-- You state "From what I have seen, I think one of the differences can be condensed down to the way in which the power in different spherical modes is added. You make the point that the modal analysis is aimed at providing expansions forthe E and H fields, which obey superposition. In general, power does not obey superposition because E from one mode will multiply with H from another to produce cross-product powers. Collin says that all the modes are orthogonal so these cross-product powers are all zero anyway and therefore the relative phases of the modes are immaterial. Is that one of the essential differences? In the simpler case of waveguide modes the powers of the different modes can be added, as shown by Marcuvitz." Alan Boswell, You are correct that the major difference between Collin and us lies in an analysis of power and energy in a radiation field, but you are not correct in what constitutes our essential difference. Very likely Collin and we would agree on what is and is not orthogonal. Our major difference lies in what field energy is included in the numerator of the Q expression. Collin first calculates the total (infinite) field energy and subtracts the inverse square energy from it. He then separates the remaining energy into parts respectively due to the electric and magnetic fields and places the larger of the two in the numerator of the Q expression. It is unarguably true that placing the larger energy into the numerator of the Q expression for a simple series or shunt circuit gives the correct result. As he and Rothschild showed, and some years later so did we, it also gives at least the approximately correct answer for a single dipole antenna. Now the problem: What happens if the radiation field consists of mixtures of TM and TE modes? By the Collin theory nothing changes, everything is as it was before. Results are universal, good small antennas are impossible, and that's the end of the story. We don't agree. Presumably all would agree an antenna that has been radiating since time equal minus infinity has radiated an infinite amount of energy and hence the total field energy is infinite. Now consider the near-field energy. Is it to be counted as part of the infinite amount of outgoing energy or is it to be placed into the numerator of the Q expression? Collin never asked that question. He made the implicit assumption that ALL near field energy should go into the Q expression. We believe that he is correct for many but not all radiation fields, and the really interesting ones are those for which he is incorrect. To put it another way: For a fixed frequency, fixed power antenna the field energy is not particularly significant. What happens if the field is modulated? The answer is that upon increasing the frequency or decreasing the magnitude some energy returns to the source, thereby affecting it. Q is a measure of that returned energy. The question is upon modulation changes how much of the local energy returns to the source and how much of it simply joins with the outbound energy? So far as we are able to determine neither Collin nor Harrington nor Fante ever addressed this question. All three made the implicit assumption that all standing energy returns to the source, yet the answer is fundamental to the operation of small antennas. We do not claim that Q for our proposed circuit is actually equal to zero (we don't claim it isn't either.) It is simply that we are unable to determine a limit greater than zero. Neither Chu's nor Collin 's analysis applies to our configuration. We did develop a method that, like Collin's, is intuitive and works fine with simple configurations. However, applying our analysis method to more complicated field structures revealed a particular one for which our calculated minimum possible Q was zero. We subjected such an antenna, as closely as we could implement it, to critical tests and found significant agreement with our analysis, both experimentally and with numerical analyses. The result includes definitive proof that Q depends upon the relative phases of different elements of the antenna, showing that the Collin approach is incorrect. Since our analysis operates on fields only, not on the source itself, it is sufficiently general to apply to photons. There we predict zero Q, and of course that is known to be the case. ******************************************************************** This email and any attachments are confidential to the intended recipient and may also be privileged. If you are not the intended recipient please delete it from your system and notify the sender. You should not copy it or use it for any purpose nor disclose or distribute its contents to any other person. ******************************************************************** -- The NEC-List mailing list <nec-list_at_gweep.ca> http://www.gweep.ca/mailman/listinfo.cgi/nec-listReceived on Fri Jan 24 2003 - 15:00:18 EST
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