Part 15 AM Basics

[rfry]

The following was written in response to a private message I received from an R-I site member. While I have already answered him privately, I thought that the response might be of general interest.

Discussion/comments invited.
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Yes, you are correct: increasing the r-f current flowing along any/all sections of a conductor increases the radiation from that conductor. And a long conductor carrying the same current as a short one produces more radiation than the short one.

If the current distribution was linear along a basic 3-m whip instead of being triangular (as it is), then the field intensity gain of the whip itself would increase by 3 dB. A linear current distribution can be approximated by capacitance loading of the whip with two or more symmetrically arranged, horizontal wires electrically connected to the top of the basic whip, and insulated from an r-f ground at their far ends. The FCC's view of this with respect to 15.219(b) could be a problem, though.

However adding length to the functional "ground lead" can add much more than 3 dB gain to an antenna system consisting of a basic 3-m whip mounted with its base at/near the surface of the earth. Again, this approach may not pass an FCC inspection for compliance with 15.219(b) -- and purely as a matter of physics, it doesn't. The FCC has issued citations to operators using such configurations, however according to posts on these boards there are many more such setups that the FCC has not cited.

To summarize the main factors affecting "Part 15" AM system efficiency on any given frequency, ~ in order of importance ...

• The quality of the impedance match between the transmitter output circuits and the antenna system feedpoint impedance
• The amount of r-f power that the final r-f stage of the transmitter can deliver into the impedance match it "sees"
• The net r-f resistance of the functional r-f ground(s) in use (something buried in the earth, typically)
• The r-f resistance of the network used to match the transmitter output impedance to the antenna system input impedance
• The amount, and distribution of the r-f current flowing on the conducting wires/paths connected to and leading away from the transmitter terminals, such as
  
  • the 3-m whip
  • the "ground lead"
  • the "safety ground" and/or the grounded structure used to support the transmitter and 3-m whip, and
  • the conductors used to supply audio and d-c power to the transmitter
  [*]The radiation resistance of the 3-m whip, whether or not top loading is used
  

Further contributors to system performance are the conductivity and dielectric constant of the earth along the propagation path to the receiver -- but generally these are beyond the control of the operator.

Each of the above topics could be expanded into several pages of text and graphics. In some cases that already has been done, and posted on several Part 15 boards over the last few years.

If "Googling" doesn't locate them then I may be able either to re-post the papers themselves, or link them to this thread.

Happy New Year, everybody.
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[Ermi Roos]

Top-loading the whip to the extent that the current distribution is rectangular (or constant along the length of the antenna) instead of triangular (which is linear along the length of the antenna) increases the field intensity gain by 6 dB, not only 3 dB. This can be shown by computer simulating the arrangement of the two horizontal wires oriented as a cross on the top of a vertical whip, as suggested by R. Fry. Extending the wires in the simulation far enough so that the current distribution is constant instead of linear increases the radiation resistance by a factor of 4, which produces a power gain of 4 or a field strength gain of 2, which is 6 dB.

 

[Ermi Roos]

Here is a "linear" equation: y = mx + b. y can represent the RF current at a point along a whip, and x can represent the distance along the whip. m is the slope of the curve, and b is the value of y when x = 0. I am posting this in order to avoid a long discussion about what "linear" means.

I recently tutored a very gifted honor student in the math portion of the SAT. This experience, and R. Fry's post above, showed me that even very bright people sometimes don't know the meaning of "linear."

 

[rfry]

...Extending the wires in the simulation far enough so that the current distribution is constant instead of linear increases the radiation resistance by a factor of 4, which produces a power gain of 4 or a field strength gain of 2, which is 6 dB.

Thank you for pointing this out. Other things equal, when the antenna current is uniform along the 3-m whip, its average value along the whip increases by a factor of two compared to the current on the whip with no capacitive loading wires at the top.

As the radiated electric field intensity is directly related to antenna current, this means that when the current doubles, field intensity increases by a factor of two -- which, when expressed in decibels is 20 * log10 (2) = 6 dB.

But even with a 6 dB difference, attaching a long, radiating conductor as a "safety ground," and/or electrically connecting the transmitter and basic whip to the top of a tall grounded tower or mast can add 15 dB or more gain to the complete antenna system, other things equal. And both configurations may not pass an FCC field inspection, which is the most important point to take away from this.

y = mx + b. y can represent the RF current at a point along a whip, and x can represent the distance along the whip. m is the slope of the curve, and b is the value of y when x = 0 ... This experience, and R. Fry's post above, showed me that even very bright people sometimes don't know the meaning of "linear."

And m represents the slope of that line, and b a constant. So that equation can produce a current value that is constant along the length of the whip, or one that tapers to zero at the far end of it.

My use of the word "linear" referred to the point that the current had a linear geometric shape, not that it was the product of a linear process.
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[Ermi Roos]

I was afraid of leaving enough wiggle-room for nit-picking, and so I will pick some addition nits. In the polynomial equation y = ax + bx^2 + cx^3 + ... + (a constant), where the highest order term is x^1, the equation is linear, quadratic for x^2, cubic for x^3, quartic for x^4, quintic for x^5, and so on to any finite integer, For x^0, the equation is a constant, y = mx +b = m+b. By setting m = 0, the equation is also a constant, y = b.

 

[rfry]

By setting m = 0, the equation is also a constant, y = b.

Glad to see that we agree, at least on this point.

 

[rfry]

...Extending the wires in the simulation far enough so that the current distribution is constant instead of linear...

Isn't a constant value a linear value?

 

[Ermi Roos]

If the constant value is a linear value, why did you call the non-constant triangular current distribution "linear?" [People are going to think that I am you using a different account.]