Homebrew, field strength help for 15.225?

[pianoplayer88key]

Hi all, I'm considering setting up a homebrew transmitter for use under Part 15.225 of the FCC rules (15,848µV/m @ 30m in the frequency band 13,553 - 13.567 kHz). Operating mode would be AM, with typical transmit bandwidth being a maximum of 12 kHz (for a 6 kHz audio bandwidth), although I may occasionally step it down to 8 kHz, 6 kHz, 4 kHz, or even 2 kHz. At this time, I have no plans to have it on 24/7. (I will not be using CW, SSB, or other modes, as the receiver I would be using to listen to this transmitter, the Tecsun PL-380, is not capable of decoding those modes.)

One of my questions relates to field strength, power output and antenna size. The rules specify a maximum field strength of 15,848 microvolts/meter at 30 meters in the band 13,553 to 13,567 kHz. According to one site, that apparently works out to about 4.8 milliwatts into a half-wave dipole or a quarter-wave vertical over a ground plane.
Most of the time, however, I will need to use a much smaller antenna due to space considerations, often only a few centimeters long, if that.
So I know I want 15,848µV/m at 30 meters, centered on 13,560 kHz. How would I figure out what size antenna I could legally use, given a certain transmitter power, OR what transmitter power I could legally use, given a certain antenna size? Transmitter power would likely be specified in milliwatts, and antenna size in meters (or in the case of a very small antenna, centimeters or millimeters).
Also what is the general law of physics, at least in free space, for field strength as a function of distance? Is it the inverse square law (which would work out to 3,962µV/m @ 60m), or the inverse proportional law (7,924µV/m @ 60m)? I'm trying to get a basic idea of how far I would expect to be able to hear this transmission until it reaches the noise floor (assuming there's no other broadcasts received on that frequency), considering the radio I'm using to receive it (Tecsun PL-380) has a specified sensitivity rating of 20µV at 26dB.

Also, how would I go about finding out how to build such a transmitter? I've done some searching on Google, and have so far come up empty. I want to comply with the rules in 15.225. Considering I may often be using different antennas, depending on available space, I would want to be able to increase or decrease the transmitter power as appropriate. The transmitter will be intended to be battery operated (most likely using 1 or 2 AA batteries), but it would be nice if there could be a provision to hook it up to an AC power line.

 

[rfry]

So I know I want 15,848µV/m at 30 meters, centered on 13,560 kHz. How would I figure out what size antenna I could legally use, given a certain transmitter power, OR what transmitter power I could legally use, given a certain antenna size? Transmitter power would likely be specified in milliwatts, and antenna size in meters (or in the case of a very small antenna, centimeters or millimeters).

The 30-m distance given in the Rule is far enough away from the radiator so that ground (and possibly other) reflections can significantly change the field intensity there, compared to what it would be in a free-space environment. Note that the net value of the peak field radiated by a horizontal dipole including the earth reflection depends on its height above the earth, and the electrical characteristics of the earth around the antenna.

Also what is the general law of physics, at least in free space, for field strength as a function of distance?

In the case of a matched, center-fed, linear, 1/2-wave dipole in free space:

E= SQRT(49.2*P / D^2)

where

E = Maximum Far-field, Free-space Field Intensity, V/m
P = Power, watts
D = Distance, meters

This shows that a power of 0.004594 watts radiated by that dipole will produce a maximum, free-space field intensity just under 15,848 uV/m at a distance of 30 meters.

Antennas with gains different than the dipole described would need different applied powers to meet the limit. Antenna software such as NEC can be used to analyze these systems, but takes a fair amount of antenna engineering background and experience to use properly.

I'm trying to get a basic idea of how far I would expect to be able to hear this transmission until it reaches the noise floor (assuming there's no other broadcasts received on that frequency), considering the radio I'm using to receive it (Tecsun PL-380) has a specified sensitivity rating of 20 µV at 26dB.

Whatever free-space field intensity (voltage) exists at a distance of 30 meters from the radiator will be reduced inversely with distance. So at 60 meters it would be 1/2 as great, etc.

Maybe others will comment on how to build a transmitter.

The meaning of all this for a typical radio hobbyist is that there is no practical way of being certain that Part 15.225 is being met. For example, even a perfectly calibrated field intensity meter could show compliance of a given system when the signal is measured near/at the earth, and be much over the limit when measured at higher elevations.

Sorry that the answer probably is not too encouraging, but it is based on engineering realities.
//

 

[Ermi Roos]

It turns out that the strange field strength limit of 15,848 uV/m at 30 m happens to be equivalent to an effective isotropic radiated power of 10 mW. This fact was stated on another website, but said website recently lost about three months of posts due to a server crash; and so the post stating this fact was lost.

This is actually not much help, because you can't apply 10 mW into an antenna and expect to meet the field strength limit. There are no isotropic radiators, except for the stars.

One approach is to use a transmitter output power a lot less than 10 mW. A poster on the other website has been using 0.5 mW of output power into his antenna for years. He may have used such a low output power to meet an older limit of 10,000 uV/m at 30 m. Low transmitter output power does not actually prove compliance, but 0.5 mW is probably low enough power to make a violation very unlikely.