calculating antenna size or transmitter power based on field strength?

[pianoplayer88key]

Hi. Does anyone know how to calculate transmitter power or antenna length, based on a desired field strength at a specified semi-near distance? Also for short distances would I need to take ground losses, etc, into account in the calculation?
For example, I've read that with a 1/2-wave dipole at 13.56 MHz, you need about 4.8 milliwatts of power to get a field strength of 15,848uV/m @ 30m. As I understand it, a 1/2-wave dipole at that frequency would be about 36.3 feet in length. That would be MUCH too large for portable operation. I'm thinking I'd want the antenna AND transmitter to be concealed in a walkman-size container, if possible, running on AA batteries. For example, if I used an antenna that's 1/512 wavelength (~1.7" or 43.2mm) long, how would I calculate the transmitter power to get 15,848uV/m @ 30m?
Let's assume I know the field strength I'm looking to get at a particular distance. I also know one of either the antenna length, or the transmitter power, but not both. Assume the antenna is directly connected to the transmitter, to eliminate any transmission line loss that may occur... although there may be 50 feet or more of audio cable connecting to the transmitter's audio input.
If I know the transmitter power and field strength at a specified distance, how would I calculate the antenna size required (while allowing for a calculation to basically tell me something's wrong when I attempt to do something that's physically impossible)? Or, if I know the antenna size and field strength @ the specified distance, how would I calculate the transmitter power? Basically what would be the formula for calculating those? I'm assuming antenna size would be calculated in fractions of a wavelength, and I could convert it to feet & inches or meters from there.
Also, what about calculating ground losses - would those need to be factored in? I'm looking at operating at around 13 MHz, for example - is it possible to use direct wave when a transmitter is inside a building? Also, assuming the TX is less than 30 meters from the edge of the building, would I need to figure out how to increase the power a little to produce the specified field strength, or would it be safer to test the system outdoors?
At this point I'm not looking into operating with other frequencies, like 27MHz, 40MHz, 49MHz, 900MHz, 2.4GHz, 5.8GHz, 24GHz, just to name a few, as I don't own a sensitive or selective receiver capable of receiving those frequencies, so would have no way to test the signal. At 13 MHz I would be using AM (not SSB, CW, or FM), and I'm not sure what I'd use at other frequencies. I'm thinking AM because of the relatively narrow bandwidth required, but my gut feeling tells me that wouldn't be a good idea at GHz+ frequencies.
Also, is there any way without a field strength meter I could at least get some basic idea if I'm in compliance? I have a Tecsun PL-380, which has a primitive wannabe signal strength meter, with a range from 15dBu to 63dBu. I understand R Fry and a couple others have PL-310 radios, and I've seen in a few of their posts that they are not perfectly accurate by any stretch of the imagination. Question... are they erratic all over the place, or are they basically consistently inaccurate across the band?
If I was going to use a PL-380 to check compliance, would there be some guideline I should go by? I assume that if I get a reading of 20dBu at a distance of 6 inches, then my setup is seriously underpowered. And, if I get a reading of 63dBu at 10 miles away, then I'm probably exceeding the limit. (Assume I'm using only the built-in whip antenna, fully extended and vertical.)

Also, when I click preview post, why is it I only get a one line high unresizeable preview pane? Is it my browser (Google Chrome 5.0.375.38 beta) or is it that way for everyone? Also I get a database error when I try to search for a user's posts from their profile page.

 

[Ermi Roos]

In general, there is no formula for calculating the antenna size and transmitter power given the field strength at a particular distance.

15,848 uV/m at 30 m roughly corresponds to 4.8 mW of radiated power from a half-wave dipole in free space. Radiated power is not the same as transmitter output power, unless the antenna system has no losses; also, an actual half-wave dipole would not be so high that it is equivalent to a dipole in free space. A real dipole would have reflections from the ground pane, which would change the dipole gain. 15,848 uV/m at 30 m also roughly corresponds to 10 mW of radiated power from an isotropic antenna. Since the notion of an isotropic antenna is a mathematical concept, and isotropic antennas do not actually exist, this is not particularly helpful.

Only a calibrated standard field strength meter can be used to prove compliance, and a receiver with a meter can only be used to get approximate results, and will not satisfy the FCC.

One operator on 13.56 MHz uses only 0.5 mW of output power from the transmitter applied to the antenna. 0.5 mW is so low that it is very unlikely that the field strength limit in the Rules will be exceeded. Using low transmitter output power does not prove compliance, but it makes a violation improbable. [If you decide to use low output power, be sure you know how to measure it. A DMM can't be used to measure RF power, for example.]

 

[pianoplayer88key]

In general, there is no formula for calculating the antenna size and transmitter power given the field strength at a particular distance.

Is that because there's too many other variables, or is there some other factor that makes it impractical?

15,848 uV/m at 30 m roughly corresponds to 4.8 mW of radiated power from a half-wave dipole in free space. Radiated power is not the same as transmitter output power, unless the antenna system has no losses; also, an actual half-wave dipole would not be so high that it is equivalent to a dipole in free space. A real dipole would have reflections from the ground pane, which would change the dipole gain. 15,848 uV/m at 30 m also roughly corresponds to 10 mW of radiated power from an isotropic antenna. Since the notion of an isotropic antenna is a mathematical concept, and isotropic antennas do not actually exist, this is not particularly helpful.

I'm aware of the 4.8mW radiated from the half wave dipole. Is there a way to calculate antenna losses? Assume that there won't be a transmission line between the transmitter and the antenna - it will be directly connected. Also there's the chance that there may be no ground other than the chassis of the transmitter itself. Is an isotropic antenna a theoretical no-loss point source, or what is it?
Also, a half wave dipole at 13.56MHz would be 36 feet 3.5 inches or 11.062 meters long. I may be very limited on space, and may only be able to use an antenna about 1.7 inches or 43.21mm long, which at 13,560kHz would be 1/512th of a wavelength.
One of the reasons I chose 13.56MHz is because it appears to have the highest field strength relative to distance allowed of any of the part 15 bands, and also the portable operation I'd be using it for essentially would make going by the transmitter power and antenna length rules impractical, as I'd be using a MUCH smaller antenna than allowed under those sections.

Only a calibrated standard field strength meter can be used to prove compliance, and a receiver with a meter can only be used to get approximate results, and will not satisfy the FCC.

I understand it's not going to be exact, but if I could at least figure out if I'm somewhere in the ballpark, or way off the mark, that would help.

One operator on 13.56 MHz uses only 0.5 mW of output power from the transmitter applied to the antenna. 0.5 mW is so low that it is very unlikely that the field strength limit in the Rules will be exceeded. Using low transmitter output power does not prove compliance, but it makes a violation improbable. [If you decide to use low output power, be sure you know how to measure it. A DMM can't be used to measure RF power, for example.]

I read about that somewhere else, too, but can't remember. I'd want to be close to the limit, though. Is there any way I could test compliance at a reasonable cost without actually buying a field strength meter? Sure, I'd love to own a FIM-41 or whatever the meter I saw referenced in another post somewhere, but I'm guessing the price exceeds what my entire gross life's income will ever be, AND looking at the specs it may not be capable of doing something I'd want to be able to do with a field strength meter of that caliber, one thing being measure the field strength of a CW signal at the atmospheric noise level, while sitting within a couple feet of a 50kW IBOC tower with a carrier frequency a tenth of a cent away from what I'm trying to measure. (In case you don't know what a "cent" is in this context, there are 1200 evenly-distributed cents in an octave. I also assume you know that an octave is a doubling or halving of frequency. In this example, if I wanted to measure a CW signal 1/10th of a cent above 1,000 kHz, I would be measuring a carrier frequency of 1,000,057.76 Hz. I also notice that I maybe need to tighten the tolerances a bit more... 1/10th of a cent may be barely noticeable at piano note frequencies, but if we could hear 1 MHz, would produce a very rapid flutter fast enough to actually produce its own musical tone. Maybe I should just say the carrier frequency is a few tenths of a Hz off.)

 

[Ermi Roos]

Field strength depends upon both the radiated power from the antenna and the directional gain of the antenna. Neither the radiated power nor the directional gain are known for any real antenna that has not been thoroughly tested, and therefore the field strength cannot be calculated.

Short antennas have very high losses, and the magnitude of the losses cannot be calculated.

Yes, an isotropic antenna is a point source. The concept is very helpful for theoretical calculations, but a point source antenna does not actually exist.

Even a calibrated standard field strength meter is not very accurate, but the FCC will accept the results from such a meter. They are not likely to accept results from the signal strenth meter from a receiver with unknown response characteristics.

 

[rfry]

Field strength depends upon both the radiated power from the antenna and the directional gain of the antenna. Neither the radiated power nor the directional gain are known for any real antenna that has not been thoroughly tested, and therefore the field strength cannot be calculated.

The inverse distance field from real monopoles of various heights when used with various radial ground systems has been accurately known for decades. The FCC even has an on-line calculator to do that for the antenna systems used by licensed AM broadcast stations... http://www.fcc.gov/mb/audio/bickel/figure8.html

NEC4 also can be used to calculate this with results that match the FCC values quite well. In fact, NEC4 is used by consultants to design the arrays used by directional AM broadcast stations, and the resulting installations meet the FCC design parameters when measured with calibrated field intensity meters -- which is required before the FCC will grant the authority to operate the station.

Short antennas have very high losses, and the magnitude of the losses cannot be calculated.

The losses when using a short antenna (in terms of wavelengths) are due to the relatively low radiation resistance of the radiator compared to the other components of a short antenna system. The radiator, itself produces EM radiation from nearly 100% of the r-f current that can made to flow on it, regardless of its electrical length.

Even a calibrated standard field strength meter is not very accurate, but the FCC will accept the results from such a meter.

As has been posted in another thread, the field intensity meter most commonly used by licensed AM broadcast stations and consultants has a specified accuracy of 3% of a standard field at the test site of the N.I.S.T -- which can't really be described as "not very accurate."

None of this helps tfcwings answer his original questions, but the information will give another perspective on the quoted statements.
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[Ermi Roos]

tfcwings was inquiring about determining field strength under section 15.225, and so the information about AM broadcast antenna systems is not applicable.

Not all antenna consultants agree with NEC results. Some prefer wipl-d, which is more accurate. NEC (pronounced, "neck") and wipl-d results agree fairly well for wire antennas at close range, but NEC does not work as well with conductive surfaces. NEC also does not compute the Sommerfeld formula for ground attenuation accurately, and so field strength as a function of distance is not computed very well. The major reason not all antenna consultants use wipl-d is its huge price compared to NEC.

The radiation resistance and the input current of a real antenna are usually not known. I have an RF current meter that reads in amps, but this is not applicable to Part 15. I suppose that a current meter for Part 15 can be designed, but such an instrument is not readily available. Computed radiation resistance is reasonably accurate in an open field, but not in the cluttered environment in which Part 15 antennas tend to be used.

The accuracy of a field strength measurement does not depend only on the accuracy of the instrument at a standard calibration site, but also upon the environment in which the measurement is made. To claim a 3 % accuracy for a field strength measurement is highly misleading. The field strength reading with a standard calibrated field strength meter tends to be an ad hoc legal definition of field strength, but it is not the actual physical field strength.

 

[pianoplayer88key]

I'm not sure if that calculator is working for me.
I put in a frequency of 1356kHz (I can always multiply/divide by 10 later as necessary), as it wouldn't let me put in 13,560kHz. Tower height above base insulator: 12 meters. Unfortunately I'm very limited on space, so even accounting for the 10x frequency error, 1.2 meters is still way too long of an antenna. I'll get to ERP shortly. Ok, so average length of ground radials is 33.2 meters, and number of them is 90. Problem is, there won't even BE any ground radials with this setup. Now, as for ERP, the lowest I could put in was 0.00001kW (10mW). This calculation results in a field of 0.579mV/m @ 1 km, which works out to 19.3mV/m @ 30m in free space (from what I understand, field strength voltage is inversely proportional to distance, unless the manual for one of Ramsey's FM transmitters, as well as other sources, is wrong), which is over the limit of 15.848mV/m @ 30m. By experimenting with the calculator, I discover (or remember) that a 100x increase in transmitter power, all other factors remaining the same, results in a 10x increase in field strength. Eventually, after some trial and error, and after the appropriate conversion factors, I come up with a power of 6.75043mW to get a field of 15.848mV/m @ 30m, using a tower height of 12 meters (at 1356kHz), and 90 radials of 33.2 meters in length. Now... where would I go from here to calculate what it would be if I used NO radials at all, and used a shorter antenna? As for figuring out how they're calculating it, using my browser's "View Source" function on their page is coming up dry.
If I was just going to experiment and set up a transmitter, is there a way I can inexpensively determine compliance? The cost of the components (capacitors, transistors, ICs, resistors, crystal (if used), etc) used to make the transmitter will probably take up about 75-80% or more of the total budget.

 

[Ermi Roos]

I want to point out that the "radiated power" I mentioned in this thread is not ERP. It is the total RF power radiated into space in all directions. ERP is antenna performance with respect to a particular hypothetical antenna, such as an isotropic, or a half-wave dipole in free space. Neither of these reference antennas are actual antennas. The isotropic does not exist at all, and the real dipole will not be high enough to be considered to be a dipole in free space.

As I mentioned in my previous posts, there is no inexpensive way to demonstrate compliance. In my opinion, the only practical way to use 15.225 is to use low enough power so that a violation is unlikely. It's possible to pay someone with the proper equipment to come out to your site to make the measurements, but that will cost lots of bucks, also.

 

[Ermi Roos]

I also have an oscilloscope current probe that can measure small RF currents. It is mostly useful for RF circuit design work. I would not rely on it for accurate measurements because it gives different indications depending on how it is clipped onto the wire carrying the current to be measured.

 

[rfry]

tfcwings was inquiring about determining field strength under section 15.225, and so the information about AM broadcast antenna systems is not applicable.

That is true, however my comments did not address his original post, but a post that responded to it.

Not all antenna consultants agree with NEC results. Some prefer wipl-d, which is more accurate. NEC (pronounced, "neck") and wipl-d results agree fairly well for wire antennas at close range, but NEC does not work as well with conductive surfaces. NEC also does not compute the Sommerfeld formula for ground attenuation accurately, and so field strength as a function of distance is not computed very well. The major reason not all antenna consultants use wipl-d is its huge price compared to NEC.

First below is an unedited analysis of the groundwave inverse distance field at 1 km for 1 kW applied to a self-resonant, ~1/4-wave vertical monopole driven against the 2-ohm r-f ground connection that is typical when using 120 each, 1/4-wavelength, buried radials. This analysis was made using a "Demo" (FREE) version of NEC-2.

Frequency = 1 MHz
Power = 1000 watts
Max field = 0.305957 V/m RMS
at X,Y,Z = 1000, 0, 0 m

Electric (E) Field (V/m RMS)

X (m) Y (m) Z (m) Ex Mag Ey Mag Ez Mag Etot
1000 0 0 0 0 0.305957 0.305957

Next below is the unedited output data for this same setup when using the FCC weblink I provided earlier in this thread:

The Inverse Distance Fields calculated here are in mV/m at 1 KILOMETER .

Frequency: 1000.00 kHz
Number of Radials: 120 radials
Correction for number of radials: 0.0000 mV/m @ 1 Kilometer
Average Length of Ground Radials: 75.000 meters
246.063 feet
0.250 wavelengths
90.062 degrees
Correction factor for length: 0.0000 mV/m @ 1 Kilometer
Wavelength: 299.793 meters
983.571 feet
Tower Height: 75.000 meters
246.063 feet
0.250 wavelengths
90.062 degrees

Predicted Field Strength from Figure 8, Section 73.190:

(Metric units)
Theoretical Field Corrected Field

At 1.00 kW: 305.814 305.814 mV/m @ 1 KILOMETER

Probably most would agree that the difference of less than 0.005 dB in the values computed by those two methodologies is negligible, in the real world.

WIPL-D, or even NEC-4 is not required to show this. NEC-2 does it, assuming that the model is set up correctly to comply with the requirements of NEC.

The accuracy of a field strength measurement does not depend only on the accuracy of the instrument at a standard calibration site, but also upon the environment in which the measurement is made. To claim a 3 % accuracy for a field strength measurement is highly misleading. The field strength reading with a standard calibrated field strength meter tends to be an ad hoc legal definition of field strength, but it is not the actual physical field strength.

Strongly disagree that the accuracy of the measurement depends on anything other than the traceable accuracy of the meter used to measure it.

The field intensity at every given location from the transmit site may vary from its theoretical, inverse distance value as a result of the propagation environment, but that does not negate the intrinsic accuracy of the meter, itself -- which, if properly used, will accurately measure the field in which it is immersed, regardless of the value of that field and/or why that value exists at that location.

RF

 

[rfry]

I'm not sure if that calculator is working for me.

The usefulness of that calculator applies only to vertical monopoles using buried radial r-f ground systems, and then only to the limits the calculator allows.

"Scaling" those results to a system at 13.56 MHz using no buried radials is just impossible -- sorry.

RF

 

[Ermi Roos]

The environment in which a field strength meter is used most certainly affects the accuracy of the field strength measurement. Consider, for example, Figure 23 of Brown et al. (this paper is often referred to by Fry), showing someone very near the loop antenna of a "conventional field intensity measuring set" making field strength measurements. The man making the measurements effectively became part of the pickup antenna of the "measuring set." The presence of a rather massive and conductive human body should have an effect on the measurement. L. D. Brewer's photo album, documenting the famous raid on his pirate station, shows an FCC agent holding the sense antenna of his FSM up in the air, probably trying to keep the mass of his own conductive body from interfering much with the field strength reading. Many other environmental factors would also affect the acccuracy of the field strength measurement.

 

[rfry]

...The presence of a rather massive and conductive human body should have an effect on the measurement.

The loop antennas in the field intensity meters used for medium-wave measurements are quite insensitive to the presence of the person holding the meter. In fact, the instruction manual for the FIM-41 states:

2.4 Measuring Field Strength
In use, the field meter is generally held in the hand, or mounted on a tripod or unipod. Of the latter
two, the unipod is preferred, since it can be easily rotated , and can remain attached to the instrument. A plate
having a hole tapped for a 1/4 - 20 screw is fastened to the bottom of the case, for attachment to a support.

The loopstick antenna used in my Tecsun PL-310 radio shows this same behavior, and that even for rather large conductors nearby. This morning I tuned the PL-310 to a local station and oriented the radio for a maximum reading, which was 81 "dBµ." I set the radio down outside, still reading 81 dBµ, and walked ten feet away from it. It continued to read 81 dBµ. Then I took it out in the garage, and while holding the radio in front of me in the same orientation to the station as before, the meter continued to read 81 dBµ when I was standing 4 feet from the car. This was true whether I was standing on the side of the car closest to the station, or the other side of the car.

This little experiment shows that the human body, or even an auto body has little affect on the field strength of medium-wave signals. The likely reasons are the long wavelengths at medium wave, and that the receiving antennas are non-resonant, or only broadly resonant.

Field intensity measurements at VHF and above are far more affected, because typically the measurement antenna is sharply resonant, and the wavelengths are close to or less than the physical dimensions of nearby objects (including humans).

RF

 

[Ermi Roos]

Although Prof. Valentin Trainotti is familiar with all sorts of antennas (since he was the head of an antenna laboratory for 40 years), he specializes in the design of electrically-short antennas for licensed AM broadcasting from places where antenna height and radial length must be limited. This is why his point of view can be extrapolated to the extreme problems encountered by Part 15 AM operators. In "Short Medium Frequency AM Antennas," IEEE Transactions on Broadcasting, September 2001, he points out that field strength measurements to compare short antenna performance to a quarter-wave monopole are difficult to make. This is because of obstructions in the environment where field strength measurements (for evaluating short antennas) are made. He also gives the accuracy of a field strengh meter at +/- 2 dB or more.

Let us also remember that this thread originally dealt with HF, not MF.

 

[rfry]

... Prof. Valentin Trainotti ...also gives the accuracy of a field strengh meter at +/- 2 dB or more.

The value of field intensity measured even with perfect accuracy can vary by 2 dB or more from the theoretical value of that field. However that error will not be an attribute of that field intensity meter itself, but of the accumulated errors in determining the true radiated power, and an incomplete accounting for the propagation characteristics of the measured path(s).

Whatever is the net, real, incident field at the point of measurement, most professional field intensity meters themselves are specified for much better than +/- 2 dB accuracy when measuring that field, especially at medium wave.

For example the Potomac Instruments FIM-41 is specified to be accurate within 3% (0.27 dB, max) when measuring an NIST standard field.

The accuracy of the NIST standard field used to calibrate meters such as the FIM-41 is stated to be +/- 0.25 dB, according to the link below which was clipped from an IEEE paper describing the NIST test ranges and methodologies.

So the maximum error in the field intensity measured by the FIM-41 including the uncertainty of the incident field used to calibrate it is +/- 0.52 dB.

http://i62.photobucket.com/albums/h85/rfry-100/Antenna_Cal_NIST.gif

RF

 

[Ermi Roos]

In his paper, Trainotti condidered field strength variations due to obstructions, and the accuracy of the field strength meter itself, as two different contributing causes of the difficulty in getting accurate field strength measurements. He gave the field strength meter accuracy as +/- 2 dB or more.

 

[rfry]

In his paper, Trainotti ... gave the field strength meter accuracy as +/- 2 dB or more.

Your comment is noted, but perhaps with due diligence at least in the case of the FIM-41, Prof Trainotti, his research staff, or anybody else should have found the website listing its specifications as given in the link below -- which show an accuracy for that field intensity meter as significantly better than +/- 2 dB. And I doubt that such improved accuracy is unique to the FIM-41.

Of course, it would have been preferable for Prof Trainotti or his staff to have done that research in a timely manner, so as to obviate making the rather universal statement about the accuracy of field intensity meters that you report as stated in his September 2001 IEEE paper.

http://www.pi-usa.com/fim2241/fim2241g.htm

RF

 

[Ermi Roos]

The Potomac website mentions the calibration accuracy, not the measurement accuracy. Even Terman's Radio Engineers' Handbook (1940) says that the loop antenna of an FSM mounted above the top of a car can have in the order of 2 dB error in the measurement of field strength in the AM broadcast band. The error is due to distortion of the RF field in the vicinity of the loop antenna by the body of the car.Terman refers to an article about the accuracy of portable field stength measuring equipment, starting on p.1 of the January, 1939 issue of the Proceedings of the IRE.

I would be cautious about presuming to be qualified to suggest that someone of Trainotti's stature needs to do due dilligence. He has certainly had enough experience with field strength measurements during his long career in antennas to know what he is talking about.

 

[Tom Wells]

Anything F E Terman said, I believe as fact.

 

[rfry]

Even Terman's Radio Engineers' Handbook (1940) says that the loop antenna of an FSM mounted above the top of a car can have in the order of 2 dB error in the measurement of field strength in the AM broadcast band.

However such 2 dB accuracy as described by Terman is not the specification of the FI meter itself, but includes the environment in which it was used (which environment was/is atypical).

Such errors could not be tolerated in the measurement of the nulls in the radiation patterns of directional AM broadcast arrays, which are made using a hand-held meter.

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