I thought I'd look at a couple of examples and go through how its calculated. The ARRL has a sample worksheet to fill out that can be seen and downloaded here (pdf). They also have a book they give away to help with this (also pdf format) – with details in chapter 5. A word of warning: that book is copyright 1998 and based on the original FCC documents. All of the distance limits are higher than the referenced “FCC Guidelines” from the previous post and now in effect.

Filling in every blank on the form seems a bit like overkill, but I’m sure there are questions in there that the majority of people just haven't dealt with so I thought I’d try to help with those.

I’m going to go through an example based on a modest station to show how you’d calculate the things they ask for. For this demonstration, I’m going to assume a 100 W transceiver and a kind of typical low power/portable stations, with a wire antenna in a nearby tree. Let's assume they're using 30 feet of RG-58 coax to get to the feed point.

A quick look at Table 1 in the previous piece shows that nothing I can radiate matters until I get to 12m (24.9 MHz) because no matter how much power I put out, I lose some on the way to the antenna and every band from 15m (21 MHz) down has an exemption from analysis for powers less than or equal to 100 W. That power limit for the 12m band is 75 Watts.

That 75 W is power

*into the antenna*and although the radio puts out 100 W, there are losses in the cable, and switches or anything else in the path to the antenna. Let’s start with loss in my coax. There are lots of brands of RG-58 coax, so I'll choose Belden 8259 or RG-58C/U. The table on Belden’s website doesn’t say what the loss is at 24 MHz, but it gives these points:

10 MHz 1.5 dB/100 ft

50 MHz 3.7 dB/100 ft.

For another type ("RG-" number) or brand of coax, you should try to look up the corresponding numbers for what you have.

I’ll do a linear interpolation (assume attenuation vs frequency is a straight line). That’s

(3.7-1.5) divided by (50-10) or 0.055 dB/100ft per MHz.

There’s 15 MHz from 10 to 25 (the top of 12m is 24.980 MHz – close enough), so we calculate the attenuation by:

1.5 + 15*.055 = 2.33dB /100ft. A 30 foot run of this coax then has 0.3 * 2.33 or 0.698 dB of loss at 25 MHz. I can use the same linear interpolation to show it has 2.58 dB/ 100 ft at 29.7 MHz (top of the 10m band).

The problem with using the loss in dB is that the power is stated in Watts, so we need to convert that loss to a percentage of 100 W. I’m guessing that’s probably a new thing to people. Remember a dB is a power ratio, where

10*log (ratio)

is the value in dB and log denotes the base 10 logarithm. We want to find the ratio that gives a loss: loss means negative dB. It’s -0.698 dB not +0.698.

(-.698) = 10 log (ratio), so

(-.698/10) = log (ratio)

10^(-.698/10) = ratio = 0.852 or 85.2%

That’s saying the power at the antenna is 85.2% of the transmitted power. The worksheet asks for the percentage of power lost, so 100%-85.2% = 14.8% lost, but they only do that to get the first number we solved for, the percentage of power that gets to the antenna.

There’s a trick you can do to be finished right here. Remember that Table 1 says my power at the antenna has to be below 75 watts. I could just crank down my power until the power at the antenna is 75W. That’s picking a power output from the radio that combined with the cable loss puts the power at the antenna at 75 W.

75W/.852 = 88 Watts

Which says if my output is 88 Watts, I’m always at or below that 75W limit, but I’m not going to go there, I’m going to the next step at Table 4a in the FCC report and the second table in that blog post.

Looking at the table for 24 MHz, I can see that assuming I put 100W into the antenna, I have four options for my antenna that lead to four different distances to choose from. The first column after the band (24.99 MHz, (12m)) shows the antenna gain in dBi.

I chose an antenna that isn’t particularly good; it’s something like a random length wire, a multiband wire, G5RV or something low gain like that. Is it 0 or 3 dBi? Let’s be generous and give it 3 dBi (everything has gain compared to a theoretical isotropic antenna, just not much). You’ll see two numbers: 1.7 or 3.8. That’s the distance to keep people away from the antenna, in meters. The difference is the smaller distance, 1.7m is for people who are aware of the risk of being near or touching the antenna – like you and your family – while the other (uncontrolled) column is for the neighbors. The number is 12-1/2 feet. The smaller is 5 feet 7 inches.

That distance can be reduced because heating is different depending on the transmitter duty cycle. The league says you can use 40% for CW, 20% for SSB with no speech processing, 40% for SSB with heavy speech processing, 50% for FM (full carrier, talk half the time, listen half the time), 50% for most digital modes – (also based on transmit 50%/receive 50%). The bottom of Table 4a says to multiply those distances by .707 if the duty cycle is 50%, so since the others are less than 50%, we can use that as an upper limit. Those become 1.2 m and 2.7 m, or 3.9 and 8.9 feet.

As the infomercial guys say, “but wait! There’s more!” Since those numbers are based on 100W and we know we’re only putting 85 Watts into the antenna, we know the minimum safe distances are even less than that.

Although values can be hard to find, anything you put around the antenna is going to attenuate the signals somewhat. The antenna distance recommendations in that FCC document are based on mounting antennas in the open. As a rough example, HF signals will go through most walls pretty well as long as their isn't a wire grid in them. Shortwave pocket radios with small antennas work acceptably in most houses and lots of people use attic-mounted antennas to avoid property restrictions.

So what happens if you do a station evaluation and conclude one of those limits is exceeded? In this case, what if that 8.9 feet just falls beyond your property line and there’s nothing you can do to guarantee that the neighbor’s kids can’t get into that your RF field. At the bottom of the League’s worksheet for evaluating your station is this section:

**Using this method, did your station exceed the FCC RF exposure limits? (Y/N)**

Controlled exposure: ___________(Y/N) Uncontrolled exposure: ____________ (Y/N)

If the station is not in compliance under all circumstances of its expected operation, attach a separate sheet describing any limitations of methods that the station operator will use to ensure compliance if people are present in areas that could be out of compliance.

In this case, you could state you limit power to keep your power below 75W at all times, in compliance with table 1, or you could say you'll only operate your station at times when the neighbor's kids are not potentially too close to your antenna, such as during the evenings or when nobody can be seen outside - if you can see outside from your operating position or with a camera.

**EDIT 052820 2235 EDT:**Left out a link for Table 4a. Added just above the small portion clipped out of that table. Roughly just above the middle of the post.

Interesting subject. Would a antenna analyzer help in these calculations? And in that do you use a analyzer to build or check your antennas? Would one be a help to someone who wants to begin building their own antennas? Thanks I read your blog everyday and find it worthwhile . Tex.

ReplyDeleteAn antenna analyzer wouldn't be the tool for this. What you need to know is the power getting to the antenna, which you could measure with a power meter, and the antenna gain. Antenna gain is very difficult to measure accurately "in the real world", so you usually use a published or modeled value.

DeleteFor (hand waving) UHF up through microwaves, they're measured in anechoic test chambers. For an HF antenna, I don't think you can get gain measurements that are as accurate as they get in one of those chambers. Antennas interact wildly with their environment. It's their job.

What antenna analyzers are great for is building and checking out your antennas, like you say. I just did a hack to my antennas to get them to work with my radio's built-in antenna tuner, and it all centered on measuring the antenna's impedance with antenna analyzer. Building your own antennas is much harder without a good antenna analyzer, also called a Vector Analyzer, or a Vector Network Analyzer.

I'll be doing a post about this relatively soon.