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I am working with a system which has EIRP of 501 watts. The ERP for it is 300-310 watts. I am using a parabolic directional antenna. What precautions do I need to take?

Though the Wifi amplifier in it is just 20W 43dBm and antenna is 24dBi which effectively gives me 67dBi EIRP which corresponds to 501 watts. How far should I stand away from the antenna to prevent any health effects? And how does the power decrease with distance? Now I am not using an omnidirectional antenna. So in case of parabolic antenna, how does EIRP or ERP work?

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    \$\begingroup\$ 67 dBm is 5kW, not 500W. \$\endgroup\$ – mkeith Jan 1 '17 at 8:40
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    \$\begingroup\$ Suspend an egg in the beam, start the stopwatch and find out. \$\endgroup\$ – Brian Drummond Jan 1 '17 at 10:52
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    \$\begingroup\$ You are basically building a death ray and the fact that you are asking really basic questions about something so serious means you are already out of your depth. You are going to seriously harm someone with what you are doing and with what little knowledge you appear to possess. There is no suitable answer that should be given here other than "employ a consultant who knows what they are doing and who can inspect everything you build". \$\endgroup\$ – Andy aka Jan 1 '17 at 11:18
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    \$\begingroup\$ @Andy: they could get free lighting from the sidelobes alone using some freestanding flourescent tubes; - my point (I agree with you) is there would probably be no safe location around this thing for quite some distance. \$\endgroup\$ – Peter Smith Jan 1 '17 at 16:42
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    \$\begingroup\$ The fact that you're asking "how far should i stand" about a 5 kW system indicates that you shouldn't be using this system. \$\endgroup\$ – uint128_t Jan 1 '17 at 19:16
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About EIRP vs ERP

We still could use EIRP1 or ERP for parabolic antennas.
EIRP uses isotropic radiators for comparison, ERP uses dipoles, I will use EIRP for this post.
You can convert from ERP to EIRP by adding \$2.15\ dB\$ to it.
EIRP can be expressed in \$W\$ or \$dBm\$, \$dBW\$, etc.
It basically describes if we had an ideal isotropic radiator, what amount of power does it need to radiate with if we want to reach the same power density as the parabolic antenna radiates in its focused beam.

The attenuation of the signal and the amount of power that we can measure in one unit of area will be the same, so if we stand \$5\ m\$ away from the isotropic radiator, and we measure a certain power density, we should already know what power density the parabolic antenna will have at the same distance.
That's how our calculations work; we will use the area of a theoretical sphere: \$4\pi R^2\$.
EIRP shows really well how powerful an RF system can be.

If you have an \$ERP = 300\ W\$ antenna which translates to \$ERP = 54.77\ dBm\$,
you can add \$2.15\ dB\$2, so it will become \$EIRP = 56.92\ dBm\$, or you can say that its \$EIRP = 57\ dBm\$ which translates to \$EIRP = 500\ W\$.

If you have a \$20\ W\$ or \$43\ dBm\$ input power to the antenna, and you add \$24\ dBi\$ to it
it will be \$67\ dBm\$ which is relatively high in the case of a \$2.4\ GHz\$ transmission, and its not \$500\ W\$ as your title suggests, but \$5\ kW\$.

If this system is really \$5\ kW\$, or even \$500\ W\$, proceed with extreme caution (and consult with other people), even after reading the description below how to calculate power levels and what should you take into consideration, before deciding to build the said system.


Legal limits

Before we even proceed to talk about safety, consider if this powerful system is even legal in your country, or if its not, proceed at your own risk.
The limit is probably much less than what you are trying to achieve, and it can raise a red flag pretty fast with the local regulator if you are using something that powerful, even if you are trying to transmit in the ISM band.
If you already have a license to transmit at this power level at \$2.4\ GHz\$, then go ahead, ignore this warning.

I take no responsibility or liability for anything written in this post.
It is your responsibility to do your research; check the calculations from the sources below, read up on other sources, listen to the people here, hire or ask an expert, etc.


Safety limits

Before we talk about how to calculate power levels in certain distances from the antenna, we should first see what is defined as safe in the case of the people who maintains the system, and the general public.

I used regulations that are accepted in the respective countries, but if you live in another one, be sure to look up the local safety regulations regarding RF devices.

Generally, in most legislation, there are two separate cases of RF radiation limit:

  • Limits for Occupational/Controlled Exposure
  • Limits for General Population/Uncontrolled Exposure

These can be called differently in some cases, but they mean the same thing.

Below you can see the RF radiation limits for the USA, Canada and the European Union at \$2.4 GHz\$.
Where units were not in the same scale or were expressed in different way, I made the necessary changes to them.

Occupational Limit on 2.4 GHz devices General Population limit on 2.4 GHz devices

*Calculated based on other units in the same row.
In the case of Power Density, I used the strictest value based on the two other.
See References 3-6 for the source tables.

In these tables you can see the maximum values that is safe for the specified duration.

Averaging Time

\$\sum S_{exp}\ t_{exp} = S_{limit}\ t_{avg}\$

If the MPE limit (Maximum Permissible Exposure) is \$1\ \tfrac{mW}{cm^2}\$, then the right hand side of the equation will become \$6\ \tfrac{mW\cdot min}{cm^2}\$.

If the exposure level is \$2\ \tfrac{mW}{cm^2}\$, the allowed time in a six-minute interval will be \$3\ min\$.
Same happens when the exposure level is \$3\ \tfrac{mW}{cm^2}\$, then the max allowed time in a six-minute interval will be \$2\ min\$.

Using the same for the actual values, the right hand side of the equation for the respective areas will be in the case of occupational limits:

  • USA - \$30\ \tfrac{mW\cdot min}{cm^2}\$,
  • Canada - \$18\ \tfrac{mW\cdot min}{cm^2}\$,
  • EU - \$31\ \tfrac{mW\cdot min}{cm^2}\$.

If it is the general population limit:

  • USA - \$30\ \tfrac{mW\cdot min}{cm^2}\$,
  • Canada - \$3\ \tfrac{mW\cdot min}{cm^2}\$,
  • EU - \$6\ \tfrac{mW\cdot min}{cm^2}\$.

I rounded down if the value was a fraction originally.


Calculations

If you want to know the power densities occurring near the parabolic antenna, we need to do some calculations.
First, we need to see what kind of power densities will occur in the direction of the beam, to understand what will happen near the device.
Because you didn't post any information about the dimensions of the dish, I am going to pick one with the same gain for the sake of explanation.

I picked the Ubiquity RD-2G24 which has \$24\ dBi\$ gain and \$650\ mm\$ diameter and \$295\ mm\$ depth.

Regions of the antenna

Aperture antenna fields

In the picture above you can see the regions or zones.
I will talk about all of them, including the surface of the parabolic antenna.

Power density on the surface

The power density of the surface can be calculated with the following equation:

\$S_{surface} = \cfrac{4P}{A}\$

\$A\$ is the surface area of the paraboloid3, and \$P\$ is the power fed to the antenna.

The exact value for this antenna will be:

\$S_{surface} = \cfrac{4\cdot 20\ W}{0.53\ m^2} \approx 151\ \cfrac{W}{m^2}\$

To get the value in \$\cfrac{mW}{cm^2}\$ you move the decimal point forward by one.

This way, you will get \$15.1\ \cfrac{mW}{cm^2}\$.

You can touch the surface of the antenna for 2 minutes in the case of US occupational regulation, in a 6 minute period.
In the Canadian regulation, that's about 70 seconds.
Although its not really recommended, because of the currents.

Power density in the reactive near-field

The power density varies highly in the reactive near-field, it cannot be defined for sure what are the power densities here, but we can find out what's the distance of the outer bounds of this zone from the surface.

\$R_{reactive} = \cfrac{\lambda}{2\pi} \approx 2\ cm\$, where \$\lambda = \cfrac{3\cdot 10^8\ \tfrac{m}{s}}{2.4\cdot 10^9\ Hz}\$.

Power density in the radiative near-field

The distance of the outer bounds of this field from the surface is:
\$R_{nf} = \cfrac{D^2}{4\lambda} = 84.5\ cm\$.

The maximum power density that can occur in the near-field:

\$S_{nf} = \cfrac{16\eta P}{\pi D}\$, where \$\eta\$ is the aperture efficiency, to calculate this, look at Reference 8.

\$S_{nf} = \cfrac{16\eta P}{\pi D} = \cfrac{16\cdot 0.6118 \cdot 20\ W}{\pi \cdot 650\ mm} \approx 96\ \cfrac{W}{m^2}\$.

Power density in the transition zone

The beginning of the far-field can be calculated in this way:

\$R_{ff} = \cfrac{0.6D^2}{\lambda} = 2.028\ m\$.

In this zone, you can pick any distance between the near-field and far-field distance.
I chose the reference distance halfway between the end of the near-field and the beginning of the far-field, so it can be calculated in this way:

\$R_{target} = \cfrac{R_{nf}+R_{ff}}{2} \approx 144\ cm\$.

To calculate the power density in this distance from the surface can be seen below.

\$S_t = \cfrac{S_{nf}\cdot R_{nf}}{R_{target}} = 56.47\ \cfrac{W}{m^2}\$

Power density in the far-field zone

This is the zone where the directivity of the antenna will come into play.
I chose \$5\ m\$ as distance from the antenna, let's see what kind of power density will it have.

\$S_{ff} = \cfrac{PG}{4\pi R^2} = \cfrac{EIRP}{4\pi R^2} = \cfrac{10^\tfrac{43\ dBm+24\ dBi}{10}\ mW}{4\pi R^2} = \cfrac{5\ kW}{4\pi\cdot (5\ m)^2} \approx 16\ \cfrac{W}{m^2}\$.

How much time can we be in the beam at exactly 5 meters from the antenna? We can calculate the time this way:

\$\cfrac{30\ \tfrac{mW\cdot min}{cm^2}}{1.6\ \tfrac{mW}{cm^2}}\cdot 60 = 1125\ s\$.

That is more than 18 minutes, so it is safe to stand there as it is already surpassed the 6 minute safety margin.

What about if we stand near the antenna, but not in the beam?
For regular checkups on the system that doesn't concern the surface area of the dish, but still near the device should be alright, no?
That's why we will look at the off-axis radiation.

Off-axis radiation

As you can find in Reference 9, it says:

For off-axis calculations in the near-field and in the transition region it can be assumed that, if the point of interest is at least one antenna diameter removed from the center of the main beam, the power density at that point would be at least a factor of 100 (20 dB) less than the value calculated for the equivalent distance in the main beam (see Reference [15]).

Picture example:

Off-axis radiation

If you are at least one diameter away from the center of the main beam, you will get \$20 dB\$ less power density than in the main beam at equal distance.

For example, I calculated \$56.47\ \cfrac{W}{m^2}\$ at \$144\ cm\$.
If we are outside of the center of the main beam with one diameter distance from it, the measured power density would be \$0.056\ \cfrac{mW}{cm^2}\$ maximum.

It is safe to stand here.

Note that it is an approximation, on Page 9 of the Ubiquity RD-2G24 documentation you can find that it has side-lobes (local-maxima) which has even lower \$dBi\$ value than it suggests in Reference 9, but it doesn't make much difference.

The F/B ratio for this antenna is \$28\ dB\$ which means that if the main beam is considered \$0\ dB\$, the back-lobe is \$-28\ dB\$.

Using the same distance above, we get \$0.009\ \cfrac{mW}{cm^2}\$.

Conclusion

It turns out, it is not that dangerous to use this system from a safe distance.
Even if you stand in the beam at \$160\ cm\$ you are around the maximum allowed radiation level, more than that, or off-axis, you are fine.

Calculating with the strictest general population limit (Canada), your distance in the beam should be minimum \$3.7\ m\$.

The dish dimensions is probably different from yours, so recalculate everything based on those data if needed.

Anything could be wrong in this write-up, as I read the health aspects from the documentations, so please, check with experts before you even connect the router and the dish together.


References

1 - EIRP - antenna-theory.com
2 - Guidelines for determining the Effective Radiated Power (ERP) and Equivalent Isotropically Radiated Power (EIRP) of an RF transmitting system - Page 2, Section 1.3, FCC
3 - US - CFR 1.1310, Radiofrequency radiation exposure limits, Table 1
4 - Canada - RSS-102, Radio Frequency (RF) Exposure Compliance of Radiocommunication Apparatus (All Frequency Bands), Table 4-6
5 - EU General Population Limit - 1999/519/EC, Table 2
6 - EU Occupational Limit - 2013/35/EU, Table B1
7 - EU Limits Summary
8 - Evaluating Compliance with FCC Guidelines for Human Exposure to Radiofrequency Electromagnetic Fields, Page 28, Equation 14
9 - Evaluating Compliance with FCC Guidelines for Human Exposure to Radiofrequency Electromagnetic Fields, Page 30, Paragraph 2

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  • \$\begingroup\$ I have one basic doubt.The amplifier I plan to use is a 20W 2.4ghz wifi amp(43dbm) whose output is connected to the antenna of 24 dbi. Now the antenna does not take any input power supply but just the signal.So the antenna magically will not convert the 20w signal to a 5kw signal because the law of conservation of energy should hold.I think when they say the antenna is 24 dbi only if it is given enough power supply will it magnify the signal to 5kw. So I think the 20w signal will remain as the 20w signal and the system would be safe to use.Please confirm. \$\endgroup\$ – Sriranjan Rasakatla Jan 3 '17 at 2:13
  • \$\begingroup\$ @SriranjanRasakatla The dBi value describes the "focusing power" of the antenna, this is the antenna gain. Any kind of signal will gets focused the same, so if you give 23 dBm to it (200 mW), it will be 23+24, so the EIRP will be 47 dBm (50 W). EIRP just describes if we have an ideal isotropic antenna, which doesn't exist IRL, what amount of power does it need to transmit to reach the same power density as the aperture antenna that we use. \$\endgroup\$ – domenix Jan 3 '17 at 2:47
  • \$\begingroup\$ @SriranjanRasakatla Although don't be mistaken; this 5kW is no joke, if it would be an isotropic antenna. As my post showed, you should still make some precautions if you decide to test out the device (don't stand in the beam for any amount of time just to make sure). And make sure other people never could be in the vicinity of the device! A 20 W Wi-Fi router sounds unusually powerful by the way, considering that these devices rarely exceed 20-30 dBm (0,1-1W). \$\endgroup\$ – domenix Jan 3 '17 at 2:59
  • \$\begingroup\$ .So the antenna magically will not convert the 20w signal to a 5kw signal because the law of conservation of energy should hold. \$\endgroup\$ – Sriranjan Rasakatla Jan 3 '17 at 8:43
  • \$\begingroup\$ The antenna does not have any seperate powersupply. It takes as input the 20watt signal from the wifi amp. So what i feel is that the signal should remain at 20w or less. Please confirm. \$\endgroup\$ – Sriranjan Rasakatla Jan 3 '17 at 10:10
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That is more than enough power to do some serious damage! Be very careful to stay well away from that beam.

The effects of microwave energy can be more subtle than you might expect. For example, even if you can't feel any heat on your skin, there's still plenty of energy to denature the proteins in the corneas of your eyes. You won't notice anything right away, but you'll slowly go blind as they cloud up over the next several months. I knew a guy to whom this happened — I lost touch with him, but I hope he eventually got transplants to restore his vision.

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  • \$\begingroup\$ Indeed - even the sidelobes would have sufficient energy to do significant damage at those power levels. \$\endgroup\$ – Peter Smith Jan 1 '17 at 15:28
  • \$\begingroup\$ I will not use the RF system and the amplifier which is capable to delivering 5KW.I will consult someone who is a professional and proceed with extreme caution. I also have a CPE210 TP Link outdoor access point.It has EIRP of 4watts. 27 dbm power with 9dbi antenna.So what precautions I should take with this CPE210. I \$\endgroup\$ – Sriranjan Rasakatla Jan 2 '17 at 15:34

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