EIRP and Field Strength

[thranduil]

Hi all guys,

I have a few doubts concerning EIRP I would like to clarify.
If i measure let say -10 dBm at the distance of 3m from the antenna. I can easily calculate field strength in dBuV/m. But if i would like to have EIRP, I think in this way: I can calculate what input power into isotropic antenna is required to produce -10 dBm at the distance of 3m and that would be EIRP. Is this correct way of thinking?

thanks

 

[jiripolivka]

Hi all guys,

I have a few doubts concerning EIRP I would like to clarify.
If i measure let say -10 dBm at the distance of 3m from the antenna. I can easily calculate field strength in dBuV/m. But if i would like to have EIRP, I think in this way: I can calculate what input power into isotropic antenna is required to produce -10 dBm at the distance of 3m and that would be EIRP. Is this correct way of thinking?

thanks

You are right. EIRP is defined as RF power input to the transmitting antenna times its gain in the desired direction (to the point you measure the power).
If you measure the power at 3m from the antenna, take also the operating wavelength. With an isotropic antenna the field may be in its "far zone", with a directional antenna it may not be the case.

 

[thranduil]

Well thanks, but I am not able to solve out something. For certain devices within 434 Mhz ISM band, maximum allowed firld strength is 72.8 dBuV/m. If i received 66.8 dBuv/m, i can calculate which power is required to drive into isotropic radiator in order to produce the same field at the distance of 3m. Using calculator from this link: https://www.daycounter.com/Calculators/Maximum-Field-Strength-Calculator.phtml I calculated i would be arround 0.0015 mW, which is a too low in my opinion. EU regulations for the same devices state 1 dBm or 10 dBm, I am not sure, but it is at least much higher then the value I got from calculator. Is there anything I am missing?

Thanks

 

[FvM]

Which regulations are you referring to? ETSI e.g. is based on EIRP values.

I also don't understand your comment. 10 dBm corresponds to 10 mW, not "much higher" than 1.5 mW.

The biggest problem in EIRP measurements is the antenna calibration. ETSI suggests a substitution antenna method to calibrate the antenna with a signal generator.

 

[thranduil]

The thing is that I encountered problem trying to understand E.U. regulation while looking at the homologisation results from the U.S. If u take a look at the calculator I provided in previous post, in order to reach 72.8 dBuV/m @ 3m u need to give isotropic antenna like 0.005 mW (miliWatts!) which is quite small in comparison to the power that is actually used. Since E.U. regulation specify 10 dBm erp for that kind of devices I also expected to get similar erp when converting from the u.s. results.
Then I used following converter **broken link removed** and then I got some similar numbers.
I think I understand now, but only in the case that the first converter is not working properly.

Thanx

 

[FvM]

I see equal results of both calculators (105 dBuV/m @ 3 m with 10 dBm EIRP). Where did you get the 72.8 dBuV/m value? 72.8 dBuV might be the antenna output voltage with a respective antenna factor.

 

[thranduil]

Well I am now even more confused. So, I have the following:
Table with the results of FCC homologisation


Here Pr refers to the measured power (at the distance of 3m).
In my opinion if i add loss@434 MHz to the measured value I should get e.r.p. of the antenna. Is that correct?

- - - Updated - - -

In fact I wanted to calculate erp and eirp of the device which signal has strength of -24 dBm at the distance of 3m.

- - - Updated - - -

in fact in fact, I wanted to see if the device tested under fcc regulations can satisfy E.U. regulations from 2013/752/EU. Because of that I took measured strength and added loss in order to get erp.

 

[FvM]

The numbers make sense, the table is apparently referring to FCC 15.231e.

The problem is that FCC doesn't provide a useable 433 MHz band for moderate transmission ranges. That's why sub-1GHz SRD in the FCC domain are mostly using the 900 MHz band.

 

[thranduil]

I think my problem is to realize the different way of performing measurements in the US and EU.
For example, in EU it is stated erp 10 dbm. This means that I should substract rec antenna gain and to add free space loss to the measured value and I have erp.
But is it possible that allowed power in 434 MHz band in EU is for 35 dB higher than in the US. If yes everything is clear.

 

[FvM]

But is it possible that allowed power in 434 MHz band in EU is for 35 dB higher than in the US. If yes everything is clear.

Yes, for the 433 MHz band and applications described in FCC 47 Section15.231e. There's an 8 dB extra for manually operated transmitter like garage door openers. I really suggest to review the document

There are of course some implications of the EIRP versus field strength limit definition. But I think that's not the primary problem so far.

 

[thranduil]

I see.
And thanx a lot for helping me FvM.
After more some more digging i came to the following.
First:
There are two equations for calculating field strength:
1) E = Pr - Gain +77.2 dB +20log(f[MHz])
2) E = 107 - Pr (this one comes from the fact that P=V^2/Z after loging)

So I would be like mega happy if somebody can explain me the relation between these two.

Second:
In the example table i provided above the first row:

Pr = -23.2
Gain = 18.6

Using first formula from above I calculate EIRP as almost 11 dBm. Which quite near to the EU regulation.

Best

 

[FvM]

You have been previously asking about the relation between EIRP and field strength.

The relation between isotropic radiated power and field strength in xx m distance (assuming far field conditions) doesn't depend on frequency, only distance and free space impedance as a constant. It's correctly derived in your previously posted link https://www.daycounter.com/Calculators/Maximum-Field-Strength-Calculator.phtml

For relation between received power and field strength respectively EIRP, antenna gain and frequency comes into play. I must confess that I neither understand the measurement conditions in the posted table nor your above calculation. In both cases, the meaning of some parameters isn't clear.

To calculate radiated from received power, you can simply apply the free space loss equation or friis formula https://en.wikipedia.org/wiki/Free-space_path_loss

Pr/Pt = 20 log(f [Mhz]) + 20 log(d [m]) - 27.55

Applying it to Pr = -23.2 - 18.6 results in an EIRP of -7 dBm, far below ETSI limits. The EIRP corresponding to the field strength in the table is however -28 dBm. The latter seems right according to FCC 433 MHz regulations.

 

[thranduil]

Hello again and thanx,

I see, I have found an article where the puzzle can be solved more or less.
It comes from two equations for power density:
Pd = E^2/377 and Pd = EIRP/4pir^2
The first equation in my previous post is actually for calculating field strength for given measured power level, frequency and I think it is derived from the fact that Pl = Pd*Ae, i.e. power on th eload equals power density times aperture.

well, is -7 dBm from previous example good rough value for predicting the results of EU tests on given device already tested under FCC regulation?

Best

 

[FvM]

well, is -7 dBm from previous example good rough value for predicting the results of EU tests on given device already tested under FCC regulation?

Yes, for 3 m distance, received power of -23 dBm and 18 dB antenna gain. But it doesn't fit the field strength values in the table.

 

[thranduil]

The point is those guys from US use some correction factors depending on the length of transmission in i think 100 ms or 1s interval.
I spoke today with a guy that works in a company for performing those tests in Germany. He told me that the results obtained under FCC rules are not comparable with the results under EU regulations, due to among others, height of the antenna. But i believe that -7 dBm in previous example would be roughly the result of measuring erp under EU regulation.