Convert dBu <--> dBm Formula?

[JohnMcNutt]

This should be a rookie question but is there are there two simple formulae that can be used to convert these numbers between each other when the gain of the antenna and feedline loss are known? We use dBm when taking actual measurements with our equipment or predicting whether receivers will have adequate performance but the FCC uses dBu to calculate interference contours.

Thanks

 

[VEBill]

The FCC's dBu is a measure of field strength, dB above 1 microvolt per meter.

While dBm is a measure of power, dB above 1 milliwatt.

The conversion between the two involves the "Antenna Factor" of the antenna. Antenna Factor is not quite the same thing as Gain; it's more like a transducer's transfer function.

If you had a calibrated antenna (as often used for EMC testing), then it would come with a chart or table that shows the Antenna Factor over frequency.

Of course, you'd need to make sure that you are measuring in the same units as the output of the Antenna Factor chart, make sure the instrument is calibrated and (presumably) 50-ohms input Z, and take into account other details such as the cable loss.

Edit: Antenna Factor antenna output would likely be given in volts, so another minor step to calculate the resultant power in dBm.

 

[JohnMcNutt]

I have not heard of Antenna Factor before. It sounds like a sort of measurement of antenna efficiency vs an ideal antenna.

The frequency band in question is VHF in the 150 range.

The FCC must have a standard antenna factor that they use because they issue licenses in watts ERP and they have their service contours in dBu.

 

[VEBill]

As mentioned, the best concept of Antenna Factor is that of a transducer transfer function, very similar conceptually to a calibrated microphone for measuring acoustic amplitude based on a voltage output.

Wikipedia has a reasonable introduction to Antenna Factor, and of course you can dig further if you like.

Antenna Factor is (more or less) a concept confined to calibrated 'EMC' antennas used to measure field strengths. In fact, that's typically how one would measure field strengths. Some all-in-one field strength measuring instruments may have it all built in, including the calibrated antenna.

Antenna Factor is not a concept usually applied to transmitter stations. For those, it's all about output power, cable losses and antenna gain pattern.

Antenna Factor doesn't enter into the relationship between a transmitter's EIRP and the resultant Field Strength in dBu - simply because those two parameters exist even before you get the calibrated measuring antenna out of its carrying case, before you even arrived on site.

The other distinction to clarify the concepts is that the EIRP exists at the transmitter antenna, while the field strength of interest is at some distant location, X miles from the transmitter. Those two parameters are related by the pathloss equation.

Antenna Factor is for the measuring antenna used at the point of interest, at that location.

Sometimes there are so many variables in the field measurements (reflections, multipath, operator experience) that one might reasonably wonder if the predicted field strength might be closer to the truth than the messy, possibly unreliable, field measurement. If you get an unexpected value, it might just be a measurement problem.

 

[VEBill]

I wonder if you should focus on the famous pathloss equation?

If you Google 32.45 dB it'll pop up.

This formula can help to string together gains and losses to predict dBm at the receiver's antenna socket.

 

[VEBill]

I went looking for the relationship between an antenna's gain and its antenna factor. It's not something I'd ever touched on so far.

There are on-line calculators, and there is a good explanation here:

http://www.micronix-jp.com/english/note/file/antenna_factor.pdf

Perhaps you can assemble all this into a spreadsheet, or it may lead to other references.

PS: Beware of trusting antenna gain specs; they're typically famously inaccurate.

 

[JohnMcNutt]

I may have discovered through your help, that converting these units is a futile exercise. If I am understanding the FCC regs correctly, dBu contours are calculated by their own set of rules and not by any real life calcuation taking the actual factors into account.

So I am now wondering if there is a simple way I can draw FCC dBu contours for myself, to see if certain locations and frequencies are feasible.

As for antennas, we use almost exclusively 1-, 2-, or 4-bay folded dipoles in the VHF 150 band. I would hazard a guess that the antenna factor is pretty much the same for each aperture across various manufacturers, as performance seems to be. I would still like to have some way to convert between the two, even if it is a little imprecise.

 

[VEBill]

The pdf linked above gives you most of the conversion. Then it's trivial to convert volts to dBm based on Z-in. So 15 minutes with the pdf formula and a spreadsheet and you'll have exactly what you wish for.

Dig into the pathloss equation, the '32.45 dB' mentioned. Predicting if a radio link will work or not is what it's for. Simple to add and subtract dB. Don't forget to include a signal margin, often about 10 dB.

If you have to take terrain into account, then there are websites that can assist by showing you the elevation profile. Some can even perform the entire path and system modeling. Many such websites are focused on helping the public with the transition to digital TV, but some are more generalized.

 

[JohnMcNutt]

If I had paid attention to my propagation software I might never have asked this question but in hindsight I am glad I did because you gave me some conceptual ideas that I did not even know existed before.

I use Radio Mobile which seems to be designed for the hobbyist but actually is quite powerful and accurate in its predictions, in my experience. Right there among the other signal strength options (dBm, μV, S-units) is dBu so I ran some experiments with it. According to the software, anyway, there is a simple fixed relationship between dBu and dBm. In this case it is around 120 for a 0 dBd antenna with 2 dB of line loss so 37 dBu is -83 dBm.

Good enough for my application and now I can attach some meaning to the FCC numbers!

Thanks again.