# Measuring RF power of a communication signal

I am running a software radio application. I need to measure the power of transmitted ofdm signal. The issue is that FCC has regulations of -50dBm/Hz. So I understand that if i need to send a signal at a bandwidth of 1Mhz, the the maximum allowed power -50dBm*10^6 which is 0.01W or 1mw.So i am trying to measure the power at output of my USRP transmitter. I just brought an oscilloscope and measured the sinusoidal signal peak to peak voltage in the oscilloscope. It was 7.2 v peak to peak. I was unsure how to use v^2/R because i don't know the resistance. when i assumed resistance to be 1, I got the power output to be 39dBm. I then checked online and found that you need to measure power spectrum. So that means I need to know power at frequency of transmission. I need a RF power analyser for the same.

How is the power at frequency spectrum related to analog power measured by oscilloscope at the output of antenna?

What should i measure and reduce if i need to keep it within desired FCC regulations? Is the power of the frequency spectrum constant?

• You could estimate the total mean power but you would have to divide the peak-to-peak voltage by the crest factor to get RMS voltage first. This Wikipedia page discusses crest factor calculations for OFDM signals. Jun 28, 2013 at 13:02
• .01W is 10 mW, not 1mW. Jun 28, 2013 at 15:42
• Also, dBM is not a common unit for power. If it were, it would mean dB relative to one megawatt. Jun 28, 2013 at 15:55
• @ThePhoton I think he meant dBm which is extremely common in RF and it is relative to the milliwatt. Jun 28, 2013 at 18:49
• @talasila, you can edit your question at any time to fix that mistake. Jun 29, 2013 at 15:05

The easy solution is to get an RF wattmeter. Those will measure transmit power directly.

Alternately, you can transmit into a $50\Omega$ dummy load, measure the RMS voltage, and calculate power as $P = V^2/50\Omega$.

This will give you total power. To calculate the spectral density, divide this by the bandwidth of your signal, which you should know since you are making it. The power in this spectrum isn't flat: some smaller areas will have greater spectral density, some will have less. I'm no expert on FCC regulations so I can't say precisely what their rules are. I also can't say precisely how they define "bandwidth".

To get an idea of the spectral density of smaller slices of spectrum within your signal, take the FFT of your transmitted signal, and each bin will give you a relative measure of power in the frequency range covered by that bin. Divide your measured total power by the sum of these bin powers, and you have a scaling factor that relates the unitless power given to the FFT to power in watts.

If the USRP and your software has fixed gain, then this scaling factor will be the same for any transmitted signal. It might be easiest to transmit a simple carrier and calculate the scaling factor that way, then apply it to more complex signals.

Note that your software probably displays the FFT in decibel units; you will want to convert these to linear units to do the math as described.

Your choice of windowing function will affect how the power spreads out between bins. See How does the energy of non-resolved spectral lines get distributed in an FFT?

• can i know the relation between measured power in analog signal at antenna to the power spectrum power as measured in frequency domain. any equation or formula as to how the total power sent converts to power in each of the frequencies present in signal. Jun 29, 2013 at 7:30
• @talasila see edits. Jun 29, 2013 at 13:31
• I have two questions.Firstly, there is an fft function in gnuradio. It uses a blackman harris window function. I see that the fft plot has a peak at centerfrequency i have set to signify that there is a signal being sent at that frequency. The peak stays for the entire bandwidth of the signal i have set. So i don't see any bins in the fft. I am unsure with the fft plot as to how to measure the bins and power in it. secondly what is the constant factor in the fft power i.e. difference between total analog power -sum of bin power frequencies. what is that constant factor? Jul 4, 2013 at 4:19
• @talasila I don't know what the factor is. You have to calculate it. I'm sure you do see bins in the FFT. When you configure the FFT block, you specify how many bins you want. I think it calls the parameter "FFT size". Jul 4, 2013 at 11:33

Making power measurements on an ODFM signal is difficult do to with the time varying power envelope. The two previous answers with a power meter and thermal diode are suggesting a method similar to that as described in EN 300 328 and EN 301 893.

However you'll need to also consider how you are going to make sure the product is compliant when building them in production.

Without knowing which FCC spec you're testing to, I can only suggest you take a look at this article on OFDM power measurement for a comparison of techniques. I'm partial to the digital spectrum analyzer that you can use to integrate over different bandwidths. A spectrum analyzer will can also be used to measure ERP of your design against a reference antenna. Don't freak out at the cost as you can always just rent one then return it.

If you update your question with the FCC reg number/description I'll check back to see if I can help more.

• I am using homeplug standard for powerline communication. I will try to get the reg number of FCC. Jun 29, 2013 at 6:46
• I think the fcc part no is 11-60. Here's the link.<fcc.gov/document/access-broadband-over-power-line-systems> Jun 29, 2013 at 7:27
• @talasila that looks like an FCC memo for updating their specs. I think you have to look through 47 C.F.R. 15.601-15.615 to find it. I unfortunately don't have time to find it. Jul 1, 2013 at 0:47

A 50 ohm dummy load (non inductive resistance) is the usual way to test the output as Phil says. The peak-to-peak voltage is 2.828 times the root-mean-square (rms) voltage. So taking this as 7.2V (across a 50R load)

then $V_{RMS} = \frac{7.2}{2.828} = 2.546 V$

\begin{align} \text{Av. power} &= \frac{{V_{RMS}}^2}{R}\\ &= \frac{(2.546V)^2}{50\Omega}\\ &= 0.13W \end{align}

• A crest factor of 2.828 is OK for an unmodulated sine wave, but OFDM signals have much higher crest factors than that (according to the wiki link in my comment above). Jun 28, 2013 at 14:15
• @MikeJ-UK very true and an excellent article btw but the simple setup and calculation shown would give an upper limit for making your own measurements/estimates of power without costing a fortune. Before production its going to have to go to a lab for accurate measurement on some very expensive equipment. Jun 28, 2013 at 16:09
• @JImDearden But i am not manufacturing a device. This is an experimental setup for varying power and extracting better performancee within the FCC specifications. So i can tolerate some error. So i am looking at some ideas. Jun 29, 2013 at 6:45