# FCC Releases "symbol rate" NPRM

Discussion in 'Amplitude Modulation' started by K5UJ, Jul 29, 2016.

No confusion here. However, I have absolutely no desire to argue this. I was just trying to point you in the right direction.

2. ### K4KYVPremium SubscriberVolunteer ModeratorQRZ Page

I might entertain your take on the issue if you supplied some 3rd party links or documentation to back it up.

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I posted actual spectrum analyzer occupied bandwidth measurements. On the 64QAM trace, the OBW points are only 5 dB down. That's a long ways from 26 or even 20 dB down. Why isn't that sufficient documentation?

However, in the interest of fully explaining OBW, let's look at the very first link returned by a Google search of "occupied bandwidth".

http://rfmw.em.keysight.com/rfcomms/refdocs/wcdma/wcdma_meas_occup_bw_desc.html

The first sentence is "As defined by 3GPP TS 34.121 section 5.8 Occupied Bandwidth (OBW) is the bandwidth containing 99% of the total integrated power of the transmitted spectrum, centered on the assigned channel frequency.".

The key word is "integrated". This implies that the calculus integral function is used to perform the measurement. The integral is otherwise known as the area under a curve. The curve in this case is the spectrum of the signal.

The spectrum analyzer can't do a textbook integral, because the step size of "infinitely small, but not zero" isn't possible. Instead the step size is equal to the resolution bandwidth (in this case, 30 kHz). So the analyzer is essentially doing a Reimann sum, which is an approximation of the area under a curve. By setting the resolution bandwidth to a low value compared to the total bandwidth, the approximation is very good.

That's what they're talking about in the third paragraph of the Keysight link:

"First, the total power found in the measured frequency range is calculated. Then, starting at the lowest frequency in the range and moving upward, the power distributed in each frequency is summed until this sum is 0.5% of the total power. This gives the lower frequency value. Next, starting at the highest frequency in the range and moving downward, the power distributed in each frequency is summed until 0.5% of the total power is reached. This gives the upper frequency value. The bandwidth between the 0.5% power frequency points is the occupied bandwidth."

"Power distributed in each frequency" is spectral power density, which is measured in dBm/Hz (or more precisely for the above measurement, dBm/30kHz).

Going back to the area under a curve concept, we can fill in the areas that contain 0.5% of the total integrated power on each side of the signal (but be aware that the vertical scale is logarithmic, so you can't just eyeball the areas).

Last edited: Oct 17, 2016
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4. ### K4KYVPremium SubscriberVolunteer ModeratorQRZ Page

What does that have to do with the definition of occupied bandwidth? That just indicates the signal level at some point along the knee of the curve. The definitions in the FCC rules have nothing to do with the attenuation at specific spot frequencies; it certainly doesn't say the signal has to be attenuated 20 or 26 dB right at the edge of the curve; in fact, it is overwhelmingly likely that the attenuation at those two frequencies will be much less.

That is precisely correct. I believe that's exactly what I stated and then reiterated in my previous posts.

If the defined bandwidth contains 99% of the total integrated radiated power (TIRP), then 1% of the total integrated radiated power lies outside that bandwidth. Comparing the TIP outside the bandwidth to the TIP inside the bandwidth, you get a ratio of 1/100. That ratio can be expressed equally well as 0.01, 1%, or 20 dB. Regardless of the shape of the curve, the points defining occupied bandwidth are those points at which there is equal extraneous power above and below the the limits of the defined bandwidth: § 2.202 (a) Occupied bandwidth. The frequency bandwidth such that, below its lower and above its upper frequency limits, the mean powers radiated are each equal to 0.5 percent of the total mean power radiated by a given emission. If the signal curve happens to be asymmetrical in shape, the defining point at one side may be farther down the knee of the curve than at the other side. Regardless of shape, if the extraneous TIP is 1% of the TIRP, then 99% of TIRP lies inside the curve, and 1% lies outside the curve. That gives us 0.5% above and 0.5% below the two defining frequency points, or 23 dB attenuation each. Adding the two equal quantities of −23 dB together gives a total of −20 dB.

That is true when you graph out a mathematical equation. The spectrum distribution that makes up the shape of a radiated signal may not follow a pattern than can readily be defined mathematically. For example, the bandwidth filter in the transmitter may be asymmetrical, there may be random dips and peaks in the passband, a notch filter could be inserted between the signal source and the modulator, etc. Formulating a mathematical equation that describes the shape of the signal would require a great effort that would serve us no useful purpose; that would best be achieved by taking measurements with whatever instruments are at our disposal.

That very clearly explains how we could arrive at, determine and measure the 0.5% figure, but what does it have to do with the 0.5% (− 23 dB) definition in the first place? That was an arbitrary choice made by the defining authorities, as illustrated by the Part 97 rule, which defines the total extraneous power for amateur radio purposes at −26 dB, placing the defining points to give us −29 dB total integrated extraneous power each side of the curve: (8) Bandwidth. The width of a frequency band outside of which the mean power of the transmitted signal is attenuated at least 26 dB below (0.25%) the mean power of the transmitted signal within the band (as opposed to 1%). Again, this is not saying that at the defining points the signal has to be precisely −29 dB, but that the total integrated power from each frequency point beyond the curve, to the respective limits of zero and infinity, is 29 dB below the TIP inside the curve. Per the Part 2 definition, that would be only 23 dB below the TIP inside the curve.

But back to the original topic of discussion, please explain how any of this contradicts my assertion that there is a 6 dB discrepancy between the FCC's Part 2 and Part 97 definitions of occupied bandwidth?