Readers of this column know that one undesired signal generates third-order distortion products, which fall in the adjacent channels to the undesired signal. So it can only cause Adjacent Channel Interference (ACI). You also know that undesired signals on two channels of the form N+K and N+2K produce third-order distortion products which principally fall in channels N and N+3K. The FCC Laboratory validated this in the FCC OET 07-TR-1003 report that can be downloaded from the FCC Web site. They found that signals of this form produce what amounts to co-channel interference into channel N. Take my word for it, they would also have found the same in channel N+3K.
WORKING THE NUMBERS
(click thumbnail)Fig. 1: Symmetrical triplet of DTV signals on Channels 30, 33 and 36. Third-order IM and triple beat X-M appear in the “beehives” centered on Channels 27 and 39. Only IM products are responsible for the outer beehives centered in Channels 24 and 43 (in blue) only.Consider two undesired signals on Channels 30 and 33 which may generate third-order intermodulation (IM3) is the front-end of receivers. The channels in which these IM3 principally appear are 2 × 30 – 33 = 27 and 2 × 33 – 30 = 36. In what I will call side channels of the IM3 “beehives”—26 and 28, and also in channels 35 and 37, the IM3 will also appear, but it is 6 dB lower in power than in the center channel of a beehive. A DTV receiver sees this as noise within the desired channel, be it channel 26, 27, 28, 35, 36 or 37 to which the viewer has tuned his receiver. As far as pairs of undesired signals are concerned, any of these channel pairs can affect reception of least two, and at the most six channels. That was the good news. Now for the bad.
You also know that triplets of undesired signals produce third-order distortion products which form what I call beehives of these distortion products (IM3 and X-M), two below the triplet, and two more above the triplet. This is shown in Fig. 1, where we have DTV signals on Channels 30, 33 and 36 and there is an inner pair of beehives on Channels 27 and 39, plus an outer pair on Channels 24 and 42. This is a symmetrical triplet as there is the same spacing between the middle signal channel and the other signal channels.
It can be shown mathematically that the IM3 for this triplet are centered in Channels 24, 27, 39 and 42 and that the triple beat X-M are centered in Channels 27 and 39. These distortion products produced the beehives in Fig. 1. You will have noted that the inner pair of beehives is bigger than the outer pair. This is because both IM3 and X-M are centered in Channels 27 and 39.
The powers of the IM and the X-M are additive. The X-M in Channel 33 and the IM3 centered in Channels 30 and 36 cannot be seen because they are masked by the much stronger DTV signals in those channels. So, how can I convince you that they are really there?
Fig. 2 shows another triplet of Channels 25, 30 and 37. This is an asymmetrical triplet with five channels between the middle channel (30) and the lower channel (25) and seven channels from the middle to the higher channel (37). Here we see nine peaks. Six of these are IM3 and three which are somewhat taller are X-M. Every one of these peaks is clearly visible and I offer this as evidence.
(click thumbnail)Fig. 2: Asymmetrical triplet of DTV signals on Channels 25, 30 and 37. The spectrum of the third-order distortion products extends over 216 MHz with a few “quiet” channels. Third-order IM is shown in blue, and triple beat X-M in red.A second piece of evidence comes from my friend, Linley Gumm, who is now retired from Tektronix Inc., where we both worked a while back. He did a simulation of this which confirms that these peaks really are concealed in symmetrical triplets. What he did was to subtract the signal from the simulated output of the nonlinear amplifier and sure enough, there are beehives centered in the signal channels, unmasked for all to behold. This simulation is shown in Fig. 3.
But wait, there is more to this. Now that you can see the unmasked beehives of third-order distortion products in the signal channels, you are seeing the noise floor within what may be the desired signal. OK, this noise is really IM3, and is the actual noise floor above which the desired signal has to be more than 15.2 dB higher for the receiver to decode the desired signal. Thanks, Linley.
Fig. 2 shows 12 channels from the lower to (and including) the upper channels. Counting the side-channels of the outermost IM3 beehives, 37 channels are affected. The IM spectrum of these distortion products extends from 13 channels below the lower signal channel to 13 channels above the upper signal channel, 37 channels. That does not mean that all 37 channels are subject to interference as there may be some “quiet” channels, but only if the signals are more than three channels apart. In Fig. 1, they are three channels apart so there are no quiet channels. A 4, 4 triplet for example will have some quiet channels.
In the Feb. 20 issue of TV Technology, Table 1 of this column showed the frequency of triplets in the FCC Channel Plan (August 2007). This table covered the 203 triplets from 1, 1 to 9, 9.
In the upper left quarter of this table, we had 111 tightly packed triplets out of the total of 203 triplets in that table. I have made 25 spectrum plots of this sub-set of tightly packed triplets from 1, 1 to 5, 5 inclusive. Scroll to the bottom of this page and click on the thumbnails to view these 25 plots. Please do so. Then you can figure out which, if any, of these fits your station’s permanent digital channel.
(click thumbnail)Fig. 3: Simulation of third-order distortion products of the 3, 3 triplet of Fig. 1 with the signal subtracted from the output of the device-under-test. Note that in Fig. 1 only two beehives below and two above the triplet are shown. Three more beehives are masked by the DTV signals in Fig. 1.
So now you see that asymmetrical triplets are capable of causing interference to many more TV channels, and there are three times more asymmetrical triplets than the number of symmetrical channel pairs (N+K, N+2K). So the N+K, N+2K is just the tip of the iceberg and for many stations it lies directly ahead.
Is this a spectrum efficient solution? No, but only because consumer DTV receivers may be overloaded by undesired signals on DTV channels. Note that I did not say DTV signals as by now you know that signals radiated by unlicensed devices after Feb. 18, 2009, and/or DTV signals can overload receivers. And perhaps by other strong signals which may reach the mixer of receivers in your community.
I believe there is a solution for those receivers unable to receive all the local signals the set owner wants to view. Such viewers could in principle buy a DTV channel preselector. This gadget, hypothetically, would have a really effective tuner controlled by the remote control which came with the DTV receiver. It would process the desired signal and reject the undesired signals because that is its sole purpose. The output of this device would be the desired signal on the desired channel, so this is not a downconverter or an upconverter; it is a frequency agile active filter.
In markets where all DTV transmitters are running about the same power and located on the same antenna farm, such as New York City, this gadget may not be needed for DTV–DTV interference. However, this gadget could be useful to viewers located between major metropolitan centers such as Philadelphia and Baltimore. It may also have a place in markets with multiple antenna farms, with some located a considerably greater distance from others, like the greater Miami area, as well as near international borders. Once people find they have interference problems, smart DTV receiver manufacturers will demand improved interference rejection of their tuner vendors and some receivers will become more cost effective in such areas and gather market share.
There is another marketing possibility for makers of these gadgets. No matter where the viewer lives, he or she is going to have problems with interference from unlicensed devices operating in what is still the broadcast TV spectrum, but which, in l1 months will be a wide open field for marketers of unlicensed devices legally operating in spectrum formerly reserved to broadcasting.
Who knows, maybe the federal government will subsidize such gadgets? Why not?
Click on a thumbnail to view the full-sized image