# Troubles With Triplets Foreseen

PART 2
Last month, this column covered DTV-DTV interference from one and two undesired signals. It also warned that interference from a triplet (three channels) is even worse. If you missed it, you can download it at www.tvtechnology.com/rhodes.

In this column, we will address the matter of triplets of undesired DTV signals.

(click thumbnail)Fig. 1: A symmetrical triplet of DTV signals in adjacent channels. Note: IM3 products extending over nine channels.I count triplets as sets of three channels operating in the same community, where the channel offsets between the middle channel and the others are each less than 10. I had to set some arbitrary limit and chose nine. An example of a symmetrical triplet is shown in Fig. 1, with Channels 30, 31 and 32 operating with about the same power. I call this a 1, 1 set of triplets. This 1, 1 set occupies only three consecutive channels, but its third-order distortion products are spread out over six additional and contiguous channels. These distortion products look, taste and smell like noise to a receiver tuned to a channel in the range 27-29 or 33-35. Now the noise in Channels 27 or 35 (–35 dBm) is not as bad as the noise in Channels 28 and 34, (–28 dBm and –29.9 dBm) and that is not as bad as the noise in Channels 29 and 33 (–25 dBm each).

Two of these signals may interfere with each other: the signal on Channel 30 hops over 31 and lands in Channel 32, and the signal on Channel 32 hops over 31 and lands in Channel 30. They not only interfere with the neighbors, but with each other too. Channel 31 is an innocent bystander, it doesn’t hurt its triplet-mates, but it hops over them to clobber the neighbors—on Channels 29 and 33.

Triplets can be symmetrical as in both Fig. 1 and Fig. 2, or asymmetrical as in Fig. 3. Symmetrical triplets are those of the form N+K and N+2K which produce IM3 in channels N and N+3K either of which might be the desired channel. Symmetrical triplets produce noise in channels N and N+3K but they also produce more in other nearby channels. The center channels of “Bee-Hives” would be channels N and N+3 for a symmetrical triplet. The centers of the Bee-Hives produced by asymmetrical triplets are not channels N and N+3 but they are close enough to channels N and N+3K that there is also considerable noise in N and N+3K. Fig. 3 is a spectrum plot of an asymmetrical triplet of Channels 30, 32 and 37.

(click thumbnail)Fig. 2: A symmetrical triplet of DTV signals on Channels 30, 33 and 36. Note: IM3 products extending over 21 channels.In spectrum plots of symmetrical triplets, some of the third-order IM products are concealed in a spectrum plot under a signal. With asymmetrical triplets, they are all visible in spectrum plots such as Fig. 3. This can be demonstrated. First, let’s do the numbers for Fig. 1, a symmetrical triplet where Fa = 30, Fb = 31, and Fc = 32. I use channel numbers instead of UHF or high VHF frequencies because we want to find the channel affected, not its frequency.

Third-order IM (2 Fa – Fb, 2 Fb – Fa, etc.) are:
2*30 – 31 = 29
2*30 – 32 = 28
2* 31 – 30 = 32
2* 31 – 32 = 30
2*32 – 30 = 34
2*32 – 31 = 33

The cross-modulation products are:
30 +/– (32 – 31) = 29 and 31
31 +/– (32 – 30) = 29 and 33
32 +/– (31 – 30) = 31 and 33

Channel numbers in bold are signal channels where the distortion products in this symmetrical triplet are masked by the signal. Note that the middle channel gets hit twice by X-M.

Now let’s do the numbers for the asymmetrical triplet of Fig. 3, which has Fa = 30, Fb = 32 and Fc = 37.

(click thumbnail)Fig. 3: An asymmetrical triplet of DTV signals with seven Bee-Hives of IM3.Third-order IM are:
2* 30 – 32 = 28
2* 30 – 38 = 22
2* 32 – 38 = 26
2* 32 – 30 = 34
2* 38 – 32 = 44
2* 38 – 30 = 46

There are no distortion products which fall in a signal channel of this asymmetrical triplet. I believe that all asymmetrical triplets spread out their distortion products and they can all be seen on a spectrum plot. Now you know where to look for spectral peaks in Fig. 3. You will see them all.

In Fig. 2, we have a symmetrical triplet of Channels 30, 33 and 36. In Fig. 3, two channels have been slightly shifted, 33 became 32 and 36 becomes 37 but what a tremendous difference in their spectra. Asymmetrical spectra are going to be much more frequently encountered than symmetrical spectra. I counted 42 cases of symmetrical triplets and 161 cases of asymmetrical triplets in the FCC table of permanent DTV channel allotments. The IM spectrum extends from Channel 22 up to 46 (Fig. 3) and from 23 up to 44 (Fig. 2). There are a whole lot of channels subject to being interfered with by a poorly performing receiver. The complexity of dealing with more than three undesired signals is beyond the scope of this column or my computational skills. However, I think that you now understand that triplets of DTV signals can really ruin a good business.

There is yet another consideration involving unlicensed devices operating in the broadcast television spectrum. In cases where there are no triplets of DTV signals closely packed in the post transition (shrunken) broadcast spectrum, triplets composed of one or more signals radiated by unlicensed devices on nearby channels can possibly combine with fewer than three DTV signals. This is potentially devastating because no viewer is safe. If he or she has one of these unlicensed devices operating in the home, there will probably be some DTV channels that are not viewable while the UD is transmitting. Viewers living in multiunit buildings will have even more problems as they have a greater possibility of a UD operating in close proximity to the television receiver.

TWO-TONE TESTING

Some months ago, my friend and colleague, Dr. Oded Bendov brought to my attention the fact that two-tone testing of DTV receiving devices to determine the linearity of (analog) tuners can’t produce valid or useful information. I never use the two-tone measurement technique, although I have mentioned it in this column and in some of my papers in IEEE Transactions on Broadcasting and IEEE Transactions on Consumer Electronics as a starting point to acquaint readers with third-order nonlinearity and intermodulation products in general. I have proposed a method of noninvasive testing based on two or even three DTV signals which is how I do it in my own laboratory. The time has come to share with you what is wrong with two-tone testing, or even triple-tone testing of DTV receiving appliances.