ication may not be the operating level of a particular system. To calculate Xm for an amplifier to be used in a given system, using manufacturer's specifications, the following formula applies: Xma =Xmspec+2(OLoper-OLspec), = (17.11) where Xma = Xm for the amplifier in question, Xmspec = Xm specified by the manufacturer of the amplifier, OLoper = desired operating output signal level (dBmV), and OLspec = manufacturer's specified output signal level. We spot the "2" multiplying factor and relate it to our earlier comments, namely, when we increase the operating level 1 dB, third-order products increase 2 dB, and the contrary applies for reducing signal level. As we said, Xm is a form of third-order product. Example 1. Suppose a manufacturer tells us that for an Xm of -57 dB for a 35-channel system, the operating level should be +50.5 dBmV. We want a longer system and use an operating level of +45 dBmV. What Xm can we expect under these conditions? Use Eq. (17.11): Xm = -57 dB + 2(+45 dBmV - 50.5 dBmV) = -68 dB. 17.3 SYSTEM IMPAIRMENTS AND PERFORMANCE MEASURES CATV trunk systems have numerous identical amplifiers. To calculate Xm for N ampli- fiers in cascade (tandem), our approach is similar to that of thermal noise, namely, Xmsys = Xma + 20 log N, (17.12) where N = number of identical amplifiers in cascade, Xma = Xm for one amplifier, and Xmsys = Xm value at the end of the cascade. Example 2. A certain CATV trunk system has 23 amplifiers in cascade where Xm is -88 dB. What is Xmsys? Use Eq. (17.12): Xmsys = -88 dB + 20 log 23 = -88 + 27 = -61 dB. 17.3.6 Gains and Levels for CATV Amplifiers Setting both gain and level settings for CATV broadband amplifiers is like walking a tightrope. If levels are set too low, thermal noise will limit system length (i.e., number of amplifiers in cascade). If levels are set too high, system length will be limited by excessive CTB and Xm. On trunk amplifiers available gain is between 22 dB and 26 dB (Ref. 1). Feeder amplifiers will usually operate at higher gains, trunk systems at 