2.3 Linearity and Distortion in RF Circuits 2 13IP31dB1323 ||5.250.22||kkvvkk== (2.77)Thus, these voltages are related by a factor of 5.25 or about 14.4 dB.Thus, one can estimate that for a single tone, the compression point is about 10 dB below the intercept point, while for two tones, the 1-dB compression point is close to 15 dB below the intercept point. The difference between these two numbers is just the factor of three (4.77 dB) resulting from the second tone.Note that this analysis is valid for third-order nonlinearity. For stronger nonlin-earity (i.e., containing fifth-order terms), additional components are found at the fundamental as well as at the intermodulation frequencies. Nevertheless, the above is a good estimate of performance.Example 2.5: Determining IIP3 and 1-dB Compression Point from Measurement DataAn amplifier designed to operate at 2 GHz with a gain of 10 dB has two signals of equal power applied at the input. One is at a frequency of 2.0 GHz and another at a frequency of 2.01 GHz. At the output, four tones are observed at 1.98, 2.0, 2.01, and 2.02 GHz. The power levels of the tones are –70, –20, –20, and –70 dBm, re-spectively. Determine the IIP3 and 1-dB compression point for this amplifier.Solution: The tones at 1.98 and 2.02 GHz are the IP3 tones. We can use (2.59) directly to find the IIP3 =+-- = - +- +-= -11311IIP320[ 20 70] 105 dBm22PPPG The 1-dB compression point for a single tone is 9.66 dB lower than this value, about –14.7 dBm at the input.2.3.6 Broadband Measures of LinearityIntercept points and 1-dB compression points are two common measures of linear-ity, but they are by no means the only ones. Two other measures of linearity that are common in wideband systems, which handle many signals simultaneously are called composite triple-order beat (CTB) and composite second-order beat (CSO) [11, 12]. In these tests of linearity, N signals of voltage vi are applied to the circuit equally spaced in frequency, as shown in Figure 2.11. Note here that, as an ex-ample, the tones are spaced 6 MHz apart (this is the spacing for a cable television system, for which this is a popular way to characterize linearity). Note also that the tones are never placed at a frequency that is an exact multiple of the spacing (in this case 6 MHz). This is done so that third-order terms and second-order terms fall at different frequencies. This will be clarified shortly.