Third-order intercept point

In telecommunications, a third-order intercept point (IP3 or TOI) is a specific figure of merit associated with the more general third-order intermodulation distortion (IMD3), which is a measure for weakly nonlinear systems and devices, for example receivers, linear amplifiers and mixers. It is based on the idea that the device nonlinearity can be modeled using a low-order polynomial, derived by means of Taylor series expansion. The third-order intercept point relates nonlinear products caused by the third-order nonlinear term to the linearly amplified signal, in contrast to the second-order intercept point that uses second-order terms. The intercept point is a purely mathematical concept and does not correspond to a practically occurring physical power level. In many cases, it lies far beyond the damage threshold of the device. Two different definitions for intercept points are in use: Based on harmonics: The device is tested using a single input tone. The nonlinear products caused by n-th-order nonlinearity appear at n times the frequency of the input tone. Based on intermodulation products: The device is fed with two sine tones one at and one at . When you cube the sum of these sine waves you will get sine waves at various frequencies including and . If and are large but very close together then and will be very close to and . This two-tone approach has the advantage that it is not restricted to broadband devices and is commonly used for radio receivers. The intercept point is obtained graphically by plotting the output power versus the input power both on logarithmic scales (e.g., decibels). Two curves are drawn; one for the linearly amplified signal at an input tone frequency, one for a nonlinear product. On a logarithmic scale, the function xn translates into a straight line with slope of n. Therefore, the linearly amplified signal will exhibit a slope of 1. A third-order nonlinear product will increase by 3 dB in power when the input power is raised by 1 dB.