Third-order intercept point

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 intercept point is a purely mathematical concept and does not correspond to a practically occurring physical power level.

In practice, the weakly nonlinear assumption may not hold for the upper end of the input power range, be it during measurement or during use of the amplifier.

As a consequence, measured or simulated data will deviate from the ideal slope of n. The intercept point according to its basic definition should be determined by drawing the straight lines with slope 1 and n through the measured data at the smallest possible power level (possibly limited towards lower power levels by instrument or device noise).

For example, say the input voltage signal is the sine wave and the device transfer function produces an output of the form where G is the amplifier gain, and D3 is cubic distortion.

If we now restrict our attention to the portion of the cos(ωt) coefficient that varies linearly with V, and then ask ourselves, at what input voltage level V will the coefficients of the first- and third-order terms have equal magnitudes (i.e., where the magnitudes intersect), we find that this happens when which is the third-order intercept point (TOI).

So, we see that the TOI input power level is simply 4/3 times the ratio of the gain and the cubic distortion term in the device transfer function.

The TOI, being related to the magnitude squared of the input voltage waveform, is a power quantity, typically measured in milliwatts (mW).

Third-order intermodulation products (D3 and D4) are the result of nonlinear behavior of an amplifier. The input power level into the amplifier is increased by 1 dB in each successive frame. The output power of the two carriers (M1 and M2) increases by about 1 dB in each frame, while the third-order intermodulation products (D3 and D4) grow by 3 dB in each frame. Higher-order intermodulation products (5th order, 7th order, 9th order) are visible at very high input power levels as the amplifier is driven past saturation. Near saturation, each additional dB of input power results in proportionally less output power going into the amplified carriers and proportionally more output power going into the unwanted intermodulation products. At and above saturation, additional input power results in a *decrease* in output power, with most of that additional input power getting dissipated as heat and increasing the level of the non-linear intermodulation products with respect to the two carriers.