Third-order intercept point

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In telecommunication, a third-order intercept point (IP3 or TOI) 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 3rd order term in the nonlinearity to the linearly amplified signal.

The intercept point is a purely mathematical concept, and does not correspond to a physical power level. In many cases, it lies beyond the damage threshold of the device.

Two different definitions for intercept points are in use, one based on harmonics, and one based on intermodulation products. Using the definition based on harmonics, the device is tested using a single input tone. The nonlinear products caused by nth order nonlinearity appear at n times the frequency of the input tone. More frequently used is the intermodulation intercept point, measured by feeding two signals with a small frequency difference into the device-under-test. The nth order intermodulation products appear then at n times the frequency spacing of the input tones. The two-tone approach has the advantage, that it is not restricted to broadband devices. It is worth noticing, that both definitions differ by 4.8 dB (10 log₁₀ 3). Care should be taken, when using existing equations, models or measurement data.

The intercept point is obtained by plotting the output power versus the input power on dB scale. Two curves are drawn, one for the linearly amplified signal at an input tone frequency, one for a nonlinear product. On a logarithmic scale, "x to the power of n" translates into a straight line with slope of n. Therefore, the linearly amplified signal will exhibit a slope of 1. A 3rd order nonlinear product will increase by 3 dB in power, when the input power is raised by 1 dB.

Intercept point definition

Both curves are extended with straight lines of slope 1 and n (3 for a 3rd order intercept point). The point where the curves intersect is the intercept point. It can be read off from the input or output power axis, leading to input or output intercept point, respectively.

Input and output intercept point differ by the small-signal gain of the device.

The concept of intercept point is based on the assumption on a weakly nonlinear system, meaning that higher order nonlinear terms are small enough to be negligible. In many situations occuring in practise, the weakly nonlinear assumption does not hold for the uppper 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). It is a frequently made mistake to derive intercept points by either changing the slope of the straight lines, or fitting them to points measured at a too high power level. In certain situations such a measure can be useful, but it is not an intercept point according to definition. Its value depends on the measurement conditions that need to be documented, whereas the IP according to definition is mostly unambiguous (some dependency on frequency and tone spacing, depending on the physics of the device-under-test).

One of the useful applications of third order intercept point is as a "rule-of-thumb" measure to estimate nonlinear products. It can be seen that the spacing between two straight lines with slopes of 3 and 1 closes with slope 2.

For example, assume a device with an input-referred 3rd order intercept point of 10 dBm is driven with a test signal of -5 dBm. This power is 15 dB below the intercept point, therefore nonlinear products will appear at approximately another 15 dB below the test signal power at the device output (in other words, 2*15 dB below the output-referred 3rd order intercept point).

A rule-of-thumb that holds for many linear radio frequency amplifiers is that the 1 dB compression point falls approximately 10 dB below the intercept point.

Important Notes:

• It is an extrapolated convergence--not directly measurable--of intermodulation distortion products in the desired output.
• It indicates how well a receiver performs in the presence of strong nearby signals.
• It is sometimes used (interchangeably with the 1 dB compression point) to define the upper limit of the dynamic range of an amplifier.
• Determination of a third-order intercept point is accomplished by using two test frequencies that fall within the first intermediate frequency mixer passband. Usually, the test frequencies are about 20 to 30 kHz apart.
• It should be emphasized, that the concept of intercept point has no meaning for strongly nonlinear systems. Such is for example the case, when a signal reaches its maximum possible value due to limited supply voltage, and is clipped.

Source: From Federal Standard 1037C and from MIL-STD-188