# Understanding the IP3 specification and linearity, Part 2

*Intercept point (IP) specifications provide a useful tool for determining the degree of linearity exhibited by electronic devices. In part one of this two-part story, the authors reviewed the basics of intercept point specifications and linearity. For an expanded view of the equations, click here. *

**Intermodulation (IM) to intercept point (IP)**

Now that we understand the origins of IM products, and particularly IM3, we are better prepared to determine its values and measure them with a common method and unit of measurement.

Please note: IMn are the intermodulation products, while IPn are the actual measures.

The previous discussion showed that the terms for i > 1 in the function transfer A are responsible for device nonlinearity. The larger they are, the greater is the distortion. Thus we can simplify and only measure the values of A

_{2}, A

_{3}, ... A

_{i}...A

_{n}.

But such absolute values are meaningless because one does not know how they compare to the useful linear performance (A

_{1}). Therefore, it is more useful to know their deviation versus the good parameter (A

_{1}), or more precisely, the ratio A

_{i}/A

_{1}or A

_{1}/A

_{i}. We will investigate the latter since it will yield a higher value for a high-linearity device.

We could start by trying to evaluate how the terms compare to A

_{0}, or A

_{2}, or any A

_{i}. But those parameters are not useful. We want a linear behavior (gain, attenuation, etc.), so only A

_{1}interests the RF engineer.

Since the dynamic of A

_{1}can be very large, it is convenient to use the dB or dBm units for the ratio. We flag the different contributors in the very original figure of y versus x, but this time the two axes are logarithmic (Figure 5).

**Figure 5. The individual behavior of terms to y in the log axes.**

From Figure 5, we find that:

- The term A
_{0}is a constant value (offset) and independent of the value of x. - The term A
_{1}x is the linear portion; in a double-log scales graph, y-x is a straight line with offset defined by A_{1}and the slope is just 1dB/dB (doubling x, results in doubling y). - The term A
_{2x²}is the quadratic term (second order). It has an offset determined by A_{2}and a slope that is exactly twice of the previous slope (2dB/dB); or restated, doubling the input x will result in quadrupling y. - The term A
_{3x3}is the third-order part. It is a straight line in the graph y-x with offset determined by A_{3}. The slope is exactly three times sharper than for the linear term (3dB/dB); or restated, doubling x will result in multiplying x by 8. - This log is applied to all the following terms and the nth-order line will have a slope of ndB/dB.

Since the higher-order terms have lines with a sharper slope, sooner or later there will be a moment (a point actually) where the high-order line will cross the first-order line. The crossing points are called intercept points (IPn).

One can easily observe that the more a device is linear, the more the first-order line is high in the graph (compared to the other lines). Therefore, a higher value is reached for IP points. Graphically, this is easy to see (Figure 6). The slope is fixed, so when the device is strongly linear, the nth-order terms will be very small. (The A

_{n}lines start from deeper values and, hence, will cross the first-order line much later, far away in the axes.)

**Figure 6. IPn as crossing points between nth-order and first-order curves.**

From Figure 6 we see that IP2 is the point where the first-order and second-order lines cross. IP3 is the point where first-order and third-order lines cross. The process continues in this fashion. The values are read in the x or y axis. There are thus two actual values for measuring the IP point: the input or output intercept point. They are noted as:

- IIPn for nth-order input intercept point, measured on the input power axis (x)
- OIPn for nth-order output intercept point, measured on the output power axis (y)