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 A₂, A₃, ... A_i...A_n.

But such absolute values are meaningless because one does not know how they compare to the useful linear performance (A₁). Therefore, it is more useful to know their deviation versus the good parameter (A₁), or more precisely, the ratio A_i/A₁ or A₁/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 A₀, or A₂, or any A_i. But those parameters are not useful. We want a linear behavior (gain, attenuation, etc.), so only A₁ interests the RF engineer.

Since the dynamic of A₁ 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).





From Figure 5, we find that:

• The term A₀ is a constant value (offset) and independent of the value of x.
• The term A₁ x is the linear portion; in a double-log scales graph, y-x is a straight line with offset defined by A₁ 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 A₂ 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 A₃. 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.)



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)