# Understanding the IP3 specification and linearity, Part 1

*In part one of this two-part story, the authors review the basics of intercept point specifications and linearity. For an expanded view of the equations, click here. Part two will discuss how to actually evaluate and interpret IPn.*

For a variety of electronic devices ranging from RF mixers to low-noise amplifiers (LNAs), linearity is an essential performance attribute. The degree of linearity demonstrated by a component can make the difference between a successful device and a unit that fails to operate as designed. Intercept point (IP) specifications provide a useful tool for determining the degree of linearity exhibited by electronic devices.

IPn, which stands for intercept points of order

*n*for some integer

*n*=2, consists of “virtual” parameters (i.e., the values are actually defined from other specifications). As a result, their values and extrapolations often remain vague. Admittedly, many electronic books or tutorials give some description of how IPn specifications are linked with input/output powers, power gain, and compression point. However, those reference works offer minimal, none, or incomplete explanations about IPn specifications and their origin.

Today, integrated functions such as an LNA, mixers, and a VCO (voltage controlled oscillator) can be built with the highest linearity (thus superior IP3) with advanced design techniques, and with proven RF processes. The design aim is to obtain the highest IP3 without sacrificing current consumption (bias circuit), gain, and size. Practically speaking, describing IPn orders up to 5, and eventually 7, can be significant. Today, however, the “order 3” (IP3) dominates when describing the normal operation of sensitive devices.

This article will use basic math and graphics to explain how IPn, and especially IP3, is generated and how its values are linked to essential quantities such as the input and output powers of a device. It will explain why high IP3 (thus, high linearity) is so important when evaluating performance. Finally, it will discuss some high-performance analog ICs in which linearity, high IP3, is a fundamental measurement of their good operation.

**Why is linearity so important?**

A principal objective for many electronic devices has been always to replicate simple, easy-to-reproduce, ideal mathematical functions. A simple illustration is the resistor which is designed to reproduce a linear relationship between voltage and current (VI). The resistor is simply the slope of the VI response.

We all know that the ideal relationship of V = R × I cannot be realized 100% of the time. One can approach it, but the inherent imperfections and limitations of the devices cause deviations in the ideal curve. This is particularly true when signals (I, V) are large and/or other conditions like temperature, humidity, and pressure vary. To compensate for these inherent deviations, we want the resistor, R, to be as linear as possible and remain so over wide ranges of signals and conditions. In reality, however, resistors have more complex curves in the (VI) characteristics (red dotted line in Figure 1).

**Figure 1. Dotted red line shows the real (imperfect) resistor. Linearity is corrupted when I and V curves become large.**

Other IC components that require well-controlled linearity include amplifiers, data converters, VCOs, mixers, and PAs. With these ICs, deviations from the ideal VI relationship lead to instabilities, failure to meet specs, and interference. They can even cause malfunctions or destroy the device and/or entire system.

**Measuring linearity**

Depending on the class of signals and their dynamic ranges, different parameters and methods are defined to visualize, evaluate, measure, and compare the linear characteristic of an actual device.

Resistor linearity is typically measured in % of a nominal value of R. This is usually enough to appreciate the error that one introduces in current and voltage on the device.

The RF functions in an LNA, mixers, filters, PA, and other components can generate very large signal dynamics and introduce harmonics, interference, and saturation as critical effects of nonlinearities. Several parameters have been defined to characterize this nonideal relationship between input and output:

- 1dB compression point (CP-1dB)
- Compression dynamic range (CDR)
- Spurious-free dynamic range (SFDR)
- Desensitization dynamic range (DDR)
- Intercept points (IPn)

Since all the above terms indicate how good (or bad) the linearity of a device is, relations do exist between them. While this examination acknowledges the above class of parameters, it focuses exclusively on the intercept points, or how IPn (n) can be 2, 3, 4, etc. It will become clear that IPn (especially IP3) reveals the most about how nonlinearity negatively affects useful signals. It causes interference to be directly injected in the desired signal bandwidth. For this reason, one can focus here only on IP3 performance, regardless of the other parameters. Thus, in a few words, the higher the IPn, the more linear is the device.