Non-linearity Consideration in RF Circuits

Introduction

Non-linearity is the enemy for many functions since it deviates from the nice proportional relationship Vout = K*Vin. K is just a constant scalar term. This is what design engineers want to get for their amplifiers, transducers, sensing interfaces, etc…

For some domains like RF, the non-linearity has other unfavorable impacts that are harmonics and intermodulation products; those are mainly responsible for perturbing useful data

This discussion, split into several blog posts, covers a particular view of the non-linearity problem in RF components. More particularly, RF people define a set of specific parameters to evaluate the linearity level of the components. Harmonics, Intermodulation products (IMn), Intercept Points (IPn), 1-dB compression points (IPn), Phase Noise, and ACPR are the most known representatives. Among them, the IP3 (intercept point of the third order) is the most popular one.

This first is an introduction to the importance of non-linearity in electronic functions in general and in RF parts in particular.

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 a resistor that 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. The 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 power amplifiers. With these ICs deviations from the ideal VI relationship lead to instabilities, failure to meet specs, and interferences. It can even cause malfunctions or destroy the device and/or entire system.

Linearity or Non-linearity in RF

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.

We will see in the further blog posts how the RF functions in an LNA, mixers, filters, PA, and other components can generate very large signal dynamics and introduce harmonics, interferences, and saturation as critical effects of nonlinearities. Several parameters have been defined to characterize this non-ideal 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 of order n (IPn)

Since all the above terms indicate how good (or bad) is the linearity of a device, relations do exist between them. While this examination acknowledges the above class of parameters, it focuses exclusively on the intercept points or 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 interferences to be directly injected into 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.

One can observe that is a datasheet of most of the existing RF components such as LNA, mixers, buffers

The special attention for RF circuits is triggered by the fact RF equipment use frequencies both as transport vehicle (i.e. carrier) and as data/information content (i.e. modulation/demodulation schemes). Corruptions and interferences act directly on them causing communication errors.

Summary

This blog post is an introduction to what is linearity and non-linearity in general and their potential impacts, especially for RF functions. Some specific terms and terminologies have been mentioned such as harmonics, intermodulation products, and intercept points which will be in the next blog posts.

In the next blog post, we will see how the non-linearity can be modelized mathematically and see how we can extract the useful parameters and predict consequences