Understanding Nonlinear Vector Analysis

October 10, 2011

  1. Introduction
  2. Measuring Nonlinear Effects
  3. A Viable Solution
  4. Conclusion
  5. Related Information


Today's R&D engineers and scientists tasked with researching and designing high-performance, active RF devices face many challenges. One key challenge involves characterizing the devices' nonlinear behavior so that it can be reduced to provide linear high-power solutions. This task is especially vital in the telecommunications industry where nonlinear device behavior contributes to information interference and the reduction in effective bandwidth.

In this industry, amplifiers are considered an indispensable component and yet due to their nonlinear behavior, are often the cause of wasted frequency spectrum. Designing a power amplifier to operate only within its region of linear operation also results in an inefficient use of the available power. Amplifiers are often driven into the nonlinear region of operation and then linearized around that point. Consequently, it has become increasingly important to understand the nonlinear behaviors of active RF components such as power amplifiers and frequency doublers which, in turn, makes accurate measurement of a device's nonlinear behavior all the more crucial.

All active devices exhibit nonlinear behaviors to varying degrees and therefore, the list of possible devices that could benefit from this measurement insight can be quite large. Examples of this are LNAs, T/R modules and converters, as well as passive devices such as inductors with magnetic cores or filters driven at high powers.

Unfortunately, making nonlinear measurements is not an easy task, especially considering that currently available tools and models for accomplishing this goal are generally difficult to use and do not provide the information required. What's needed is a solution specifically designed to accurately measure the nonlinear effects of active RF devices. With this information, designers will then be better equipped to control and minimize nonlinear device behavior and more accurately, easily and quickly create linear high-power solutions.

Measuring Nonlinear Effects

Agilent has introduced two primary methods for measuring the nonlinear effects of a device under test (DUT): nonlinear component characterization and X-parameters. Nonlinear component characterization provides calibrated, vector-corrected waveforms of the incident, transmitted and reflected waves from the DUT. Vector calibration, power calibration and the use of a poly-harmonic phase reference and calibration removes the systematic error terms.With this measurement, all receivers must be measured simultaneously for each frequency point. The information derived from nonlinear component characterization measurements enables the engineer to better understand and more deterministically control the nonlinear behavior of the DUT.

X-parameters are the logical, mathematically-correct extension of S-parameters into a nonlinear, large-signal operating environment (see the sidebar, "A Closer Look at X-Parameters"). X-parameter measurements require an additional source which is used to drive the DUT with both a large and small signal tone at the appropriate frequencies and phases, at the same time. Careful control of the phase and amplitude of these signals is therefore critical. Measuring the amplitudes and phases of the scattered waves under these conditions allows for the identification of X-parameters. These parameters provide the engineer with information on such things as device gain and match, while the device is operating in either a linear or nonlinear state. The X-parameters can be extracted into Agilent's Advanced Design System (ADS) or displayed like S-parameters.

A Closer Look at X-Parameters

X-parameters are to nonlinear measurements what S-parameters are to linear measurements. Consider, for example, that S-parameters were developed as a method to analyze and model the linear behavior of RF components and play a key role in analyzing, modeling and designing complex systems which cascade multiple individual components. They are related to familiar measurements such as S11 input match, S22 output match, S21 gain/loss, and S12 isolation, and can be easily imported into electronic simulation tools. While extremely useful and powerful, S-parameters do have limitations and are defined only for small-signal linear systems.

S-parameters are measured using traditional network analyzers. To a smaller extent, network analyzers can also provide insight into the nonlinear behavior of devices via approximation techniques such as using un-ratioed receiver measurements and offsetting the measurement receivers' frequency from the source stimulus frequency. By employing these techniques, simple gain compression, harmonic amplitude only, frequency converter match, conversion loss/gain, and group delay can be measured.

In contrast to S-parameters, X-parameters were developed to represent and analyze the nonlinear and linear behavior of RF components in a much more robust and complete manner. As an extension of S-parameters under large-signal operating conditions, the devices are driven into saturation (the real-word operating environment for many components) and then the X-parameters are measured under these conditions. When making this measurement, no knowledge is used or required concerning the internal circuitry of the DUT. Rather, the measurement is a stimulus response model of the voltage waves. In other words, the absolute amplitude and cross frequency relative phase of the fundamental, and all related harmonics, are accurately measured and represented by X-parameters.

Because the X-parameters relate cross-frequency dependencies, there are usually many more X-parameters than S-parameters, such as in the case of the gain of the output fundamental frequency to the input third harmonic. Here, there are eight X-parameters for this simple case with only one harmonic and no power dependency. In contrast, there can never be more than four S-parameters.X-parameters also depend explicitly on the large signal state of the device, making input power a variable. In contrast, S-parameters are assumed to be power independent.

The accurate and robust nature of X-parameters makes them extremely useful for engineers and scientists trying to better understand the nonlinear behavior of their active components. As an example, consider the design of a power amplifier in which the designer drives the amplifier into the nonlinear region to get the maximum output power and to extract the maximum efficiency. A feedback circuit is then used to compensate for the nonlinear effects, causing the output to behave like a high-power linear device.

In this case, the typical approach to suppressing the power amplifier's harmonic outputs is through the use of filters and other components. But, if the filtering component's input match does not match the output match of the specific harmonic of interest (generated by the amplifier), then the harmonic's attenuation level could be significantly different from what the designer anticipates. This situation may cause the designer to brut force a solution by 'trial and error' -- a very tedious and time consuming experience at best. One way to avoid this dilemma is by obtaining accurate phase and amplitude information from the X-parameters and then employing appropriate simulation tools. With this approach, designers can design the most robust systems possible in the shortest amount of time and with the highest degree of accuracy.

A Viable Solution

Utilizing a solution that employs both nonlinear component characterization and X-parameters provides critical insight, essential to accurately measuring a device's nonlinear behavior. Agilent Technologies' Nonlinear Vector Network Analyzer (NVNA) supports both methods in a highly integrated, powerful and simple to use instrument. With a minimum amount of external hardware, this solution effectively converts a 4-port PNA-X microwave network analyzer into a high-performance nonlinear analyzer from 10 MHz to 67 GHz (Figure 1). Because the NVNA is based on a standard PNA-X microwave network analyzer, it provides all the power, flexibility and measurement capability of the PNA-X for linear measurements. It can then easily switch into the NVNA mode for nonlinear measurement.

Figure 1: Agilent’s NVNA software, for use with the PNA-X microwave network analyzer, establishes a new industry standard in RF nonlinear network analysis from 10 MHz to 50 GHz.

Figure 1: Agilent’s NVNA software, for use with the PNA-X microwave network analyzer, establishes a new industry standard in RF nonlinear network analysis from 10 MHz to 67 GHz.

With the NVNA's nonlinear component characterization, all of the DUT's input and output spectra are measured. Both the amplitude and phase of the full spectra -- fundamental, harmonics, mixing terms and cross-frequency products -- are then displayed in the PNA-X network analyzer. The relative phase and absolute amplitude of any of the frequencies of interest can also be displayed. With this information, the designer can design a matching circuit to remove the nonlinear effects of, for example, the third harmonic as the amplitude and phase of that spectral component is explicitly known. This data can be displayed in frequency, time or power domains, as well as in terms of user-defined ratios such as I/V to display dynamic loadlines.

With its ability to display data in various domains, the NVNA provides the designer with greater insight into nonlinear component behavior. For example, if the DUT's output is distorted in the time domain, the designer can change to the frequency domain display and observe the individual frequency components' amplitude and phase. Next, the power can be varied to observe the sensitivity and level of significance which that spectral component has for given power levels, relative to the fundamental frequency of interest. The designer might also want to measure the group delay through a frequency doubler. This is a relatively easy task with the NVNA as it can measure the input and output stimulus phase -- relative to the calibrated phase reference -- as well as the signals amplitude. As an additional benefit, all measurement-based data collected with the NVNA can be exported to design models of the designer's choice.

The NVNA's other method of measuring nonlinear component behavior is through the use of nonlinear scattering parameters or X-parameters. Such functionality provides an accurate portrayal of both nonlinear device and cascaded nonlinear device behavior using measurement-based data. Additionally, the X-parameters can be accurately cascaded from individual devices using Agilent's ADS to simulate and design more complex modules and systems. These parameters separate out a critical term from the measurement, XT, which enables accurate nonlinear design and simulation by taking cross-frequency mismatch properly into account for nonlinear components.

When a single-tone stimulus is applied to the DUT, the X-parameters capture the device behavior at the fundamental frequencies and harmonics. Using a two-tone stimulus captures the fundamentals, harmonics and mixing products behavior. This is particularly useful in analyzing the bandwidth dependent characteristics and gaining additional insight into memory effects. X-parameters can also be extracted from 3-port mixers and converters. One large tone is applied to the RF and one large tone is applied to the LO. All three ports will be fully characterized in a similar fashion to the previously stated two port amplifier case. Combinations of amplifiers and mixers/converters can then be cascaded to predict and optimize module and system design and performance.


Accurately measuring and reducing a device's nonlinear behavior is crucial to creating linear high-power solutions for use in a range of applications in aerospace and defense and telecommunications, just to name a few. While conventional solutions to this challenge fail to provide the information and accuracy required, Agilent's NVNA software uses component characterization and X-parameters to quickly, easily and with the highest degree of accuracy measure nonlinear behavior in a DUT. With its full match correction and accurate amplitude, as well as cross-frequency relative phase information, the NVNA is today providing a new standard in accuracy and insight into the behaviors of nonlinear components.

About Agilent Technologies

Agilent Technologies Inc. (NYSE: A) is the world's premier measurement company and a technology leader in communications, electronics, life sciences and chemical analysis. The company's 19,000 employees serve customers in more than 110 countries. Agilent had net revenues of $5.4 billion in fiscal 2007. Information about Agilent is available on the Web at www.agilent.com.


Press Release: Agilent Technologies Introduces World’s Highest Performing 67 GHz PNA-X Vector Network Analyzer
  Agilent Technologies Expands Industry’s Most Flexible PNA-X Network Analyzer for Active Device Test with 13.5, 43.5, 50 GHz Models
  Agilent Technologies Introduces Breakthrough Technology to Analyze Nonlinear Behaviors of Active Components

Understanding Component Characterization Using the PNA-X Series Microwave Network Analyzers

Agilent Documents:

For more information, go to www.agilent.com/find/nvna


Janet Smith, Agilent
+1 970 679 5397

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