X-parameter technology has developed rapidly since its pioneering introduction by Agilent with the Nonlinear Vector Network Analyzer (NVNA) in 2008. See [8] for a recent introduction. Agilent provides a complete set of mainstream interoperable SW and HW tools based on X-parameters that are already redefining how the industry characterizes, models, and designs nonlinear components and systems. Several real customer applications are presented illustrating the power and ease-of-use of X-parameters to solve a broad spectrum of important industry problems where modern components exhibit both high-frequency and nonlinear behavior. Moreover, with newly available simulation-based X-parameter design flow capabilities in Agilent ADS 2009U1 and significantly augmented NVNA-based X-parameter measurement capability, the many benefits of the X-parameter paradigm are now extended to a much wider set of components and customer applications than ever before.

Integrating Power Amplifiers into Cell Phones

The drive for improved battery life in personal communication devices requires the constituent power amplifiers to operate more efficiently. The price of efficiency is nonlinearity, namely the generation by the PA of distortion products in-band and also at harmonics that can interfere with the proper functioning of the cell phone. A critical problem for the industry is how to easily integrate such PAs into a handset and ensure, at the design stage, that the amplifier will still meet the overall system specifications when it interacts with other components, such as additional amplifiers or the antenna, in the phone. A concrete example of this problem is a dual-band GSM / Edge PA amplifier manufactured by Skyworks for integration into a cell phone manufactured by Sony-Ericsson [1].

Sony-Ericsson needed to characterize the effects of the amplifier output mismatch at the fundamental frequency and its implications for both power added efficiency (PAE) and levels of second harmonic distortion produced by the amplifier at the output. Without expensive, cumbersome, time-consuming, and ultimately impractical harmonic load-pull characterization, there was no systematic way to solve this problem without building and testing the phone. Sony-Ericsson designer Dr. Joakim Eriksson had read about X-parameters from the technical literature and asked Agilent to help by applying this technology to his problem. The Skyworks amplifier is shown in Fig. 1a. An X-parameter model of the full amplifier, including all control pins, was constructed from NVNA measurements. Comparison of the model simulation to data-sheet characteristics is shown in Fig. 1b. Sony-Ericsson used the IP-protected model to predict the output match as a function of the phase of signals incident into to the GSM_output port while the amplifier was driven hard into compression. The harmonic levels of distortion components produced were also simulated. The prediction of the X-parameters for the mismatch under drive is illustrated by the red elliptical shape in Fig. 1c. The previous best industry-standard methodology (“Hot S-parameters”) is shown in blue. Independent validation measurements using the NVNA are the colored symbols. The bottom line is that X-parameters predict mismatch under large input drive, Hot S22 does not.”

X-parameters solved the Sony-Ericsson problem. The process of characterizing the amplifier and two others from different manufactures on the NVNA, extracting the X-parameters, creating the complete PA model, and predicting the mismatch and other FOMs in ADS, took three days. The data acquisition time at the customer site using racks of equipment including load-pull systems took one month. Moreover, the X-parameter solution was much more complete. It provided a fully functional, measurement-based nonlinear model of the amplifier that could be freely shared without compromising IP, and re-used for a much wider range of applications and computations in ADS. Dr. Eriksson was so impressed with the benefits and new capabilities that he exclaimed, “We didn’t think this was possible!” The conclusion is that X-parameters enable predictive nonlinear design of important nonlinear systems from fundamentally nonlinear constituent building blocks. X-parameters solve, now, important industry problems, more completely, with more benefits, and in a fraction of the time it would take to deploy much less comprehensive industry standard solutions. This is why major companies are working to integrate X-parameters into their mainstream characterization, modeling, and design flows. As an example about how component providers are moving, Agilent Technologies will selectively offer GaAs and InP MMICs to the external market with accompanying X-parameter models. In fact, both the HBT amplifier (Agilent part number HMMC 5200) and the integrated InP 50GHz mixer (Agilent part number 1GC1-8068) will be among the first ICs available with X-parameter models.see for more information.

The X-parameters of a component allow system integrators to design-in the part and compare how well (or how poorly) the part works in the system. When used in ADS, the X-parameters serve as a fully interactive, “nonlinear electronic data sheet” that provides dramatically more component information necessary for large-signal applications than can be provided by stacks of paper or an Excel spreadsheet. Using X-parameters in ADS eliminates expensive and time-consuming bread-boards of the actual component. The electronic datasheet benefit is also a potential competitive advantage for the amplifier provider, who can provide downloadable “virtual X-parameter samples” of their component to their customers. X-parameters completely protect the IP of the component, but are faithful to the actual nonlinear performance (if measured) or fidelity to the models from which they were generated (if generated from simulation).This represents a significant evolution of the electronic eco-system including component manufacturers and system integrators.

X-parameters enable the prediction of nonlinear figures of merit (FOMs) of cascaded nonlinear interacting functional blocks, as in the Sony-Ericsson example. Let’s take adjacent channel power ratio (ACPR) as a specific case. ACPR is a scalar FOM. It is not generally possible to predict, say, ACPR of an entire chain of nonlinear components from knowledge only of the ACPR of the constituent parts. X-parameters contain the vector (magnitude and phase) properties of distortion from which predictions can be made, using ADS, about how components interact and how distortion propagates through chains of nonlinear components. With X-parameters, it is possible to predict, using ADS, not only the ACPR of the component, but also how the ACPR varies due to mismatch effects that it might encounter when inserted into a circuit or system design. In fact, X-parameters enable the cascading of nonlinear components just as S-parameters do for linear components. Therefore, the overall nonlinear FOMs of a system can be computed with high accuracy in the design stage, from knowledge only of the X-parameters of the constituent nonlinear components. This is a game-changing proposition for nonlinear design.

Generation X: Second Generation X-parameter technology

Simulation-based X-parameter design flow: high-fidelity IP-protected behavioral models for hierarchical design and simulation speedup.

With the release of second generation X-parameter technologies, there are now two complete bottom-up design verification flows available from Agilent. These are depicted in Fig.2. A comparison of major advantages of both the measurement-based and simulation-based X-parameter design flows are indicated in Fig. 3.

Generating X-parameters from schematics

The new simulation-based X-parameter design flow in ADS2009U1 provides a host of additional benefits addressing long-expressed but previously unmet customer design and simulation needs. Nonlinear RF circuits and systems can be extremely complicated, containing hundreds or even thousands of nonlinear components. Simulating an entire circuit at the transistor level of description may not be possible, given the complexity of the thousands of nonlinear equations. Even if the entire circuit can be simulated, the simulation may be so slow as to preclude or limit the designer’s ability to efficiently optimize its performance. Now, with ADS2009U1, it is possible to apply X-parameters as a hierarchical design enabler directly within the simulator. A new “X-parameter generation” capability is built-in to ADS2009U1 that allows the user to convert their complicated component models from schematics directly into X-parameters! This enables the performance characteristics of a sensitive design to be captured, and be sent to potential customers with complete IP security and fidelity of function. The new ADS capability is sufficiently general to generate multi-tone and multi-port (mixer and converter) simulation-based models. An example is given of an actual InP integrated 50 GHz mixer (Agilent part # 1GC1-8068) in Fig. 4. This circuit contains over 40 heterojunction bipolar transistors realized in Agilent’s proprietary InP IC technology, each of which is represented with an Agilent HBT model [2]. The accuracy of the X-parameter representation compared to the detailed circuit-level model is typical. Moreover, the X-parameter model maintains significant accuracy compared to the circuit model even under significant mismatching of the IF port.

Improved X-parameter simulation component for dramatic speed improvement

A significantly improved X-parameter simulation component in ADS2009U1 can now take full advantage of the inherent speed of X-parameters. X-parameters are inherently fast because they describe the component behavior in the mathematical langue native to the simulation algorithms used to solve the nonlinear problem most efficiently [3], in this case harmonic balance and circuit envelope analysis. In some cases, simulation speedup by a factor of 100 has been achieved by replacing complex circuits and “compact” transistor models with X-parameters. The X-parameters are high-fidelity behavioral representations of the models from which they are generated. In fact, X-parameters can effectively replace all the various point behavioral models previously offered in ADS and provide many additional benefits. Reduction of complexity while maintaining accuracy enables simulation of larger parts or even the entire design, rather than having to make due simulating only a subset of functional blocks and hoping their mutual interaction can be ignored.

Prior even to fabricating a device such as a PA, it is possible to start designing systems around it by starting from circuit-level models of the component, then converting them into X-parameters and designing efficiently at the next level of abstraction. Eventually, when the component is actually manufactured, it is possible simply to substitute actual NVNA- measured X-parameters for the virtual X-parameters to provide a bottom-up detailed measurement-based verification.

Hierarchical design of nonlinear RF systems with X-parameters

X-parameters enable a hierarchical nonlinear design flow, for which there is no generic equivalent. It is quite analogous to what is common practice for S-parameters in the design of linear systems from linear components. For example, the X-parameters of individual amplifier stages can be combined to produce a single X-parameter representation of the cascaded structure. This in turn can be combined with X-parameters of a mixer or converter and the entire front-end of an RF nonlinear system can be hierarchically extracted and reused. An example of an RF system designed with a measurement-based amplifier model from an actual Agilent HMMC 5200 HBT amplifier, and a simulation-based X-parameter model of an actual Agilent 1GC1-8068 InP 50GHz Mixer is is shown in Fig 5.

Second Generation X-parameter measurement capabilities.

Load-dependent X-parameters
It is often desired to design matching networks for high-power transistors and PAs so as to optimize scalar performance FOMs such as power delivered and power added efficiency. High power transistors have characteristic output impedances closer to 1 ohm that the typical 50 ohm environment of traditional VNA-based receivers, so the measurement is more complicated. Traditionally, load-pull has been the measurement methodology of choice for such purposes. However even with complete load-pull data it is not generally possible to generate full two-port nonlinear functional block models of the component for generic design purposes. For example, classic load-pull does not provide sufficient information to design and optimize multi-stage amplifiers where accurate input-to-output phase and scattered waves including harmonics at the input port are required. By enabling X-parameter measurements to work seamlessly with automatic tuners, X-parameters systematically solve these problems and provide much more comprehensive component information immediately usable in the ADS simulator for nonlinear design. “The data is the model.”

Earlier this year, Agilent and channel partner Maury Microwave teamed up to introduce another industry breakthrough: arbitrary load-dependent X-parameters. This is an interoperable SW/HW solution involving Maury ATS load-pull SW, Maury load tuners, new Agilent NVNA option 520, and the enhanced X-parameter simulation component in ADS. A picture of the HW is shown in Fig. 6. The Maury SW runs on the Agilent PNA-X based NVNA. Simple graphical input allows complex load states to be specified throughout the Smith chart. X-parameters are measured, and using embedded Agilent IP, calibrated for uncontrolled harmonic impedances presented to the DUT by the tuner and corrected for any imperfection in achieving desired gridded impedance states. A complete nonlinear two-port functional block X-parameter model representing the component’s nonlinear behavior versus power, frequency, complex load, and bias is instantly created from these measurements. A simple drag-and drop file transfer is all that is needed to begin immediate nonlinear design of matching circuits, multi-stage amplifiers etc. The seamless link between advanced nonlinear measurements and nonlinear design capability prompted Gary Simpson, Director of RF Device Characterization at Maury Microwave Corporation, to proclaim this commercial solution “a breakthrough for the industry.”

This solution is highly automated, extremely accurate, and provides much more benefit than conventional load-pull. It reduces to S-parameters in the small-signal limit. Unlike conventional load-pull, it includes full input-to-output phase information and the magnitudes and cross-frequency phases of harmonics as well. Not only is the new X-parameter solution a superset of S-parameters and Load-Pull, it provides a much more comprehensive instant generic large-signal model for design in ADS.

A concrete example of applying arbitrary load-dependent X-parameters to a commercial packaged transistor is shown in Fig. 7. The X-parameters are able to predict the detailed current and voltage waveforms of the transistor at any impedance over the entire Smith chart! The model can be cascaded even under very strong mismatch conditions and predict the effects of inter-component interaction – perfect for multi-stage design. This new design approach is complementary to conventional active device models. It is especially attractive where there are no good “compact” device SPICE or ADS transistor models available, such as the case for novel technologies (e.g. GaN) or new component realizations [5,6]. This approach enables measurement-based simulation of time-domain waveforms under very strong compression at virtually any impedance. For the first time, practical commercial measurement tools can provide the information that large-signal simulators produce; it is essentially “experimental harmonic balance.”

As an added bonus, the capabilities of arbitrary load-dependent X-parameters are so powerful that they can also predict the effects of independently tuning the harmonic terminations of the components, even though these terminations are not independently controlled during the characterization process [7]. This is validated in Fig. 8 for a 10W GaN transistor. This examples demonstrates that for many high power device and amplifier applications, it is not necessary to use time-consuming, expensive, harmonic load-pull systems which require many more load states (each load at each port at each harmonic controlled separately) to obtain the sensitivity of device performance to harmonic terminations. This is another case where X-parameters cause customers to say “we didn’t think this was possible.”

Multi-tone X-parameter capabilities, already available in ADS2009U1, will soon be available as an application on the NVNA. This will enable the magnitude and phase of tone-spacing dependent intermodulation distortion to be characterized, and be used immediately by the ADS2009U1 X-parameter simulation component. This calibrated nonlinear cross-frequency vector distortion information can be used for designing distortion cancellation circuits and apply other design principles, such as derivative superposition [9], that previously could be applied only if there was confidence in accurate nonlinear device models. Extending the NVNA to measure three-port devices, such as mixers and converters, is also underway. This capability will fundamentally change the way these foundational components are characterized and designed into RF systems.

Additional X-parameter measurement enhancements

NVNA instruments now are available in 13.5 GHz, 26 GHz, 43.5 GHz, and 50 GHz versions. X-parameters can therefore be measured to twice the frequency that they could be measured at the introduction of the original NVNA in 2008. Moreover, with a new Agilent applications note, customers can now measure X-parameters on power devices up to 250W! This makes the benefits of X-parameters applicable to market segments including base station amplifiers and high-power transistors.

X-parameter based transistor modeling

X-parameters offer a significant value by providing a complimentary approach to transistor modeling, compared to the traditional physically-based or empirical “compact” models. Compact models, such as the Berkeley BSIM 4 MOSFET [10] model and the Agilent HBT [2] compound hetero-junction bipolar transistor model are very comprehensive models with scores of nonlinear equations. They each have over 100 parameters that must be extracted to associate the model with a given process technology. Accurate state-of-the art models take years to develop, and can then takes days or weeks to properly extract. There is an urgent need for fast, accurate, and easily extractable nonlinear models from measurements of devices for which there is not a good compact model. This is especially true in new technology areas, such as GaN. Fortunately, there is a simple X-parameter based procedure that provides an attractive alternative. Simply measure the X-parameters of the component on the NVNA, drag-and-drop the resulting file into ADS, and you’re off designing nonlinear circuits immediately. Figures 7 and 8 are examples of such models. Another example from an NVNA and X-parameter customer at National Nano Device Labs in Taiwan is the extraction of X-parameters from a novel annular Si transistor for which there was no available model. The results were reported at the International Microwave Symposium in June, 2009 [5]. The X-parameter model demonstrated an excellent prediction to intermodulation distortion measurements over a wide range of input power, and also predicted very well the detailed time-domain distorted waveforms under very large-signal excitations. Results were reported by Guyan et. al at the2009 IEEE ARFTG conference validating arbitrary load-dependent X-parameters for a GaAs MESFET transistor under WCDMA stimulus [6]. These examples illustrate the power of X-parameters as an accurate, technology independent device modeling approach. With X-parameters, there is no need to wait for a Ph.D. expert to implement and debug a new compact transistor model. There is no need to spend days or weeks of a modeling engineer’s time to extract the hundreds of parameters of a conventional model in order to design with the component. X-parameters are much easier, more automated, and more repeatable to extract from measurements on the NVNA than standard compact models are to extract from DC and linear S-parameter measurements. Moreover, measurement-based X-parameter models are extremely accurate because the nonlinear data, properly characterized by the NVNA, are the basis for simulating the component behavior when used for design in ADS.


X-parameters have moved from exciting research demonstrations to mainstream commercial measurement instruments (Agilent NVNA) and EDA design tools (Agilent ADS) [11]. Interoperable NVNA-based X-parameter measurements and simulation-based X-parameter design flows in Agilent ADS provide the same ease-of-use as familiar linear S-parameters but with unprecedented power and much greater benefits. X-parameters unify linear S-parameters, nonlinear load-pull, and modern wave-form measurements for more complete nonlinear characterization and predictive nonlinear design of RF and microwave components and systems. Agilent has developed industry-leading products for each piece of the nonlinear puzzle, with extensive built-in IP, and designed them fit together, seamlessly. Dramatic time and cost savings have been realized using X-parameters to do familiar things better. Completely new capabilities engendered by X-parameters enable novel characterization, design, and verification approaches, providing substantial competitive advantages to customers who both create and consume nonlinear components from transistors to RF and microwave nonlinear systems.

The author thanks the extended Agilent X-parameter team for their contributions and Agilent management for support.


[1] J. Horn, J. Verspecht, D. Gunyan , L. Betts, D. E. Root, and Joakim Eriksson, “X-Parameter Measurement and Simulation of a GSM Handset Amplifier,” 2008 European Microwave Conference Digest Amsterdam, October, 2008
[2] M. Iwamoto and D. Root, Agilent HBT Model: Overview. Compact Model Council Meeting, December, 2006
[3] D. E. Root, J. Wood, and N. Tufillaro, “New Techniques for Non-Linear Behavioral Modeling of Microwave/RF ICs from Simulation and Nonlinear Microwave Measurements,” in 40th ACM/IEEE Design Automation Conference Proceedings, Anaheim, CA, USA, June 2003, pp. 85-90
[4] G. Simpson, J. Horn, D. Gunyan, and D.E. Root, “Load-Pull + NVNA = Enhanced X-Parameters for PA Designs with High Mismatch and Technology-Independent Large-Signal Device Models,” IEEE ARFTG Conference, Portland, OR December 2008
[5] Chiu et al “Characterization of annular-structure RF LDMOS transistors using polyharmonic distortion model,” in IEEE MTT-S International Microwave Symposium Digest, 2009 pp 87-90.
[6] D. Gunyan et al, “Nonlinear Validation of Arbitrary Load X-parameter and Measurement-Based Device Models,” IEEE MTT-S ARFTG Conference, Boston, MA, June 2009.
[7] J. Horn et al, “Harmonic Load-Tuning Predictions from X-parameters,” IEEE PA Symposium, San Diego, Sept. 2009
[8] D. E. Root et al “X-parameters: The new paradigm for measurement, modeling, and design of nonlinear RF and microwave components,” Microwave Engineering Europe, December 2008 pp 16-21.
[9] Webster, D.; Scott, J.; Haigh, D; “Control of circuit distortion by the derivative superposition method,” IEEE Microwave and Guided Wave Letters, Vol 6, no. 3, March 1996 pp123-125.
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