X-parameters were developed by Agilent Technologies to describe the behavior of both linear and nonlinear components in response to large-signal conditions. X-parameters reduce exactly to Sparameters in the small-signal limit and have the same simple use model as S-parameters. Because they contain information on all the harmonics and intermodulation spectra generated in response to large signals, they are much more powerful than S-parameters and any other nonlinear models available in the industry. X-parameters correctly characterize impedance mismatches and frequency mixing behavior to allow accurate, much faster simulation of cascaded nonlinear Xparameter blocks (e.g., amplifiers and mixers) in design.
X-parameters can be obtained in one of two ways: generated from a circuit-level design in Agilent's Advanced Design System (ADS) software or measured using the Nonlinear Vector Network Analyzer (NVNA) software running inside the Agilent PNA-X network analyzer. When generated from a circuitlevel design, they offer a simple means of quickly and accurately capturing a component's nonlinear behavior and saving it as transportable RF intellectual property (IP) models that can be used for circuit or system designs. X-parameter models can be used to share design performance without revealing design topology.
Agilent has published the equations underlying the X-parameter theory and the Xparameter files are in an open, non-encrypted format. Agilent has taken these steps to enable broad industry adoption and to encourage others to join in the development of the technology. To gain a better understanding of how circuit-level designers can easily generate fast and accurate, transportable X-parameter models, consider the example of a two-stage MMIC power amplifier (PA) designed in ADS for 3GPP Long Term Evolution (LTE) applications (Fig. 1). The goal is to generate a 50-O X-parameter model of the component. The same process outlined in this article can be used to generate accurate X-parameter models for mixers and other nonlinear components.
The first step in creating an Xparameter model is to generate the component's X-parameters. In ADS, this can be done by inserting the circuit-level design into a schematic page, attaching it to an X-parameter source, load, and bias, and clicking the "Simulate" button. In seconds, an X-parameter model is generated that can be e-mailed to the system integrator for immediate use.
To validate the accuracy of the generated model and compare it with the actual circuit-level MMIC PA, both the X-parameter model and MMIC PA design are inserted into a nonlinear simulation setup and nonlinear simulation and analysis are performed. Figure 2 shows the magnitude and phase of the fundamental, as well as the second and third harmonics of both results. This comparison clearly demonstrates that the X-parameter model has the same accuracy as that of the circuit level design and, therefore, a system integrator can insert the MMIC PA model into an LTE uplink transmit system design and use it as if it were the actual circuit-level PA.
The MMIC PA model was generated assuming a 50-O load and works well within a system matched to 50 O, accurate within about a 2.0:1 VSWR. If non-50-O modules are used in the system, a designer must be able to sweep the entire load over the Smith chart and generate a model that would work with any load impedance, not just in the 50-O region.
Figure 3 helps show the importance of load-dependent models. It shows the MMIC PA connected to a duplexer and antenna. If the load impedance on the PA is unknown, an impedance mismatch in magnitude and phase could result at both fundamental and harmonic frequencies. The only way to accurately predict the behavior of the PA in the system under any load impedance is a load-dependent X-parameter model that contains accurate information on the magnitude and phase of the fundamental frequency and all the harmonics.
An example of a design problem would be where the gamma load of the second harmonic on the PA creates distortion that degrades cell phone performance and possibly even PA efficiency and shortens battery life. To correct the problem, the exact magnitude and phase content of the second harmonic tone must be known in order to filter the unwanted harmonic signals. Unlike other available industry models that capture nonlinear behavior only on the fundamental frequency, the X-parameter model accurately captures the behavior on all the harmonics. By providing complete information on the magnitude and phase of the second harmonics, the model allows designers to filter out this unwanted second harmonic and improve the overall design and performance of the cell phone.
Generating a load-dependent model is simple and follows the process previously outlined, with the exception that a load sweep must be added to the design. A designer simply inserts the circuit-level PA design into a template in ADS, clicks the Simulate button and a model is automatically generated. This newly generated load-dependent X-parameter model is fully IP-protected and is automatically stored in the project's data set folder and can be immediately shared with the system integrator for accurate higher up simulation and tradeoff analysis on matched or mismatched cascaded modules.
Figure 4 shows simulation results from both the load-dependent model and the circuit-level PA with a gamma of 0.7 and phase between -180 and +180 deg. With these criteria, the generated model is accurate with any load impedance within 70 percent of the Smith chart. The overlaid power and power-added-efficiency (PAE) contours of the model and the circuit level PA demonstrate the accuracy of the X-parameter model to the circuitlevel PA.