Very few phenomena in nature are purely linear. The same can be said for active devices in PCBs. At low signal levels, many devices can be approximated as linear, but their behavior becomes nonlinear at progressively higher signal levels. This is where a number of creative analysis techniques become important for determining the nonlinear behavior of many devices.

PCBs that include nonlinear components can be complex and can exhibit plenty of complicated signal integrity issues. Signal problems are usually addressed during interconnect design and layout. Simple linear passives can be addressed rather easily, but nonlinear devices can exhibit a number of unique signal integrity problems that arise due to their inherent nonlinearity. Simulations are very useful for determining the best design choices to alleviate signal integrity problems related to nonlinearity.

## What is Load Pull Analysis?

The central idea of load pull analysis is to examine how a device under test (DUT) responds to changes in the input impedance of a particular load. In this analysis, the load impedance presented to an active driver is changed, specific performance metrics and measured, and the resultant performance contours can be plotted for different load impedance values. In essence, you are comparing signals received at the load to the driver’s intended output as a function of load impedance.

As part of PCB design, the goal in load pull analysis is to simulate various performance metrics that are important for the particular application, and to gather numerical results that can be compared with real measurements. Load pull analysis has found a solid home in amplifier design, transistor characterization, and design of RF circuits and components.

As part of large-signal network analysis, load pull analysis is an excellent technique for examining the behavior of a nonlinear DUT at large signal level. As an example in RF design, the DUT’s or load’s nonlinear response can produce two-tone intermodulation products in adjacent channels, known as adjacent channel power ratio (ACPR). Even low-level intermodulation products can reduce download speeds in mobile devices that use a variety of modulation techniques, particularly in 5G systems that use carrier aggregation.

The results from load pull analysis as part of large-signal network analysis in this example can be used to determine appropriate driving power levels to bring signal integrity issues like intermodulation products within design standards, examine the effect of nonlinear signal integrity effects on bit error rates, and properly impedance match a load to the DUT at the desired frequency.

## Extracting Useful Design Insights from Load Pull Analysis

An important insight that can be gained from load pull analysis is to determine the appropriate range of load impedance values that will produce the desired output power or other performance metric for a DUT. You can also examine how the output is affected by variations in the load impedance. This is normally done at a specific frequency, although this process can be extended to modulated signals in order to examine distortion and intermodulation.

This is done by plotting performance contours on a Smith chart at a fixed input power. An example for showing the power delivered to a load from an amplifier that contains an FET is shown below. Each contour shows the load resistance and reactance values that produce a fixed power output value. At high frequencies, when parasitics become important, the contours tend to move away from the real axis. This will tell you the load resistance and reactance (i.e., impedance) that will produce the desired performance characteristics of the DUT. Note that these contours will also change if the input power is changed.

*Smith chart for a DUT*

During layout, if the load component has impedance that differs from value producing the best performance metrics for the DUT, you can then determine the required level of impedance matching. You can then use this information to select an appropriate termination resistor or design an impedance matching network at the particular frequency of interest.

## X-parameters vs. S-parameters

The results from load-pull analysis can be used to determine the X-parameters for a DUT in an N-port network. X-parameters are simply a generalization of S-parameters to nonlinear devices. If you know the X-parameters for a nonlinear DUT, then you can easily determine the relationship between input and output signals in an N-port network at a given frequency. X-parameters are really a functional map between input and output signals, meaning that the output from the DUT will be a function of the input power.

One might naturally ask “can’t I just determine the S-parameters for my DUT?” In the large signal regime, the answer is a solid “no.” S-parameters are explicitly defined in terms of the linear response of a two-port network (or more generally for an N-port network). S-parameters are only a linear approximation of X-parameters.

Each X-parameter for an output signal is normally written as a n-degree polynomial function of the input power at the particular frequency or impedance value of interest. X-parameters are normally determined at a specific frequency. When the output signal from the DUT is compared with the input signal, you plot the amplitude of the output signal and the phase difference as a function of input power. You can then use regression to determine the functional relationship between the input power and the output power for the DUT at specific load impedance values and frequencies.

When working with a signal that contains multiple harmonics, X-parameters can be generalized to multiple discrete frequencies, just like S-parameters. This nicely accounts for nonlinear frequency mixing. You will normally need to take Fourier transforms of time-domain waveforms or work directly in the frequency domain to determine the X-parameters for the DUT.

*Generalized X-parameters for input and output signals with multiple discrete frequencies*

For a signal with an arbitrary spectrum, determining a functional relationship between input and output signals is more difficult. This is where a set of 2-D maps (e.g, output power vs input frequency and load impedance, each at a particular input power) would need to be generated to get a generalized relationship for X-parameters of the DUT.

Diagnosing signal integrity problems can be tricky as your designs become more complex. Thankfully, the powerful signal integrity and power integrity tools in Sigrity are here to help. The Sigrity PowerSI package provides the tools designers need to analyze nonlinear effects in RF systems in the time domain and frequency domain, including load pull analysis. You can also examine how these nonlinear signal integrity effects impact other circuits on your board and how they are related to your PCB layout. This unique tool considers a range of IC packages for use in nonlinear circuit analysis.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.

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