For more than a quarter of a century, microwave engineers have had the benefit of a foundation of mutually interacting components of measurement, modeling, and simulation to design and test linear components and systems. S-parameters are perhaps the most successful behavioral models ever. They have the powerful property that the S-parameters of individual components are sufficient to determine the S-parameters of any combination of those components. S-parameters of a component are sufficient to predict its response to any signal, provided only that the signal is of sufficiently small amplitude. We have presented the PHD modeling approach. It is a black-box frequency-domain model that provides a foundation for measurement, modeling, and simulation of driven nonlinear systems. The PHD model is very accurate for a wide variety of nonlinear characteristics, including compression, AM-PM, harmonics, load-pull, and time-domain waveforms. The PHD model faithfully represents driven nonlinear systems with mismatches at both the fundamental and harmonics. This enables the accurate simulation of distortion through cascaded chains of nonlinear components, thus providing key new design verification capabilities for RF and microwave modules and subsystems

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Polyharmonic distortion modeling

This paper aims at providing a global perspective on electromagnetic nonreciprocity and clarifying confusions that arose in the recent developments of the field. It provides a general definition of nonreciprocity and classifies nonreciprocal systems according to their linear time-invariant (LTI), linear time-variant (LTV) or nonlinear nonreciprocal natures. The theory of nonlinear systems is established on the foundation of the concepts of time reversal, time-reversal symmetry, time-reversal symmetry breaking and related Onsager- Casimir relations. Special attention is given to LTI systems, as the most common nonreciprocal systems, for which a generalized form of the Lorentz reciprocity theorem is derived. The delicate issue of loss in nonreciprocal systems is demystified and the so-called thermodynamics paradox is resolved from energy conservation considerations. The fundamental characteristics and applications of LTI, LTV and nonlinear nonreciprocal systems are overviewed with the help of pedagogical examples. Finally, asymmetric structures with fallacious nonreciprocal appearances are debunked.

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What is Nonreciprocity

The paper presents the power amplifier design. The introduction of a practical harmonic balance capability at the device measurement stage brings a number of advantages and challenges. Breaking down this traditional barrier means that the test-bench engineer needs to become more aware of the design process and requirements. The inverse is also true, as the measurement specifications for a harmonically tuned amplifier are a bit more complex than just the measurement of load-pull contours. We hope that the new level of integration between both will also result in better exchanges between both sides and go beyond showing either very accurate, highly tuned device models, or using the device model as the traditional scapegoat for unsuccessful PA designs. A nonlinear model and its quality can now be diagnosed through direct comparison of simulated and measured wave forms. The quality of a PA design can be verified by placing the device within the measurement system, practical harmonic balance emulator into the same impedance state in which it will operate in the actual realized design.

Waveform Inspired Models and the Harmonic Balance Emulator

According to Mike McKinley of Georgia Tech, it's "the holy grail of microwave instrumentation and measurements," it's "a new measurement science" according to Don DeGroot of Connected Community Networks and "an enabling path to taking nonlinear models to a higher level of fidelity and value" says Larry Dunleavy of Modelithics. I prefer to call it large-signal network analysis (LSNA). Today, LSNA is undoubtedly still in its infancy. A small community knows about the theoretical concepts, and a happy few have access to LSNA hardware. This community is growing rapidly, however, and I have no doubt that the people of this community will soon revolutionize the microwave measurement business as profoundly as S-parameter technology did in the 1980s. I hope with this article to inspire you to join this rapidly growing LSNA community that is improving microwave measurements and is on its way to building a multimillion dollar business.

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Large-signal network analysis

RF I-V waveform measurement and engineering systems are now finally enabling practical waveform engineering to be directly undertaken with systems capable of supporting continuous wave stimulus reaching a high level of maturity. On-going research and development activities are presently addressing the multitone requirement. The availability of RF I-V measurement and engineering capability extends the characterization opportunities for both high-frequency/speed transistor technology developers and circuit/system designers; terminal waveforms are the unifying theoretical link between transistor technology, circuit design, and system performance. Design support can involve the direct utilization of such a measurement system in the design investigation/evaluation loop of either power transistor technology or PAs. This eliminates the black box design processes and allows for the development of new intelligent design processes that are completely founded on theoretical waveform analysis. Alternatively, it can also indirectly support the amplifier investigation/evaluation loop by supporting the development or improving the accuracy of nonlinear transistor models or by providing CAD-accessible behavioral or behavioral model parameter datasets. W can now only hope that, triggered by the availability of RF waveform measurement and engineering systems, we will see a renaissance in theoretical waveform mathematical analysis addressing not only power and efficiency but also design sensitivity and linearity.

Practical waveform engineering

We present an optimal experiment design methodology and a superior and fully automated model generation procedure for identifying a class of broad-band multiharmonic behavioral models in the frequency domain. The approach reduces the number of nonlinear measurements needed, minimizes the time to generate the data from simulations, reduces the time to extract the model functions from data, and when used for simulation-based models, takes maximum advantage of specialized simulation algorithms. The models have been subject to extensive validation in applications to real microwave integrated circuits. The derived model is valid for both small and large amplitude drive signals, correctly predicts even and odd harmonics through cascaded chains of functional blocks, simulates accurately load-pull behavior away from 50 /spl Omega/, and predicts adjacent channel power ratio and constellation diagrams in remarkably close agreement to the circuit model from which the behavioral model was derived. The model and excitation design templates for generating them from simulations are implemented in Agilent Technologies' Advanced Design System.

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Broad-band poly-harmonic distortion (PHD) behavioral models from fast automated simulations and large-signal vectorial network measurements

An improved circuit simulator for simulating the response of a circuit to a transient. The stimulating signal is represented by one or more carriers having time varying modulation envelopes. The simulator differs from a harmonic balance simulator in that the currents provided by each of the device subroutines include an additional term at each carrier frequency having the time dependency of the modulation envelope at that frequency. These additional current terms necessitate a time-domain solution of the simulation problem; however, the time steps are now determined by the time variation of the envelope instead of the time variation of the carrier. As a result, the number of time steps needed in the simulation is greatly reduced. The present invention may be implemented by modifying a conventional harmonic balance simulator. The modifications involve adding code to the various device routines to provide the current term corresponding to the modulation envelope. In the preferred embodiment of the present invention, either a charge term or a current term that depends on present and past values of the modulation envelope is provided by each device routine. The sum of the charge terms at each carrier frequency is then differentiated to provide the sum of the envelope current terms.

Method for simulating a circuit

A model of a device is generated. An input port of the device is stimulated with a large amplitude signal having a central frequency. A first port of the device is perturbed with a small amplitude signal tone. The small amplitude signal tone is at a frequency offset slightly from a harmonic of the central frequency. Spectral component frequencies of a resulting signal from the device are obtained to determine model coefficients for the device. At least some of the spectral component frequencies occur at frequencies offset slightly from harmonics of the central frequency.

Behavioral model generation

A signal analyzer has an analysis scale and a display scale that are independently selectable. The signal analyzer receives a first representation of an applied signal and provides from the first representation at least two alternative representations. A first selective input enables a designated one of the alternative representations to be applied to a filter to reduce variance of the designated representation. The signal analyzer then converts the received one of the alternative representations having reduced variance to at least two alternative display scales. A second selective input enables a designated one of the alternative display scales to be displayed on a monitor, display screen or other output device of the measurement instrument or system. Independent control of the first selective input and the second selective input via a user interface enables the analysis scale—the scale, or representation, to which the filter is applied, to be selected independently of the scale on which the representation having reduced variance is displayed.

David D. Sharrit

Papers

Broad-band poly-harmonic distortion (PHD) behavioral models from fast automated simulations and large-signal vectorial network measurements

Method for simulating a circuit

Behavioral model generation

Signal analyzer having independent analysis and display scales

Verfahren zur Simulation einer Schaltung