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6 - Memory

Published online by Cambridge University Press:  05 October 2013

David E. Root ,
Jan Verspecht ,
Jason Horn  and
Mihai Marcu
David E. Root
Affiliation:
Agilent Technologies
Jan Verspecht
Affiliation:
Agilent Technologies
Jason Horn
Affiliation:
Agilent Technologies
Mihai Marcu
Affiliation:
Agilent Technologies
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Summary

Introduction

X-parameters were introduced in Chapter 2 as frequency-domain nonlinear mappings. The X-parameter functions are defined on the complex amplitudes of the incident CW signals, returning the complex amplitudes of the scattered CW signals. For fixed power, bias, and load conditions, these input and output amplitudes are constant (in time) complex numbers. As such, X-parameters were defined only for steady-state conditions.

Real applications deal with signals that vary in time and the corresponding time-varying responses of DUTs to such stimuli. In particular, signals used in wireless communications can have independent time-varying values for the amplitudes and phases associated with each of the multiple carriers involved. These time-dependent modulations contain the information associated with the signal. Much of communication systems design is devoted to trying to preserve the information content of these signals while efficiently amplifying, transmitting, and then demodulating them at the receiver to recover the information.

This chapter introduces the notion of dynamics into the signals and into the mappings between input and output stimuli that define the DUT as a nonlinear dynamic system. The envelope domain is introduced to define the class of signals considered. Quasi-static applications of static X-parameters are introduced as methods for estimating the DUT’s response to modulated signals, and limitations are discussed. Examples are provided of phenomena that require the abandonment of the static nonlinear system description. This introduces the notion of memory, where the response of the system depends not only on the instantaneous value of the input signal, but also on the history of the input signal. The concept of modulation-induced baseband memory is articulated.

Type
Chapter
Information
X-Parameters
Characterization, Modeling, and Design of Nonlinear RF and Microwave Components
 , pp. 150 - 188
Publisher: Cambridge University Press
Print publication year: 2013

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References

Rudolph, M., Fager, C., and Root, D. E., Eds., Nonlinear Transistor Model Parameter Extraction Techniques. Cambridge: Cambridge University Press.CrossRef
Soury, A. and Ngoya, E., “Handling long-term memory effects in X-parameter model,” in IEEE Int. Microwave Symp. Dig., Montreal, Canada, June 2012, pp. 1–3.Google Scholar
Verspecht, J., Horn, J., Betts, L., Gillease, C., and Root, D. E., “Extension of X-parameters to include long-term dynamic memory effects,” in 2009 IEEE MTT-S Int. Microwave Symp. Dig., Boston, MA, June 2009, pp. 741–744.CrossRefGoogle Scholar
Wood, J., Root, D. E., and Tufillaro, N. B., “A behavioral modeling approach to nonlinear model-order reduction for RF/microwave ICs and systems,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 9, part 2, pp. 2274–2284, Sept. 2004.CrossRefGoogle Scholar
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Xu, J., Iwamoto, M. M., Horn, J., and Root, D. E., “Large-signal FET model with multiple time scale dynamics from nonlinear vector network analyzer data,” in IEEE MTT-S Int. Microwave Symp. Dig., Anaheim, CA, May 2010, pp. 417–420.Google Scholar
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Verspecht, J., Horn, J., Nielsen, T., and Root, D. E., “Extension of X-parameters to include long-term memory effects,” in IEEE ARFTG Conference, Clearwater Beach, FL, Dec. 2010.Google Scholar
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Root, D. E., Sharrit, D., and Verspecht, J., “Nonlinear behavioral models with memory: formulation, identification, and implementation,” IEEE MTT-S Int. Microwave Symp. Workshop (WSL) on Memory Effects in Power Amplifiers, San Francisco, CA, June 2006.Google Scholar
Verspecht, J., Gunyan, D., Horn, J., Xu, J., Cognata, A., and Root, D.E., “Multi-tone, multi-port, and dynamic memory enhancements to PHD nonlinear behavioral models from large-signal measurements and simulations,” in IEEE MTT-S Int. Microwave Symp. Dig., Honolulu, HI, June 2007, pp. 969–972.Google Scholar

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