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  • Print publication year: 2013
  • Online publication date: October 2013

6 - Memory



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.

Rudolph, M., Fager, C., and Root, D. E., Eds., Nonlinear Transistor Model Parameter Extraction Techniques. Cambridge: Cambridge University Press.
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.
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.
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.
Root, D. E., Wood, J., and Tufillaro, N., “New techniques for nonlinear behavioral modeling of microwave/RF ICs from simulation and nonlinear microwave measurements,” in 40th ACM/IEEE Design Automation Conf. Proc., Anaheim, CA, June 2003, pp. 85–90.
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.
Pedro, J. C. and Maas, S. A., “A comparative overview of microwave and wireless power-amplifier behavioral modeling approaches,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 4, Apr. 2005.
Soury, A., Ngoya, E., and Nebus, J. M., “A new behavioral model taking into account nonlinear memory effects and transient behaviors in wideband SSPAs,” in 2002 IEEE MTT-S Conf. Dig., Seattle, WA, June 2002, pp. 853–856.
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.
Wood, J. and Root, D. E., Fundamentals of Nonlinear Behavioral Modeling for RF and Microwave Design. Norwood, MA: Artech House, 2005, chap. 3.
Additional reading
Roblin, P., Root, D. E., Verspecht, J., Ko, Y., and Teyssier, J. P., “New trends for the nonlinear measurement and modeling of high-power RF transistors and amplifiers with memory effects,” IEEE Trans. Microw. Theory Tech., vol. 60, no. 6, part 2, pp. 1964–1978, 2012.
Root, D. E., Iwamoto, M., and Wood, J., “Device modeling for III-V semiconductors: an overview,” IEEE CSIC Symp., Monterey, CA, 2004, pp. 279–282.
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.
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.