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  • Cited by 50
  • Print publication year: 2013
  • Online publication date: October 2013

5 - Multi-tone and multi-port cases



In this chapter, the general X-parameter formalism is applied in two different cases of great practical interest beyond the simplest case of nearly matched components under large drive considered in Chapter 3. Specifically, X-parameter expressions are developed by spectral linearization around an LSOP defined by the DUT in response to two large incident signals, as opposed to the case of just one large signal considered in Chapter 3.

The first case is an example of two signals whose frequencies, f1 and f2, are the same, but are incident with distinct phases at different ports. This is an important subcase of a commensurate frequency relationship, namely f1/f2 = n/m for n and m integers. The second case considers incommensurate frequencies, where the ratio of the two signal frequencies is irrational. Whether or not the signals are commensurate affects the dimension of the LSOP as well as the form of the time-invariant X-parameter equations, as will be evidenced below.

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Woodington, S., Saini, R., Williams, D., Lees, J., Benedikt, J., and Tasker, P. J., “Behavioral model analysis of active harmonic load-pull measurements,” in 2010 IEEE MTT-S Int. Microwave Symp. Dig., Anaheim, CA, may 2010, pp. 1688–1691.
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Additional reading
Hashmi, M. S., Ghannouchi, F. M., Tasker, P. J., and Rawat, K., “Highly reflective load-pull,”IEEE Microwave, vol. 12, no. 4, pp. 96–107, 2009.
Horn, J., Woodington, S., Saini, R., Benedikt, J., Tasker, P. J., and Root, D. E.; “Harmonic load-tuning predictions from X-parameters,” in IEEE PA Symp., San Diego, CA, Sept. 2009.
Root, D. E., Horn, J., Nielsen, T., et al., “X-parameters: the emerging paradigm for interoperable characterization, modeling, and design of nonlinear microwave and RF components and systems,” in IEEE Wamicon 2011 Tutorial, Clearwater, FL, Apr. 2011.
Saini, R. S., Woodington, S., Lees, J., Benedikt, J., and Tasker, P. J., “An intelligence driven active loadpull system,” in IEEE Microwave Measurements Conf. (ARFTG), Anaheim, CA, 2010, pp. 1–4.
Simpson, G., Horn, J., Gunyan, D., and Root, D. E., “Load-pull + NVNA = enhanced X-parameters for PA designs with high mismatch and technology-independent large-signal device models,” in IEEE ARFTG Conf., Portland, OR, Dec. 2008, pp. 88–91.
Tasker, P., “Practical waveform engineering,”IEEE Microwave, vol. 10, no. 7, pp. 65–76, 2009.
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 2007 IEEE MTT-S Int. Microwave Symp. Dig., Honolulu, HI, June 2007, pp. 969–972.