Signal-Flow-Graph Analysis of Weakly Nonlinear Microwave Circuits Around a Large-Signal Operating Point

• Published in: IEEE transactions on microwave theory and techniques Vol. 71; no. 9; pp. 1 - 12
• Main Authors: Amakawa, Shuhei, Sugimoto, Ryotaro, Tokgoz, Korkut Kaan, Lee, Sangyeop, Ito, Hiroyuki, Kishikawa, Ryoko
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Circuits; Closed form solutions; Contours; Exact solutions; Frequency mixing; Graphical representations; Harmonic analysis; Impedance; Integrated circuit modeling; intermodulation distortion; Linear circuits; Microwave amplifiers; Microwave circuits; Nonlinear circuits; Parameters; polyharmonic distortion model; Reflectance; S-functions; Scattering parameters; Signal flow graphs; uncertainty propagation; X-parameters
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.2023.3248152

A signal flow graph (SFG) representation of small-signal responses of nonlinear microwave circuits around a large-signal operating point is developed using the X-parameters. It is shown that, unlike the SFGs for linear circuits, negative-frequency nodes need to be included explicitly. The development elucidates the circuit-operational meaning of the elusive T-type small-signal X-parameters, which represent the interaction between positive-and negative-frequency components. As an example, such an SFG is used to derive a closed-form expression of the output power of an amplifier as a function of the load reflection coefficient. It is then used to plot approximate load-pull power contours. The result is consistent with the expressions of the optimum load reflection coefficient derived by Root et al. (EuMIC 2017) and power contours derived by Peláez-Pérez et al. (TMTT 2013). SFGs provide an alternative systematic means to derive closed-form expressions in terms of X-parameters and gain illuminating insights into the workings of weakly nonlinear circuits.