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

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 interaction between positive- and negative-frequency components. As an application example, such an SFG is used to derive a closed-form expression of the output power of a power 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 and more general than the expression of the optimum load reflection coefficient derived analytically by Root et al. (EuMIC 2017). SFGs provide a systematic means to derive closed-form expressions in terms of X-parameters and to gain illuminating insights into the workings of weakly nonlinear circuits.