A Novel Analytical Design Approach for Determining the Optimum Load to Minimize Harmonic Output Power Based on X-Parameters

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

“…9(b). If the optimum load reflection coefficient turns out to lie far from the center of the Smith chart, the region of validity can and should be shifted by choosing a different value of R ref when "measuring" X-parameters [15], [16], [19]. This is nearly equivalent to lifting the load-independence assumption (Section II).…”

“…Here we show that ( 17) can be used to get approximate load-pull power contours. |B 2,1 | 2 gives the power presented to the load by the PA, but part of it will be reflected by the load according to (19) unless Γ L,1 = 0. The power absorbed by the load is given by…”

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

“…The accuracy could be improved, for example, by shifting the region of good accuracy to a region of interest (e.g. high output power) by making a clever choice of load impedance [20], [24] (although this does not enlarge the region of good accuracy), by making X-parameters loaddependent [11], [15] (at the cost of long measurement time), by considering higher-order derivatives [39], [40], and/or by using more sophisticated extrapolation than Taylor expansion [41]. But since pursuing numerical accuracy is not the purpose of this paper, we just use load-independent X-parameters with a fixed load impedance of 50 Ω in the following.…”

“…This was a known limitation of load-independent X-parameters. If the optimum load reflection coefficient turns out to lie far from the center of the Smith chart, the region of validity can and should be shifted by choosing a different value of load impedance that defines the LSOP [19], [20], [24]. In this load-dependent case, the LSOP term of (9) becomes dependent on A 2,1 (or on Γ L,1 via A 2,1 = Γ L,1 B 2,1 [11], [15], [16], [23]) as follows:…”

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

“…Similar frameworks to X-parameters include "S-functions" [12], [13], [14]. Although X-parameters can be black-box models of nonlinear devices and circuits [15], [16], applications of X-parameters toward analytic design or modeling of nonlinear circuits and devices have recently made great progress [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27]. Dunsmore [28, p. 427] described the findings of [22] as "a breakthrough."…”