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Nonlinear Microwave Circuit Design phần 10

và tất cả các sóng hài bậc lẻ là 180 ◦ ofphase ra tại đầu ra, và do đó hủy bỏ, tín hiệu sóng hài thứ hai và tất cả các giai điệu thậm chí đặt hàng đang trong giai đoạn đầu ra, và kết hợp. Như sắp xếp, do đó, đảm bảo cách ly nội tại giữa đầu vào và đầu ra mà không cần phải cho các bộ lọc. | NONLINEAR ANALYSIS STABILITY AND BIFURCATIONS 349 loads at the relevant frequencies can be chosen so to satisfy Barkhausen s criterion or the instability criterion as defined in Section 5.2. If the stability factor is greater than 1 then the large-signal state must be modified for example by increasing the amplitude of the large-signal source or the bias point or the loads at harmonic frequencies in order to enhance the mixing properties of the active device in large-signal regime. If the design is performed at two ports at different frequencies the potential stability of the reduced network may be caused by the frequency-converting out of diagonal terms in the conversion matrix which connect the input and the output of the network if this is the case the potential instability vanishes for decreasing amplitude of the large periodic signal at 0 since no frequency conversion takes place for a small amplitude of the local oscillator. The instability appears only for a sufficiently large amplitude of the periodic large signal. In the opposite case that instability must be avoided the loads of the two-port network must be chosen so that the circuit is stable for all perturbation frequencies 0 osc ro very much as in linear amplifiers. This approach is quite general but 0 requires a modified formulation in the case that osc -ị because of the coincidence of upper and lower sidebands 6 . 8.3 NONLINEAR ANALYSIS STABILITY AND BIFURCATIONS 8.3.1 Stability and Bifurcations In this paragraph the parametric analysis of nonlinear circuits is introduced which allows the detection of bifurcations and the determination of the stable and unstable regions of operations of the circuit. In the previous paragraph a criterion for the determination of the stability of a nonlinear regime has been described. The reason why this criterion has been introduced lies in the capability of the harmonic or spectral balance algorithm to yield a solution even if the solution itself is not stable. A .