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Time-Varying Root-Locus of Large-Signal LC Oscillators

Time-varying root-locus of a large-signal LC oscillator is obtained via semi-symbolic analysis, where the complex frequency s is a symbol. The steady-state circuit behavior is modeled by its time-varying small-signal admittance matrix within one oscillation period. The roots of the characteristic equation are computed with the QZ method. The time-varying root-locus analysis capabilities are demonstrated on a GHz range 130 nm complementary metal-oxide-semiconductor cross-coupled LC oscillator, and they complement the results obtained with the traditional numerical computer-aided design methods.