Prediction of odd-mode instabilities under output mismatch effects
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A methodology is presented to predict odd-mode instability in power amplifiers under output mismatch effects, as in the case of amplifiers connected to an antenna. This kind of instability is often observed in multi-device configurations, due to their symmetry properties. Unlike the single-ended situation, there is a cancellation of odd multiples of the oscillation frequency at the circuit output, so there is no impact of the load-impedance values at the sideband frequencies. The odd-mode instability only depends on the impedance terminations at the fundamental frequency and its harmonic terms, and can only be detected within the circuit unstable loop, instead of the antenna-connection terminals. The possible unstable modes are related with the eigenvectors of an outer tier conversion matrix accounting for the symmetry properties of the circuit topology. Under sufficient low-pass filtering of the amplifier output network, the analysis parameters can be limited to the magnitude and phase of the reflection coefficient at the fundamental frequency. This analysis involves a computationally efficient graphical technique to detect potential instabilities and a bifurcation-detection method to determine the instability boundaries in the Smith chart. The two main types of instability from periodic regime are considered, respectively associated with incommensurable and subharmonic oscillations. Results have been validated through pole-zero identification and experimental measurements.