Stability investigations based on two-port describing functions

Stability of a nonlinear, tuned amplifier has been investigated based on the describing function method. On stability, this paper means global asymptotic stability. The tuned amplifier comprises a saturated amplifying device with feedback and two resonators, at the input and the output. Describing function method here means introduction of the two-port describing functions.

Describing function method is applied, extended for two ports. Results from complex analysis and matrix algebra are heavily used. The two resonators have identical resonant frequency and bandwidth. Instability is represented by non-vanishing output perturbation for zero-input perturbation. Applying a simple transistor model with saturation and feedback, stability is analyzed in the form of output voltage as a function of input voltage.

Two-port scattering and admittance describing functions have been introduced. At a certain input voltage amplitude, instability appears in the form of unwanted sidebands, then at a higher input voltage, instability disappears, in good agreement with experiments. The hand calculated stability limits are in good agreement with the computer analysis.

The paper is based on an early publication of the author (Baranyi and Ladvánszky, 1984). Here, the full material is presented, explained step by step, extended and revised. All neglections that were earlier made in the author’s paper have been avoided here. This paper has significant tutorial value as well.