Perturbation theory for generalized van der Pol-type resonant-tunneling-diode oscillators

Abstract

We generalize the van der Pol oscillator model to account for a realistic nonlinearity of the resonant-tunneling-diode (RTD) 𝐼-𝑉 curve. In the case of weak nonlinearity, perturbation theory is applied, and analytical expressions are derived for first-order corrections to the oscillation frequency, quadrature component (phase shift), and higher harmonics. Applicability requirements for perturbation theory are discussed. These requirements are always satisfied at sufficiently high frequencies, but they can fail already at frequencies as low as a few hundred GHz for RTDs with thicker barriers and at slightly above 500 GHz for thin-barrier RTDs, where oscillators transition to a strongly nonlinear regime. Calculation results for the above corrections for several RTD wafers, with typical parameters for sub-THz and THz oscillators, are presented. In particular, our calculations indicate that first-order correction terms play an essential role in the mechanism of variation of the RTD-oscillator frequency with bias. Taking into account the realistic nonlinearity of the RTD 𝐼-𝑉 curve leads to significant quantitative and even qualitative differences in the behavior of RTD oscillators, compared to the conventional van der Pol oscillator model. The presented generalized model lays the groundwork for a more accurate analysis of nonlinear phenomena in RTD oscillators, it can serve as a reference for numerical simulations, it is also essential for qualitative and semiquantitative analysis of RTD oscillators.