Frequency-Domain Analysis of an Oscillator With an Exceptional Point of Degeneracy

Oscillators based on coupled transmission lines with an exceptional point of degeneracy (EPD) have shown great potential as highly sensitive microwave sensors. However, research into their behavior has thus far been limited to the small-signal regime. In this work, we will perform an in-depth nonlinear analysis using the describing function and harmonic balance (HB) methods. We will begin by deriving a simple EPD condition in terms of the input admittance of the coupled transmission lines. This EPD condition can easily be evaluated using a new graphical method based on representing the zero-value contours of the real and imaginary parts of the oscillator’s total admittance, including the active contribution. Moving forward, we will perform an exhaustive calculation of all the periodic and quasi-periodic oscillation modes in the frequency domain and analyze their evolution versus the load resistance. We will demonstrate that there are two different types of quasi-periodic modes, although only one is of interest for the sensing application. A detailed bifurcation analysis will provide valuable insight into the impact of the most relevant parameters on the oscillator’s behavior. The circuit has been implemented with two cross-coupled transistors and a Marchand balun, obtaining good experimental results.