Abstract
Harmonic balance provides steady-state solutions only and has significant shortcomings when addressing oscillatory regimes. As a result, complementary methodologies are required both to ensure the stability of the solution obtained and to design/simulate oscillator circuits. The complexity of the stability analysis increases with the number of active elements and the intricacy of the topology, so there can be uncertainties in the case of complex structures. On the other hand, as recently demonstrated oscillators enable a compact and low-cost implementation of RFID readers and radar systems, which comes at the expense of a more complex performance, very difficult/impossible to simulate with commercial HB. This work presents a review of recent advances on stability and oscillation analysis at circuit level and through semi-analytical formulations. At circuit level, a method for the stability analysis of complex microwave systems is presented, based on the calculation of the characteristic determinant, extracted from the commercial simulator through a judicious partition of the system into simpler blocks. This determinant will be used for the first time to obtain the stability boundaries through a contour-intersection method, able to provide multivalued and disconnected curves. At a semi-analytical level, a realistic numerical model of the standalone oscillator, extracted from HB simulations, is introduced in an analytical formulation that describes the oscillator interaction with other elements. Here it will be applied to a self-injection locked radar, in which the oscillator is injected by its own signal after this signal undergoes propagation and reflection effects. A procedure to determine the stability properties considering the time delay of the signal envelope is presented for the first time. Using the same self-injection concept, a new stabilization method to reduce the phase-noise of an existing oscillator with minimum impact on its original frequency is described.
Highlights
Most Microwave designers make use of the harmonic balance method (HB) due to its efficient and accurate handling of distributed elements [1]–[3]
The blocks considered in the partition must be stable under open circuit (OC) or short circuit (SC) terminations at the sideband frequencies kωo+ arising under a small perturbation at, which must be verified without affecting the steady-state solution at kωo
A method to obtain the stability boundaries in multi-device circuits using the newly defined characteristic determinant has been presented for the first time
Summary
Most Microwave designers make use of the harmonic balance method (HB) due to its efficient and accurate handling of distributed elements [1]–[3]. Because the active blocks are stable under an OC termination, the impedances ZA,k (s), k = 1 to N, cannot exhibit any RHS poles either This is because ZA,k (s) agrees with the voltage-to-current closed-loop transfer function obtained under the excitation Ik. the determinant in (2) cannot exhibit any poles in the RHS. Pole-zero identification has been applied (in a conventional manner) to a closed-loop transfer function This is calculated inside the SC-terminated NIC, introducing a test current I in parallel at a node and obtaining the ratio between the node voltage and the test current Z = V/I [see Fig. 2(b)]. That the conventional pole-zero identification (applied to a closed-loop transfer function) [15]–[19] is used to verify the stability of the blocks considered in the partition. The identification of the determinant is based on the rigorous procedures developed in [15]–[19]
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