226 research outputs found
Design of Double Barrier Ceramic Radio Frequency Vacuum Window
Vacuum windows are an essential part of any radio frequency (RF) system which launches/couples RF power from an atmospheric to a vacuum environment. This paper describes the RF design of a double barrier ceramic coaxial vacuum window. Alumina 99.5% pure is considered as ceramic barrier material while inner and outer conductors are oxygen-free copper. As the initial design approach the thickness, slope, depth of ceramic in the conductor is varied and the performance of the window is studied. The design is optimised to achieve the best insertion loss, return loss response for operating frequency range up to 65MHz
Recommended from our members
k-Inductive Barrier Certificates for Stochastic Dynamical Systems
Barrier certificates are inductive invariants that provide guarantees on the safety and reachability behaviors of continuous dynamical systems. For stochastic dynamical systems, barrier certificates take the form of inductive “expectation” invariants. In this context, a barrier certificate is a non-negative real-valued function over the state space of the system satisfying a strong supermartingale condition: it decreases in expectation as the system evolves. The existence of barrier certificates, then, provides lower bounds on the probability of satisfaction of safety or reachability specifications over unbounded-time horizons. Unfortunately, establishing supermartingale conditions on barrier certificates can often be restrictive. In practice, we strive to overcome this challenge by utilizing a weaker condition called -martingale that permits a bounded increment in expectation at every time step; unfortunately this only guarantees the property of interest for a bounded time horizon. The idea of -inductive invariants, often utilized in software verification, relaxes the need for the invariant to be inductive with every transition of the system to requiring that the invariant holds in the next step if it holds for the last steps. This paper synthesizes the idea of -inductive invariants with barrier certificates. These refinements that we dub as -inductive barrier certificates relax the supermartingale requirements at each time step to supermartingale requirements in -steps with potential -martingale requirements at each step, while still providing unbounded-time horizon probabilistic guarantees. We characterize a notion of - inductive barrier certificates for safety and two distinct notions of -inductive barrier certificates for reachability. Correspondingly, utilizing such -inductive barrier certificates, we obtain probabilistic lower bounds on the satisfaction of safety and reachability specifications, respectively. We present a computational method based on sum-of-squares (SOS) programming to synthesize suitable - inductive barrier certificates and, demonstrate the effectiveness of the proposed methods via some case studies.</p
- …