In this article, we present a physically oriented design of broadband RF negative non-Foster capacitors. The design procedure is based on the matrix decomposition of Linvill's floating negative impedance converter (NIC). The decomposition allows optimization of the NIC circuit regarding the accuracy of generated capacitance. Furthermore, it provides a clear physical picture of the influence of particular circuit elements on the system properties. The methodology is verified by the design and measurements of a negative capacitor in a 0.5-2 GHz range, suitable for applications in bandpass filters with the NIC-based impedance inverters. Experimental results were found to be in good agreement with the theoretical predictions, verifying the correctness of the presented approach.