UC Santa Cruz

Estimating the frequency and phase of a signal is a fundamental problem in signal processing and communication. Extended Kalman Filter (EKF) is one of the approaches, and most of the implementations are in digital technologies. The fast frequency estimator (FFE), as an application of extended Kalman Filter, is an analog circuit which can determine the amplitude, frequency and phase of a sine wave signal with noise. This work has built and analyzed the model of a continuous-time FFE. We approximately derive the FFE transfer function in steady state, which is a second-order type-2 feedback system. Compared with a second-order type-2 phase-locked loop (PLL), the bandwidth of the FFE is a variant during the acquisition. Thus, the architecture of FFE breaks the tradeoff between loop bandwidth and acquisition time with changeable loop dynamics, which is a main improvement over the PLL. The design and operation of the FFE are described in detail and verified by simulations using Cadence SpectreRF. The circuit of the FFE is divided into three main blocks: the main oscillator block performing the update of the state equations, and the K and P matrix blocks, which solve the Riccati equation of the analog FFE. A quadrature LC oscillator and a two-stage ring oscillator with injection signals are proposed to implement the main oscillator block and K matrix block, respectively. A simplified implementation of the P matrix block is proposed based on the study of the phase of all the signals. The FFE could be used instead of the PLL in the application of Clock Recovery. Compared with the PLL, the FFE achieves much more rapid acquisition with changeable loop dynamics.