A Time-Domain Frequency Analyzer Based on Goertzel Algorithm

This article presents a novel time-domain implementation of the second-order Goertzel frequency analyzer, which can be extended for use in infinite impulse response (IIR)/finite impulse response (FIR) filters. A set of time-domain arithmetic circuits, including a one-step time register (TR), time amplifier (TA), time adder, and unit delay operator (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${z}^{-1}$ </tex-math></inline-formula>), are introduced to overcome the limitations of conventional time-domain filters. The working principles and nonidealities of each block are analyzed and compared with the existing methods. The proposed filter is implemented in a 180-nm CMOS process with a 0.9-V supply voltage. The designed frequency analyzer is tunable to extract the amplitude and phase angle of signals up to 400 Hz. Simulation results, targeting a 280-Hz signal at a 19.88-kHz sampling frequency, demonstrate that the filter can detect the amplitude and phase of a voltage signal in the time domain with an error below 5%. The filter achieves a resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$76.7~\text {dBV/s}$ </tex-math></inline-formula>, consumes less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$24~\mu \text {W}$ </tex-math></inline-formula> of power, and the estimated silicon area is almost <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.828~\mathrm {mm}^{2}$ </tex-math></inline-formula>.