Design of low power Teager Energy Operator circuit for Sleep Spindle and K-Complex extraction

This work presents an ultra-low-power subthreshold four-quadrant multiplier and a subthreshold programmable second order Butterworth Gm-C Low-Pass Filter (LPF) targeted for realizing optimized Teager Energy Operator (TEO). The ultra-low-power and low voltage strategies involve weak inversion biasing, reducing multiplier power consumption and eliminating summation block from the general TEO algorithm. The circuits dynamic range and bandwidths are designed for the Sleep Spindle (SS) and K-Complex (K–C) frequency range of the Electroencephalogram (EEG) signal. The ideal TEO response is initially modelled using MATLAB and Simulink in order to verify the theoretical basis. The final circuits are then simulated using Analog Devices’ LTSpice MOSFET models of 90 ​nm BSIM4 version 4.3 level 54. The multiplier simulations prove a dynamic range of ±40 ​mV ​at a supply voltage of 0.6 ​V with a linearity error of 2.6%. The Total Harmonic Distortion (THD) at 16 ​Hz for an input of 20 ​mV AC signal and another fixed input at 1 ​mV is 0.2159%. The LPF is operated at ± 0.6 ​V with a low static power consumption of 1.95 ​nW. Programmability of the LPF has control over both gain and bandwidth, offering the designer a choice over the group delay. The overall transient response of the TEO demonstrates its amplitude and frequency tracking capability in accordance with its theoretical performance. The final TEO circuit achieves the lowest static power consumption reported in the sleep research literature of 53.59 ​nW. This makes the proposed TEO circuit, the lowest power consuming joint EEG waveform detecting Application Specific Integrated Circuit (ASIC).