Design of analog nonlinear transformations based on a Gilbert multiplier for energy detection

Abstract This paper focuses on the design of two analog nonlinear transformations dedicated to analog signal processing such as energy detection: the square function and the Teager Energy Operator (TEO). Both requiring an analog multiplier, this paper firstly analyses the design equations of a MOS Gilbert cell in order to operate around the mid supply voltage. Considering this, an analog multiplier, having a differential input range of ±400 mV, has been designed using an AMS 0.35 μm technology and a voltage supply (VDD) of 3.3 V. It has a core area of 620 μm2 and offers power-gating capability, which enables a power consumption of 2.28 μW when a duty cycle of 0.25% is considered. Next, an analog square function and an analog TEO, have been implemented and manufactured using the designed Gilbert cell. The analog square function has a core area of 0.9 mm2 and measurement results show that it is able to compute the square value of its differential input voltage with a mean precision of 2.92% in 5 μs assuming a differential input voltage of ±400 mV with a common voltage of VDD/2. Moreover, it generates 700 mV spikes when 200 mV pulses are applied on its input. Finally, the designed analog TEO has been implemented using its discrete time equation instead of its continuous time equation since it does not require derivatives computing. It has a core area of 2.2 mm2, an active power consumption of 6.21 mW and a standby power consumption of 1.43 nW. Measurement results shows that it generates until 250 mV spikes when 200 mV pulses are applied on its input.