Generalized Bell-Shaped Membership Function Generation Circuit for Memristive Neural Networks

Analog Gaussian Function Circuit: Architectures, Operating Principles and Applications

“…The variance tunability is also enhanced by altering Delbruck's Simple Bump [1,2], which consists of a non-symmetric current correlator, shown in Figure 13a and a simple differential pair. Some of the proposed modifications include a symmetric current correlator [24,32], shown in Figure 13b, a differential difference pair [5,6,17,18,24,[52][53][54], shown in Figure 14 and/or adding additional transistors to the standard differential pair [24,27,32,55]; an example is shown in Figure 15. Any combination of current correlators and differential blocks can implement a Gaussian function curve, for example, Figure 16.…”

“…Any combination of current correlators and differential blocks can implement a Gaussian function curve, for example, Figure 16. Moreover, there are researchers who made significant modifications to Delbruck's Simple Bump [17,18,24,[52][53][54]. Specifically, the variable width (VW) Bump, shown in Figure 17, used in [17,18,[52][53][54], adds multiple current mirrors along with the (non symmetric) current correlator and the [24] combines the symmetric current correlator with current substructors.…”

“…In general, the desired tunability in the Gaussian function curve's variance is achieved by connecting a control voltage to the Body node of some of the differential block's transistors. By incorporating a differential difference pair [5,6,17,18,24,[52][53][54] an increased linearity [56], along with additional output currents are provided. In either case, the control voltage provides sigmoidal shaped curves I 1 , I 2 with adjustable slopes or symmetric displacement of currents.…”

“…Regarding the technology, most implementations are in CMOS process, while two of them are tested with discrete components. In the case of [6,24] PTM, transistor models and quad MOS transistor arrays (Advanced Linear Devices) are used, respectively. In general, the power consumption ranges from a few nW to a couple µW, with the power supply being lower than 1.8 V (except from [6]).…”

“…Some of the implementations are used for Machine Learning (ML) applications [15,16], neuromorphic systems [17,18], smart sensors [19,20] and fuzzy or neuro-fuzzy systems [21,22]. Gaussian function circuits are specific analog circuits that provide an output current, which is a typical Gaussian function [23] or a bell-shaped curve [24]. The main three characteristics of a Gaussian function curve, shown in Figure 2, are the height (amplitude), the mean value (center) and the variance (width) [1,2].…”