An ultra-low power, ±0.3 V supply, fully-tunable Gaussian function circuit architecture for radial-basis functions analog hardware implementation

Analog Gaussian Function Circuit: Architectures, Operating Principles and Applications

“…Many Gaussian function circuits have been proposed in a effort to achieve low power consumption, area efficiency and high accuracy, for example [5,9,32,33]. This Section presents and analyzes the existing Gaussian function circuits, and categorizes them based on their operating principle.…”

“…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.…”

“…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.…”

“…Here, κ p and κ n are the slope factors for PMOS and NMOS transistors, respectively, V G , V S , V D and V w are the gate voltage, source voltage, drain voltage and bulk voltage, respectively, V T is the thermal voltage and I o p and I o n are the characteristic currents (preexponential current) for PMOS and NMOS transistors, respectively [57]. Specifically, by using ( 4) and ( 5) the output current of [5] is expressed as:…”

“…Since the first Gaussian function circuit (also called the Bump circuit) was introduced by Delbruck (Delbruck's Simple Bump) in 1991 [1,2] (shown in Figure 1), many research groups have focused on improving this architecture and/or incorporating it in various fields [3][4][5][6][7][8][9][10][11][12][13][14]. 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].…”