MATHEMATICAL DESCRIPTION OF DIFFERENTIAL EQUATION SOLVING ELECTRICAL CIRCUITS

We show that the working principle of the differential equation solving analog electrical circuits is exactly the same as the Picard's method available for numerically solving the ordinary differential equations. The integrator circuit (low-pass filter) uses an initial condition and electrical input signal to generate the Maclaurin's series of a time varying function in recursion. This direct connection between the differential equation solving electrical circuits and Picard's method can be exploited to simplify the procedure of Picard's method to solve any order linear and nonlinear differential equations.

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RECENT DEVELOPMENTS IN NEURODYNAMICS AND THEIR IMPACT ON THE DESIGN OF NEURO-CHIPS

International Journal of Neural Systems ◽

10.1142/s0129065793000249 ◽

1993 ◽

Vol 04 (04) ◽

pp. 309-316 ◽

Cited By ~ 2

Author(s):

ULRICH RAMACHER ◽

PETER SCHILDBERG

Keyword(s):

Differential Equations ◽

Discrete Analog ◽

Digital Design ◽

Neuron Models ◽

Learning Dynamics ◽

Pass Filter ◽

Low Pass Filter ◽

Single Pattern ◽

Recent Developments ◽

Low Pass

Neurons can be modeled either by equations or differential equations. For the latter, a low-pass filter must be added to the analog function blocks associated with the McCullogh and Pitts type of static neuron in order to provide the time-dependent neuron solution. The low-pass filter enhances stability and enables a time-continuous analog implementation much more compact than that attained with time-discrete analog or pure digital design. A few examples of equations as well as differential equations are known for that part of learning. However, much less than for the recall mode, it is clear how to design learning neuro-chips for temporal pattern processing. It is shown here that a partial differential equation can be used to provide a unified description of both the recall and learning dynamics of a neural network as well as to investigate systematically the VLSI potential for analog time-continuous neuro-chips. It turns out that the recall and learning dynamics can be divided into causal as well as noncausal solutions. The first type of solution includes oscillating or spiking neurons. The second type of solution allows for a much simpler signal representation but leads to the problem of storing the temporal signal of each neuron for as long a time as a single pattern lasts. As this is prohibitive for larger networks and time-varying patterns, the analog VLSI implementation of causal neuron models is suggested.

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The Application Research of Six-Axis Force Sensor Used by Trans-Femoral Prosthesis

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.683.741 ◽

2013 ◽

Vol 683 ◽

pp. 741-744 ◽

Cited By ~ 3

Author(s):

Hua Long Xie ◽

Fei Li ◽

Guo Cun Kang

Keyword(s):

Force Sensor ◽

Window Function ◽

Femoral Prosthesis ◽

Data Filtering ◽

Application Research ◽

Pass Filter ◽

Low Pass Filter ◽

Type Selection ◽

Low Pass ◽

Working Principle

Intelligent bionic leg (IBL) is an advanced trans-femoral prosthesis. First, the conception and structure component of IBL are introduced. Then, working principle of six-axis force sensor is analyzed in detail. The type selection and design of filter are discussed. In the end, the data filtering of low pass filter based on hamming window function is established and simulation is done. The simulation indicates that force and torque signal has a significant improvement after filtering and the filter designed in the paper is reasonable.

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A novel differential equation model for a microstrip low-pass filter

Microwave and Optical Technology Letters ◽

10.1002/mop.10609 ◽

2002 ◽

Vol 35 (5) ◽

pp. 368-370 ◽

Cited By ~ 7

Author(s):

J. S. Hong ◽

Y. W. Liu ◽

B. Z. Wang ◽

K. K. Mei

Keyword(s):

Differential Equation ◽

Equation Model ◽

Differential Equation Model ◽

Pass Filter ◽

Low Pass Filter ◽

Low Pass

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Phase Sensitive Detection Based on FPAA

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.433-440.5714 ◽

2012 ◽

Vol 433-440 ◽

pp. 5714-5721

Author(s):

Jin Shan Gao ◽

Shi Jie Wang

Keyword(s):

Sensitive Detector ◽

Pass Filter ◽

Low Pass Filter ◽

Phase Errors ◽

Programmable Analog ◽

Field Programmable ◽

Low Pass ◽

Working Principle ◽

Phase Sensitive ◽

Phase Sensitive Detector

Application of FPAA (field programmable analog array) for the construction of phase-sensitive detector is described. The working principle of the phase sensitive detector is introduced. With software called Anadigmdesigner2, a signal selection circuit, a inverting circuit, a rectifier and a low pass filter circuit are achieved. The simulation of the phase-sensitive detector circuit designed is made. Phase rang from 75º to 115 º, phase errors detected are below ±0.392%.

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