SU442490A1 - Capacitive grid model for solving elliptic type boundary value problems - Google Patents

Description

one

This invention relates to the field of analog computing.

Capacitive grid models for solving elliptic-type boundary value problems are known, which contain capacitors connected in two-dimensional grids and coupling capacitors.

Grids made in this way have large gauges, are complex and expensive to manufacture.

The proposed device is distinguished by the fact that in order to reduce the size and impact of the design, it contains double-sided metallized dielectric films, on which are printed by printing and followed by etching the electrodes of two-dimensional grid capacitors, and metalized films with capacitors arranged on the dielectric bars, which are packed between double-sided metallized films with two-dimensional grid capacitors.

This will simplify the device and reduce its size.

FIG. Figure 1 shows the arrangement of electrodes on a dielectric film (two-dimensional grid); in fig. 2 is a three-dimensional grid construction scheme; in fig. 3 shows the design of the electrodes of the coupling capacitors along the third coordinate and the supply busbars.

2

The proposed capacitive grid model allows us to solve two-dimensional and three-dimensional boundary-value problems of elliptic type, described by the equation

di

di

Oh and

(X- 1 + - 1 y -) + - 1 - I

their j oy oy j oz ag j

- / (L-, y, g), (I)

under boundary conditions 1, P and 1P of the genus,

where l, i, Z - spatial coordinates; L - variable coefficients; - source floor.

The device consists of main electrodes 1, electrodes 2 of variable area, two-dimensional grid capacitors forming a variable capacitance between adjacent electrodes 1, electrodes 3 for coupling capacitors with main electrodes i but coordinate. The electrodes 1-3 are located on different sides of the dielectric film 4 and form the capacitances of the elements of the grid model on the X, Y plane.

The system of these electrodes, forming a capacitive grid, is produced by means of typographical printing with acid-resistant paint on a bilateral metal-insulated dielectric film with subsequent etching of unprotected areas.

By changing the area of the electrode 2, the values of AX and Ay can be set along the X and Y coordinates. In this case, the capacitive conductivities are determined by the formula

Lx-.O) S 5 ,,,,

where 0 is the circular frequency of the alternating current

sources of boundary conditions; C is the communication capacity;

5 - the area of overlap of the electrodes 2 and 1; e is the dielectric constant of the film; d is the film thickness.

Since w, e., D are constant values, La values; and Ay are only functions of the area of the electrodes 2 superimposed on the electrodes 1.

, (3)

where K const

On a grid, the nodes of which are connected by capacitors when setting voltages or currents of sinusoidal form to the boundary nodes, we can approximately solve the boundary value problems of the equation

-f (h) -0- (4) dx dx J du du j

In this case, the film 4 with electrodes 1, 2 and 3 can be manufactured in mass circulation, and the area of the electrodes 2 can be reduced by mechanical, electrical or chemical means.

The results of solving a typical boundary value problem on a layout and comparing them with an exact solution are satisfactory for most practical problems.

FIG. Figures 2 and 3 show a device consisting of n two-dimensional grids connected by capacitors (electrodes 1 and 3) along the Z coordinate. Dielectric bars Z with film 5 and electrodes 6 located on an insulating film and envelope bar Z are used for this purpose.

FIG. 2 shows three layers of a three-dimensional capacitive model (in section). It consists of two two-coordinate capacitive grids Zj and Zj-f-AZ, constructed according to the scheme in FIG. 1. Between these grids, at each step HF, 2AH, two bars are installed 7. One of them (7i) serves to establish a capacitive coupling between the grids Zj and Zj-j-AZ along the Z coordinate using conductive enamel 8 applied between electrodes 1 and 3 forming the coupling capacitors. The second bar (Tz) is designed to output tires from one row of node points of each two-coordinate grid, for example, from row Jj and row da Xy -} - AH.

The number of bars with electrodes 9 is 2mz, where mz is the number of grid points along the Z coordinate (Fig. 3 shows the location of electrodes 6 and 9 on the unwrapped film of 5 bars and Jz).

The area of the electrode 6 determines the capacitance of the coupling capacitor along the Z coordinate (similar to the action of electrodes 2 and 1). By changing the area of the communication electrode 6, it is therefore possible to set the coefficient AZ as

Z function. Boundary conditions are supplied through tires 9. Tires of the same type are used to measure stresses at model points.

Subject invention

Capacitive grid model for solving elliptical type boundary problems, containing capacitors connected in two-dimensional grids, and communication capacitors, characterized in that, in order to reduce size and simplify the design, it contains two-sided metallized dielectric films on which are printed by printing. and subsequent etching

electrodes of capacitors of two-dimensional grids, and metallized films with capacitors of communication located on dielectric bars, which are laid in a package between bilateral metallized films

with capacitors of two-dimensional grids.

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