SU78876A1 - An electrical device for determining and visual reading on the screen of a cathode ray tube of the roots of an algebraic equation of the nth degree - Google Patents

Description

co5 (n - - / cj 9 O

 sin (n - and) 9 0

(2)

No. 78876- 2 For integer powers of r, there is a decomposition in the Fourier series;

/ sin "it sin2u), sin 3 (0

r o.2 | 2

 4-4 (i: ± - ° ... -1 (3)

etc. for d.

On this basis, it is possible to create a device that makes it possible to obtain the coordinates of the real and imaginary components of their / cosOy on the screen of the cathode ray tube. and TJJ,. the desired roots of the equation to be solved.

The device has ac sources that create sinusoidal voltages with frequencies co, 2co, tso.

Of these voltages, they are composed of mixers M, Mch ... Mn (transformer or rheostat) of degree r in accordance with the decomposition in the Fourier series with the desired degree of accuracy. The latter is achieved by selecting the proper value of m. The output signal of the mixers, is controlled by means of keys K, in time with the fundamental harmonic supplied from the generator G of square-wave pulses. This ensures that the output of the M-L1 mixers opens only in the gap when sinci) O, as a result of which a series of signals is obtained at the output, + ((SO.

The output of each mixer, after multiplying by a constant factor smaller than one, is modulated in cells.

L), Lg / 1 ", high frequency, i.e. multiplied by sinu / and cosoi,

smivt and cos2y sinnwf and cosnu /, respectively, the degree of module root obtained at the output of this mixer. For this purpose, a system of modulators В - В, В „, лл

frequencies y, 2vnv. Voltages at the outputs of the modulators of the bb

and B are summarized in the cells 2i and E2, at the output of which

voltage U and U are obtained, varying in time as the left-hand sides of equations (2).

The rsinu and rzosvt voltages are applied to the deflection plates C and Ci of the cathode ray tube ET, and the electron beam is unlocked at the moment when the voltages Ui and (/ 2 are equal to zero at the same time).

For this purpose, each of the voltages U and Uz is amplified in amplifiers U and UZ, detected in cell D, and Mz vi is passed through a limiter.

Due to the large force, the steepness of the voltage wave Ui and L / z received at the same time can be made sufficiently large when crossing the zero, so that after differentiation and detection (with a cut) a series of pulses will be obtained at the time of the transition of U and Uz through zero. These pulses are sent to the comparator K, at the output of which a pulse is received, "unlocking the CRT tube only if the pulses coincide in time from Ui and Uz. As a result, on the screen of the tube there are in t m light points, the coordinates of which give the real and imaginary components of the sought roots.

Subject invention

An electrical device for determining and visual reading on the screen of a cathode ray tube of the roots of an algebraic equation of the nth degree, characterized in that, in order to simplify the decisive circuit, the latter contains a system of alternating sinusoidal voltage sources with frequencies co, 2 (o, tco and P

modulators with output voltages varying by law:

cofsiny /, (atzosvt (wt) smnvt, (mt) cosnvt;

so that the voltages from the outputs of the modulators can be applied after summing the deflection plates of the cathode ray tube, unlocked when the real and imaginary components are equal to zero, of the equation being solved.

- 3 - № 78876

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