US2887576A

US2887576A - Electronic squaring circuit

Info

Publication number: US2887576A
Application number: US468175A
Authority: US
Inventors: Harmuth Henning
Original assignee: Individual
Current assignee: Individual
Priority date: 1954-11-10
Filing date: 1954-11-10
Publication date: 1959-05-19
Anticipated expiration: 1976-05-19

Description

y 1959 H. HARMUTH 2,887,576

ELECTRONIC SQUARING CIRCUIT Filed Nov. 10, 1954 INVENTOR.

HENNING HARMUTH United States Patent O ELECTRONIC SQUARING CIRCUIT Henning Harmuth, Red Bank, N.J., assignor to the United States of Americaasrepresented by the Secretary of the Army I Application November 10, 1954, Serial No. 468,175

2 Claims. (Cl. 250-27) (Granted under Title 35, US. Code (1952), sec. 266) The invention described herein may be manufactured and usedby or for the Government of the United States for governmental purposes, withoutthe payment of any royalty thereon.

The invention relates to a new and useful electronic squaring circuit for use in analog computers or the like. The circuit operates to derive an algebraic square function of a voltage representative of another function, and performs this operation without the use of any mechanical linkage or other moving parts.

Electron tube circuits have been previously used for squaring circuits. The tubes used in such circuits are normally operated on the curved portion of their static characteristics where the grid voltage-plate current curves follow a square law relationship. Such previous circuits have, however, produced only a rough approximation of the algebraic function due to the presence of higher order current components in the output circuit. While the magnitude of such higher order components is usually small, the fourth order component particularly, cannot always be disregarded.

It is the principal object of the present invention to produce an electronic squaring circuit in which the higher order current components are eliminated from the output circuit.

It is a further object of the present invention to devise a method for eliminating'high order components from the output of an electrical squaring circuit,

It is a further object of the present invention to provide a squaring circuit wherein the higher order components of suificient magnitude to affect the result are removed from the output circuit.

It is a still further object of the invention to provide a circuit which exhibits a quadratic relationship between its input and output circuits.

Other objects and many attendant advantages of the invention will become more readily apparent as the same becomes better understood from the following detailed description and the drawing wherein:

The sole figure is a schematic drawing of an electronic squaring circuit constructed in accordance with the principles of the invention.

The squaring circuit, as shown in the drawing, comprises a phase inverting input device such as a transformer 11 having a primary winding 13 and a centertapped secondary winding 15. Obviously, however, any of the conventional phase inverter circuits well known in the prior art may be used in place of transformer 11. The primary winding 13" is connected to a pair of input terminals 17 and 19. The center tap of the secondary winding 15 is connected to ground and the ends thereof are connected through a pair of resistors 21 and 23 to the input circuits'of a pair of

electron discharge tubes

25 and 27. The

electron discharge tubes

25 and 27 are illustrated as triodes but need not be of this type. charge tube which has a portion of its characteristic which follows a square law variation of output to input may be used. Pentodes, for example, will serve equally Any dis- 37 of a source of bias voltage not shown. The cathodes of

tubes

25 and 27 are grounded and the anodes thereof' are connected in parallel through

leads

39, 41, 43 and a plate resistance 42 to positive terminal 47 of a source of plate supply not shown. A load or utilization device such as meter 45 is coupled through a condenser 44 between the anodes of the tubes and a ground terminal 46 to measure the A.C. component of the voltage on the anodes.

The secondary winding 15 is also connected through a pair of

condensers

49 and 51 across a second pair of

grid leak resistors

53 and 55 and to

grids

66 and 68 of a second pair of

electron discharge tubes

65 and 67. The junction between the

grid leak resistors

53 and 55 is con nected to a terminal 57 which is adapted to be connected to the same negative terminal of the bias source (not shown) as the terminal 37. The cathodes of discharge.

tubes

65 and 67 are connected to ground while the anodes are connected in parallel by leads 69 and 71 and are in turn connected to the plate supply terminal 47 through the lead 73 and the resistor 42. It will be noted that the anode-cathode circuits of all four electron discharge devices areconnected in parallel.

The values of the resistors and condensers used in the discharge tube input circuits are chosen to bear a predetermined relationship to one another. The absolute values used are not critical but the relationship between them should be substantially as set out below,

The value ofthe

grid leak resistors

33 and 35 is chosen as a reference basis. These resistors should be equal and their ohmic resistance may be designated as R. The resistance of the resistors 21 and 23 should then be approximately equal to R( /21).

The

condensers

49 and 51 together with the

grid leak resistors

53 and 55 constitute phase shift networks. The manner in which the relative value of their circuit constants is obtained is set out below in the description of the circuit operation.

The upper portion of the circuit described above, which includes the

electron discharge tubes

25 and 27, has its grid circuits connected in push-pull and its anodecathode circuits connected in parallel. The magnitude of the bias voltage, e is chosen so that the tubes operate on the curved portion of their characteristics where the grid voltage and plate current maintain a square law relationship.

,Under these conditions of operation, i and i the plate currents through the

tubes

25 and 27 respectively, may be shown to be power series of the form:

where i =the current through tube 25, i =the current through tube 27, e =the input voltage and a a a a and 51 are constants.

It will be noted that the

tubes

25 and 27 are connected so that their currents add in the meter 45 so that the two expressions of plate current set out above must be added to obtain the total plate current through

tubes

25 and 27.

Adding Equations land 2, the terms containing odd powers of the signal input voltage cancel out with the result that the total current expression is:

Since the odd terms have been eliminated, the current through

tubes

25 and 27 thus 'bears a non-linear relationship to the signal input voltage and the total current is one containing even power components only.

Since a squaring circuit is desired the even powers above the second must be eliminated from the current expression, or at least as many of them as may be significant in magnitude. This is accomplished by the operation of the discharge tubes'65 and 67 together with their input networks which include

condensers

49 and 51 and the

grid resistors

53 and 55.

f The condenser 49 and the resistor 55 constitute a phase shift network and to eliminate the fourth order component of current their values are chosen to satisfy the relationship:

where:

R the resistance of the resistor 55 in ohms, w=21r the frequency of e,, and C=the capacitance of the condenser in farads.

' It will be apparent therefore, that this network causes a phase shift of 45 and that the voltage applied to the grid 68 of tube 67 may be written in complex notation as:

The values of condenser 51 and resistor 53 are equal to those of condenser 49 and resistor 55 and satisfy the same relationship. The voltage on the grid 66 of tube 65 may be Written as:

:

Tubes

65 and 67, being connected in the same manner as

tubes

25 and 27, their respective platecurrents will he of the form:

Reducing the complex quantities of Equations 4 and 5 and adding them the sum of the plate currents of

tubes

65 and 67 is:

Now adding Equations 3 and 6 to obtain the total plate current of all the tubes:

7 are those of the sixth order and above.

current component of the voltage drop across resistor 42.

The value read on meter 45 will therefore be:

where It will be noted that the 2a term of Equation 7 which is the constant or direct current component disappears from the final result due to the condenser coupling.

The remaining higher order even terms in the power expansion which are not cancelled from the output current These terms may, if desired, be removed from the output current by an extension of the same principle though their magnitude is usually so small that for most practical purposes they may be neglected. If it is desired to remove the sixth order terms a further pair of square law biased electron discharge tubes is necessary. These additional tubes would be connected with their plate circuits in parallel with the

tubes

25, 27, 65 and 67, and would have their grids energized from the secondary winding 15 through phase shifting networks that would proto the sum of the above currents through the tubes. The

meter 45 is coupled to the anodes of the tubes through condenser 44 and hence measures ,only the' alternating 1r Z radians or where n is the lowest order component to be removed by the particular pair of tubes.

The particular location of the phase shifting circuits for the grid circuits of the tube is, of course, not critical. It will be obvious, for example, that the phase shift circuit could be connected to input terminals 17 and 19 and the output thereof connected to a phase splitting or shifting transformer which, in turn,.would be connected to the grid circuit of the

tubes

65 and 67.

It will be apparent that the above described squaring circuit, constructed in accordance with the principles of the invention, emphasizes the second order or square component of the input function while eliminating the other components which may cause a significant error in the output.

While there has been disclosed What is considered at present to be the preferred embodiment of the invention, it will be obvious to those skilled in the art that various changes and modifications may be made therein without departing from the invention, and it is therefore the aim of the appended claims to cover all such changes and modifications as fall within the true spirit and scope of the invention.

What is claimed is:

1. An analogue electronic squaring circuit comprising a first means for producing a first voltage proportional to a value to be squared, a second means for producing a second voltage proportional to the value to be squared, means connected to the first and second means for producing two voltages each dilfering from the square of the first and second voltages by the inclusion of a fourth order voltage component of substantial magnitude, means connected to the second means for shifting the phase of the second voltage through forty-five degrees whereby the fourth order voltage components will be one hundred and eighty degrees out of phase, means for combining the squared voltages whereby said fourth order voltage components will cancel, and means for indicating the combined voltages.

2. In an analogue electronic squaring circuit comprising a first means for producing a first voltage, a second means connected thereto for producing a voltage in its output differing from the square of the first voltage by the inclusion of a fourth order voltage component of significant magnitude, the improvement which comprises a third means producing a second voltage equal in magnitude to the first voltage, fourth means connected to said third means for producing a voltage in its output diifering from the square of the second voltage by the inclusion of a fourth order voltage component of the same significant magnitude, means for shifting the phase of the second voltage relative to the first voltage through an angle equal to forty-five degrees whereby the fourth order voltage components in the outputs of said second and fourth means will be in phase opposition, means for combining the outputs of said second and fourth means and means connected to said last named means for indicating the combined voltage thereof.

References Cited in the file of this patent UNITED STATES PATENTS