Inverse tangent generator

Claim 2

A function generator including in combination first means for providing a first quantity proportional to z+Tw and a second quantity proportional to 2-z-Tw, the first means comprising means for providing a quantity T proportional to where N0-1, where Do is at most 1.7525, and where D1 is at least 1.1553, and second means for determining the ratio of the first quantity to the second quantity as an approximation to the tangent of an angle A ranging between 0* and 90*, where z A/45 and where w z- 1/2 z2.

Claim 3

A generator as in claim 1 wherein x is at least 1, wherein N1 and D2 are each at least 0.035151, wherein Do is at most 1.751942, and wherein D1 is at least 1.220236.

Claim 4

A generator as in claim 1 wherein Dx 1 is greater than Nx.

Claim 5

An inverse tangent generator including in combination a linear potentiometer having a resistance R and a 0* terminal and a 90* terminal and a slider, first input means providing a potential proportional to the sine of an angle A ranging between 0* and 90*, second input means providing a potential proportiOnal to the cosine of such angle, means connecting the first and second input means in series to provide a resultant potential E, means applying the resultant potential across the terminals of the potentiometer, means connected to the slider for drawing therefrom a current proportional to where z A/45, where w z- 1/2 z2, where No 1, where Do is at most 1.8301, and where D1 is at least unity, means for comparing the voltage at the slider with the voltage at the junction of the first and second input means, third input means for positioning the slider in accordance with such angle, and means responsive to the comparing means for controlling one of said input means.

Claim 6

An inverse tangent generator including in combination a linear potentiometer having a resistance R and a 0* terminal and a 90* terminal and a slider, first input means providing a potential proportional to the sine of an angle A ranging between 0* and 90*, second input means providing a potential proportiOnal to the cosine of such angle, means connecting the first and second input means in series to provide a resultant potential E, means applying the resultant potential across the terminals of the potentiometer, means connected to the slider for drawing therefrom a current proportional to where z A/45, where w z- 1/2 z2, where No 1, where Do is at most 1.8301, and where D1 is at least unity, means for comparing the voltage at the slider with the voltage at the junction of the first and second input means, third input means for positioning the slider in accordance with such angle, and means responsive to the comparing means for controlling one of said input means.

Claim 7

A generator as in claim 4 wherein x 0, wherein Do is approximately equal to 1.8015, and wherein D1 is equal to unity.

Claim 8

A generator as in claim 4 wherein x 0, wherein Do is approximately equal to 1.752342, and wherein D1 is approximately equal to 1.155436.

Claim 9

A generator as in claim 4 wherein x is at least 1, wherein N1 and D2 are each at least 0.035151, wherein Do is at most 1.751942, and wherein D1 is at least 1.220236.

Claim 10

A generator as in claim 4 wherein Dx 1 is equal to Nx.

Claim 11

A generator as in claim 4 which further includes means for selectively reversing the potentials and the order of series connection of the first and second means.

Claim 12

In a function generator including in combination a first linear potentiometer having a 0* terminal and a 90* terminal and a slider, a source of potential, means applying the source to the 90* terminal of the potentiometer, means including the source for providing a voltage across the terminals of the potentiometer, means connected to the slider for drawing therefrom a transfer current proportional to where A is an angle ranging between 0* and 90*, where z A/45, where w z- 1/2 z2, where No1, where Do is at most 1.7525, and where D1 is at least 1.1553, and means for positioning the slider in accordance with such angle.

Claim 13

In a function generator including in combination a first linear potentiometer having a 0* terminal and a 90* terminal and a slider, a source of potential, means applying the source to the 90* terminal of the potentiometer, means including the source for providing a voltage across the terminals of the potentiometer, means connected to the slider for drawing therefrom a transfer current proportional to where A is an angle ranging between 0* and 90*, where z A/45, where w z- 1/2 z2, where No1, where Do is at most 1.7525, and where D1 is at least 1.1553, and means for positioning the slider in accordance with such angle.

Claim 14

A generator as in claim 10 wherein x is at least 1, wherein N1 and D2 are each at least 0.035151, wherein Do is at most 1.751942, and wherein D1 is at least 1.220236.

Claim 15

A generator as in claim 10 wherein Dx 1 is equal to Nx.

Claim 16

A generator as in claim 10 wherein the transfer current means includes means for providing a voltage opposing the flow of transfer current and of such magnitude that the ratio of the resultant voltage to the slider voltage is approximately equal to 0.9896.

Claim 17

A generator as in claim 10 wherein x 0 and wherein the transfer current means includes means for providing a voltage opposing the flow of transfer current and of such magnitude that the ratio of the resultant voltage to the slider voltage is approximately equal to 0.865474.

Claim 18

A generator as in claim 10 wherein x is at least 1 and wherein the transfer current means includes means for providing a voltage opposing the flow of transfer current and of such magnitude that the ratio of the resultant voltage to the slider voltage is at most 0.856542 for 2 0 and z 0.

Claim 19

A generator as in claim 10 wherein the voltage providing means includes means comprising a high negative gain amplifier for coupling the slider to the 0* terminal of the potentiometer.

Claim 20

A generator as in claim 10 wherein the transfer current means comprises a storage circuit having an input and providing an output, means including a switching device for selectively connecting the slider to the input and to the output of the storage circuit, and means for periodically actuating the switching device.

Claim 21

A generator as in claim 10 wherein x 0 and wherein the transfer current means comprises a short-circuited potentiometer having a resistance value which is approximately equal to 0.155436 times the resistance of the first potentiometer.

Claim 22

A generator as in claim 10 wherein x is at least 1 and wherein the transfer current means comprises a short-circuited potentiometer having a resistance value which is at least 0.158650 times the resistance of the first potentiometer.

Claim 23

A generator as in claim 10 wherein x 0 and wherein the transfer current means comprises a second potentiometer shunting the first and having a resistance value which is approximately equal to 1.310872 times the resistance of the first potentiometer.

Claim 24

A generator as in claim 10 wherein x is at least 1 and wherein the transfer current means comprises a second potentiometer shunting the first and having a resistance value which is at most 1.194134 times the resistance of the first potentiometer.

Claim 25

A generator as in claim 10 wherein the transfer current means includes means for providing a voltage aiding the flow of transfer current.

Claim 26

A generator as in claim 10 wherein the transfer current means includes means for providing a voltage of such polarity and magnitude that the ratio of the resultant voltage to the slider voltage has a value which is greater than 0.855 but less than 19.