Apparatus for numerical signaling of positions, including digital-to-analog converter

Claim 2

In a system for producing two signals Es and Ec respectively proportional to the sine and cosine of an angle theta which is the sum of two variable angles theta 1 and theta 2, the combination comprising first and second algebraic signal combining devices whose output signals Es and Ec are proportional to an algebraic combination of their respective input signals, means for additively supplying to said first device a first input signal which is in effect proportional to the sine of theta 1, means for additively supplying to said second device a first input signal which is in effect proportional to the cosine of theta 1, means responsive to the output signal from said second device for additively supplying to said first device a second input signal which is in effect proportional to the product of the tangent of theta 2 and the output signal Ec of said second device, and means responsive to the output signal from said first device for subtractively supplying to said second device a second input signal which is in effect proportional to the product of the tangent of theta 2 and the output signal Es of the first device.

Claim 3

The combination set forth in claim 1 further characterized by means for producing a first variable signal which in absolute magnitude is effectively proportional to sin theta '', means for supplying said first variable signal as said first input signal to said first device in an additive sense when theta 1 lies in the first or second quadrants, means for supplying said first variable signal as said first input signal to said first device in a subtractive sense when theta 1 lies in the third or fourth quadrants, means for producing a second variable signal which in absolute magnitude is effectively proportional to cos theta 1, means for supplying said second variable signal as said first input signal to said second device in an additive sense when theta 1 lies in the first or fourth quadrants, and means for supplying said second variable signal as said second signal to said second device in a subtractive sense when theta 1 lies in the second or third quadrants.

Claim 4

In a digital-to-analog converter for producing two signals which vary as sine and cosine functions of a number mn where m and n are higher and lower order portions of a changeable composite number mn, means for digitally signaling the values of m and n, first and second algebraic signal combining devices having output signals designatable as Es and Ec, respectively, means responsive to the signaling of the m values for producing a first input signal which is in effect proportional to sin m Alpha where Alpha is an angle of predetermined size, means responsive to the signaling of the m values for producing a second input signal which is in effect proportional to cos m Alpha , means for additively supplying said first and second input signals as inputs to the first and second devices, respectively, means responsive to the signaling of the n values and the output signal Ec for producing a third input signal which is in effect proportional to Ectan n Beta where Beta is a predetermined submultiple of the angle Alpha , means responsive to the signaling of the n values and to the output signal Es for producing a fourth input signal which is in effect proportional to Estan n Beta , and means for supplying said third and fourth input signals as additive and subtractive inputs to said first and second devices, respectively, whereby the ratio (Es/Ec) of said output signals Es and Ec is proportional to the tangent of an angle (m Alpha + n Beta ) as the number mn takes on different values.

Claim 5

In a digital-to-analog converter for producing two signals which vary as sine and cosine functions of a number mn where m and n are higher and lower order portions of a changeable composite number mn, means for digitally signaling the values of m and n, first and second algebraic signal combining devices having output signals designatable as Es and Ec, respectively, means responsive to the signaling of the m values for producing a first input signal which is in effect proportional to sin m Alpha where Alpha is an angle of predetermined size, means responsive to the signaling of the m values for producing a second input signal which is in effect proportional to cos m Alpha , means for additively supplying said first and second input signals as inputs to the first and second devices, respectively, means responsive to the signaling of the n values and the output signal Ec for producing a third input signal which is in effect proportional to Ectan n Beta where Beta is a predetermined submultiple of the angle Alpha , means responsive to the signaling of the n values and to the output signal Es for producing a fourth input signal which is in effect proportional to Estan n Beta , and means for supplying said third and fourth input signals as additive and subtractive inputs to said first and second devices, respectively, whereby the ratio (Es/Ec) of said output signals Es and Ec is proportional to the tangent of an angle (m Alpha + n Beta ) as the number mn takes on different values.

Claim 6

The combination set forth in claim 3 further characterized in that the number mn may have either a positive or negative sign, and including means signaling the sign of said number mn, together with means responsive to said sign-signaling means for reversing the effective polarities with which said third and fourth signals are supplied to said first and second devices when the number sign is negative as contrasted to the effective polarities when the number sign is positive.

Claim 7

The combination set forth in claim 4 further including means responsive to said sign-signaling means for reversing the effective polarity with which said first input signal is supplied to said first device when the number sign is negative as contrasted to the effective polarity of that signal when the number sign is positive.

Claim 8

The combination set forth in claim 3 further characterized in that said means for supplying said first and second input signals as inputs to the first and second devices includes (a) means for supplying said first input signal in an additive sense to said first device when the angle m Alpha lies in the first or second quadrants, (b) means for supplying said first input signal in a subtractive sense to said first device when the angle m Alpha lies in the third or fourth quadrants, (c) means for supplying said second input signal in an additive sense to said second device when the angle m Alpha lies in the first or fourth quadrants, and (d) means for supplying said second input signal in a subtractive sense to said second device when the angle m Alpha lies in the second or third quadrants.

Claim 9

The combination set forth in claim 6 and wherein said means (a) and (b) comprise first and second switching transistors both connected to receive said first input signal and respectively connected to supply such input signal to additive or subtractive input terminals of said first device, means responsive to signaling of the m values for turning said first and second transistors respectively on and off when the angle m Alpha lies in the first or second quadrants and for turning said first and second transistors respectively off and on when the angle m Alpha lies in the third or fourth quadrants; and wherein said means (c) and (d) comprise third and fourth transistors both connected to receive said second input signal and respectively connected to supply such input signal to additive or subtractive input terminals of said second device, and means responsive to signaling of the m values for turning said third and fourth transistors respectively on and off when the angle m Alpha lies in the first and fourth quadrants and for turning said third and fourth transistors respectively off and on when the angle m Alpha lies in the second or third quadrants.

Claim 10

In a system for producing two signals which in magnitude are respectively proportional to the sine and cosine of an angle which is the sum of two discretely variable angles m Alpha anD n Beta , where n and m are the integers of higher and lower order portions of a changeable number mn, Alpha is an angle of predetermined value, and Beta is a submultiple of the angle Alpha , the combination comprising means for digitally signaling the values of the integers m and n, first and second algebraic signal combining devices respectively having means for producing an output signal Es and Ec which is proportional to an algebraic combination of a plurality of input signals applied thereto, a first plurality of resistors Ra1, Ra2, Ra3...Rax which in their values are a function of sin m Alpha as m takes on values 0, 1, 2,...X, a second plurality of resistors Rb1, Rb2, Rb3...Rbx which in their values are a function of cos m Alpha as m takes on values of 0, 1, 2,...X, third and fourth pluralities of resistors which in their values are a function of tan n Beta as n takes on values of 0, 1, 2,...X, a reference signal source producing a reference signal Er, means responsive to the digital signaling of the integer m for selectively connecting the corresponding one of said first plurality of resistors in a circuit between said reference signal source and an input of said first device so as to supply additively an input signal to the latter which is effectively proportional to Ersin m Alpha , means responsive to the digital signaling of the integer m for selectively connecting the corresponding one of said second plurality of resistors in a circuit between said reference signal source and an input of said second device so as to supply additively an input signal to the latter which is effectively proportional to Ercos m Alpha , means responsive to the digital signaling of the integer n for selectively connecting the corresponding one of said third plurality of resistors in a circuit between the output of said second device and an input of said first device so as to supply additively an input signal to the latter which is effectively proportional to Ec tan n Beta , and means responsive to the digital signaling of the integer n for connecting the corresponding one of said fourth plurality of resistors in a circuit between the output of said first device and an input of said second device in a manner to supply subtractively an input signal to the latter which is effectively proportional to Es tan n Beta , whereby the ratio (Es/Ec) of said output signals is equal to the tangent of the sum of the angles m Alpha and n Beta as the number mn takes on different values.

Claim 11

In a system for producing two signals which in magnitude are respectively proportional to the sine and cosine of an angle which is the sum of two discretely variable angles m Alpha anD n Beta , where n and m are the integers of higher and lower order portions of a changeable number mn, Alpha is an angle of predetermined value, and Beta is a submultiple of the angle Alpha , the combination comprising means for digitally signaling the values of the integers m and n, first and second algebraic signal combining devices respectively having means for producing an output signal Es and Ec which is proportional to an algebraic combination of a plurality of input signals applied thereto, a first plurality of resistors Ra1, Ra2, Ra3...Rax which in their values are a function of sin m Alpha as m takes on values 0, 1, 2,...X, a second plurality of resistors Rb1, Rb2, Rb3...Rbx which in their values are a function of cos m Alpha as m takes on values of 0, 1, 2,...X, third and fourth pluralities of resistors which in their values are a function of tan n Beta as n takes on values of 0, 1, 2,...X, a reference signal source producing a reference signal Er, means responsive to the digital signaling of the integer m for selectively connecting the corresponding one of said first plurality of resistors in a circuit between said reference signal source and an input of said first device so as to supply additively an input signal to the latter which is effectively proportional to Ersin m Alpha , means responsive to the digital signaling of the integer m for selectively connecting the corresponding one of said second plurality of resistors in a circuit between said reference signal source and an input of said second device so as to supply additively an input signal to the latter which is effectively proportional to Ercos m Alpha , means responsive to the digital signaling of the integer n for selectively connecting the corresponding one of said third plurality of resistors in a circuit between the output of said second device and an input of said first device so as to supply additively an input signal to the latter which is effectively proportional to Ec tan n Beta , and means responsive to the digital signaling of the integer n for connecting the corresponding one of said fourth plurality of resistors in a circuit between the output of said first device and an input of said second device in a manner to supply subtractively an input signal to the latter which is effectively proportional to Es tan n Beta , whereby the ratio (Es/Ec) of said output signals is equal to the tangent of the sum of the angles m Alpha and n Beta as the number mn takes on different values.

Claim 12

The combination set forth in claim 8 further characterized in that said four selective connecting means each comprise a plurality of field effect transistors associated with the individual resistors of the corresponding plurality of resistors, and means controlled by electrical digital signaling of the integers m and n for selectively rendering different ones of said transistors conductive.

Claim 13

The combination set forth in claim 8 further characterized in that the integers m and n are respectively constituted by different ranges of values for the numbers dex and xxf of a composite changeable number def which is represented by electrical digital signals.

Claim 14

The combination set forth in claim 10 further including a digital counter having a plurality of decade stages and having means to signal the value of a changeable multidigit decimal number, said counter having its three lowest order stages d, e, f connected to signal the values of the composite number def.

Claim 15

In a system for producing two signals which in magnitude are respectively proportional to the sine and cosine of an angle theta which is the sum of two variablE angles theta 1 and theta 2 where theta 1 may change in predetermined steps of Alpha * through 360* and theta 2 may change over a range equal to Alpha *, the combination comprising first and second algebraic signal combining devices whose output signals Es and Ec are proportional respectively to an algebraic combination of their input signals, means for supplying to said first device a first input signal which is in effect proportional in magnitude to the sine of theta 1 as theta 1 takes on different values, means for supplying to said second device a first input signal which is in effect proportional in magnitude to the cosine of theta 1 as theta 2 takes on different values, means responsive to the output signal Ec from said second device for supplying to said first device a second input signal which in effect is substantially proportional to the product Ectan theta 2 as theta 2 takes on different values, means responsive to the output signal Es from said first device for supplying to said second device a second input signal which in effect is substantially proportional to the product Estan theta 2 as theta 2 takes on different values, means causing the first input signal for said first device to be applied thereto in an additive sense when theta 1 lies in the first or second quadrants but in a subtractive sense when theta 1 lies in the third or fourth quadrants, and means for causing the second input signal for said second device to be applied thereto in an additive sense when theta 1 lies in the first or fourth quadrants but in a subtractive sense when theta 1 lies in the second or third quadrants.

Claim 16

In a system for producing two signals which in magnitude are respectively proportional to the sine and cosine of an angle theta which is the sum of two variablE angles theta 1 and theta 2 where theta 1 may change in predetermined steps of Alpha * through 360* and theta 2 may change over a range equal to Alpha *, the combination comprising first and second algebraic signal combining devices whose output signals Es and Ec are proportional respectively to an algebraic combination of their input signals, means for supplying to said first device a first input signal which is in effect proportional in magnitude to the sine of theta 1 as theta 1 takes on different values, means for supplying to said second device a first input signal which is in effect proportional in magnitude to the cosine of theta 1 as theta 2 takes on different values, means responsive to the output signal Ec from said second device for supplying to said first device a second input signal which in effect is substantially proportional to the product Ectan theta 2 as theta 2 takes on different values, means responsive to the output signal Es from said first device for supplying to said second device a second input signal which in effect is substantially proportional to the product Estan theta 2 as theta 2 takes on different values, means causing the first input signal for said first device to be applied thereto in an additive sense when theta 1 lies in the first or second quadrants but in a subtractive sense when theta 1 lies in the third or fourth quadrants, and means for causing the second input signal for said second device to be applied thereto in an additive sense when theta 1 lies in the first or fourth quadrants but in a subtractive sense when theta 1 lies in the second or third quadrants.

Claim 17

In a digital to analog converter for producing two signals which in magnitude are sine and cosine functions of a number mn where m and n are higher and lower order portions of a changeable composite number mn, the combination comprising means for digitally signaling the values of m and n as the composite number mn changes, first and second algebraic combining devices having means to produce respective output signals designatable as Es and Ec which are the algebraic combination of input signals respectively applied thereto, means responsive to the digital signaling of the m values for supplying to said first device a first input signal which is in effect proportional in magnitude to sin m Alpha where Alpha is an angle of predetermined size, and the angle m Alpha can vary in steps from 0* to 360*, means responsive to the signaling of the m values for supplying to said second device a first input signal which is in effect proportional in magnitude to cos m Alpha means responsive to the output signal Ec from said second device and to the digital signaling of the n values for supplying to said first device a second input signal which is in effect proportional to the product Ectann Beta , where Beta is a predetermined sub-multiple of the angle Alpha and the angle n Beta is always less than 90*, means responsive to the output signal Es from said second device and to the digital signaling of the n values for supplying to said second device a second input signal which is in effect proportional to the product Es tan n Beta , means responsive to the digital signaling of the m values for producing first and second control signals when the angle m Alpha respectively lies in the first or second quadrants and in the third or fourth quadrants, means responsive to the digital signaling of the m values for producing third and fourth control signals when the angle m Alpha respectively lies in the first or fourth quadrants and in the second or third quadrants, means responsive to said first or second control signals for causing the first input signal for the first device to be applied thereto respectively in an additive or a subtractive sense and means responsive to said third or fourth signals for causing the first input signal for the second device to be applied thereto respectively in a subtractive or an additive sense.

Claim 18

In a digital to analog converter for producing two signals which in magnitude are sine and cosine functions of a number mn where m and n are higher and lower order portions of a changeable composite number mn, the combination comprising means for digitally signaling the values of m and n as the composite number mn changes, first and second algebraic combining devices having means to produce respective output signals designatable as Es and Ec which are the algebraic combination of input signals respectively applied thereto, means responsive to the digital signaling of the m values for supplying to said first device a first input signal which is in effect proportional in magnitude to sin m Alpha where Alpha is an angle of predetermined size, and the angle m Alpha can vary in steps from 0* to 360*, means responsive to the signaling of the m values for supplying to said second device a first input signal which is in effect proportional in magnitude to cos m Alpha means responsive to the output signal Ec from said second device and to the digital signaling of the n values for supplying to said first device a second input signal which is in effect proportional to the product Ectann Beta , where Beta is a predetermined sub-multiple of the angle Alpha and the angle n Beta is always less than 90*, means responsive to the output signal Es from said second device and to the digital signaling of the n values for supplying to said second device a second input signal which is in effect proportional to the product Es tan n Beta , means responsive to the digital signaling of the m values for producing first and second control signals when the angle m Alpha respectively lies in the first or second quadrants and in the third or fourth quadrants, means responsive to the digital signaling of the m values for producing third and fourth control signals when the angle m Alpha respectively lies in the first or fourth quadrants and in the second or third quadrants, means responsive to said first or second control signals for causing the first input signal for the first device to be applied thereto respectively in an additive or a subtractive sense and means responsive to said third or fourth signals for causing the first input signal for the second device to be applied thereto respectively in a subtractive or an additive sense.

Claim 19

In a digital to analog converter for producing two signals which in magnitude and polarity are sine and cosine functions of a number mn where m and n are higher and lower order portions of a composite changeable number, means for digitally signaling the values of m and n and the sign of the number mn, means responsive to signaling of the m values for producing a first input signal effectively proportional to and agreeable in polarity with sin m Alpha where Alpha is an angle of predetermined size, means responsive to signaling of the m values for producing a second input signal effectively proportional to and agreeable in polarity with cos m Alpha , first and second algebraic signal combining devices having output signals designatable as Es and Ec, respectively, first coupling means for normally supplying said first and second input signals as additive inputs to said first and second devices, means responsive to the signaling of the n values for producing a third input signal effectively proportional to and agreeable in polarity with Ectan n Beta where Beta is a predetermined submultiple of the angle Alpha , means responsive to the signaling of the n values for producing a fourth input signal effectively proportional to and agreeable in polarity with Estan n Beta , second coupling means for normally supplying said third and fourth input signals as additive and subtractive inputs to said first and second devices, respectively, means responsive to the signaling of a negative sign for the number mn for causing said first coupling means to reverse the effective polarity of said first input signal, and means responsive to signaling of said negative sign for causing said second coupling means to reverse the effective polarities of said third and fourth input signals.

Claim 20

In a digital to analog converter for producing two signals which in magnitude and polarity are sine and cosine functions of a number mn where m and n are higher and lower order portions of a composite changeable number, means for digitally signaling the values of m and n and the sign of the number mn, means responsive to signaling of the m values for producing a first input signal effectively proportional to and agreeable in polarity with sin m Alpha where Alpha is an angle of predetermined size, means responsive to signaling of the m values for producing a second input signal effectively proportional to and agreeable in polarity with cos m Alpha , first and second algebraic signal combining devices having output signals designatable as Es and Ec, respectively, first coupling means for normally supplying said first and second input signals as additive inputs to said first and second devices, means responsive to the signaling of the n values for producing a third input signal effectively proportional to and agreeable in polarity with Ectan n Beta where Beta is a predetermined submultiple of the angle Alpha , means responsive to the signaling of the n values for producing a fourth input signal effectively proportional to and agreeable in polarity with Estan n Beta , second coupling means for normally supplying said third and fourth input signals as additive and subtractive inputs to said first and second devices, respectively, means responsive to the signaling of a negative sign for the number mn for causing said first coupling means to reverse the effective polarity of said first input signal, and means responsive to signaling of said negative sign for causing said second coupling means to reverse the effective polarities of said third and fourth input signals.

Claim 21

In a system for producing two signals Es and Ec which are respectively proportional to the sine and cosine of an angle theta which is the sum of two changeable angles theta 1 and theta 2, the combination comprising first and second algebraic signal combining operational amplifiers having the same gain and negative feedback resistors Rf for respectively producing output voltages Es and Ec, a source of reference voltage Er, a changeable resistance Ra connected between said source and an input of said first amplifier to additively supply to the latter a first input signal which in effect is proportional to Er(Rf/Ra), a changeable resistance, Rb connected between said source and an input of said second amplifier to additively supply to the latter a first input signal which in effect is proportional to Er(Rf/Rb), a first changeable resistance connected Rc between the output of said second amplifier and an input of said first amplifier to additively supply to the latter a second input signal which in effect is proportional to Ec(Rf/Rc), a second changeable resistance Rc connected between the output of said first amplifier and an input of said second amplifier to subtractively supply to the latter a second input signal which in effect is proportional to Es(Rf/Rc), means for changing the value of said resistance Ra to make it equal to (Rf/sin 1), as the angle theta 1 takes on different values, means for changing the value of said resistance Rb to make it equal to (Rf/cos theta 1) as the angle theta 1 takes on different vAlues, and means for changing the values of said two resistances Rc to make their values equal to (Rf/tan theta 2) as the angle theta 2 takes on different values, whereby the output signals Es and Ec vary in proportion to sin ( theta 1+ theta 2) and cos ( theta 1+ theta 2), and the ratio (Es/Ec) varies in proportion to tan ( theta 1+ theta 2) as the angles theta 1 and theta 2 individually take on different values.

Claim 22

In a system for producing two signals Es and Ec which are respectively proportional to the sine and cosine of an angle theta which is the sum of two changeable angles theta 1 and theta 2, the combination comprising first and second algebraic signal combining operational amplifiers having the same gain and negative feedback resistors Rf for respectively producing output voltages Es and Ec, a source of reference voltage Er, a changeable resistance Ra connected between said source and an input of said first amplifier to additively supply to the latter a first input signal which in effect is proportional to Er(Rf/Ra), a changeable resistance, Rb connected between said source and an input of said second amplifier to additively supply to the latter a first input signal which in effect is proportional to Er(Rf/Rb), a first changeable resistance connected Rc between the output of said second amplifier and an input of said first amplifier to additively supply to the latter a second input signal which in effect is proportional to Ec(Rf/Rc), a second changeable resistance Rc connected between the output of said first amplifier and an input of said second amplifier to subtractively supply to the latter a second input signal which in effect is proportional to Es(Rf/Rc), means for changing the value of said resistance Ra to make it equal to (Rf/sin 1), as the angle theta 1 takes on different values, means for changing the value of said resistance Rb to make it equal to (Rf/cos theta 1) as the angle theta 1 takes on different vAlues, and means for changing the values of said two resistances Rc to make their values equal to (Rf/tan theta 2) as the angle theta 2 takes on different values, whereby the output signals Es and Ec vary in proportion to sin ( theta 1+ theta 2) and cos ( theta 1+ theta 2), and the ratio (Es/Ec) varies in proportion to tan ( theta 1+ theta 2) as the angles theta 1 and theta 2 individually take on different values.

Claim 23

The combination set forth in claim 15 further including means for reversing the effective polarity of said first input signal for said first amplifier when the angle theta 1 lies in the third or fourth quadrants as contrasted to the first or second quadrants, and means for reversing the effective polarity of said first input signal for said second amplifier when the angle theta 1 lies in the second or third quadrants as contrasted to the first or fourth quadrants.

Claim 24

The combination set forth in claim 15 wherein said angle theta 1 is changeable to take on a plurality of values in equal steps between 0* and 360*, said resistance Ra comprises a plurality of resistors respectively having values equal to (Rf/sin theta 1) as theta 1 varies in equal steps between 0* and 90*, said resistance Rb comprises a plurality of resistors respectively having values equal to (Rf/cos theta 1) as theta 1 varies in equal steps between 0* and 90*; and means for rendering effective that one of the resistors in the resistance Ra and that one of the resistors in the resistance Rb which corresponds to (a) the angle theta 1 when the angle theta 1 lies in the first quadrant, (b) the angle (180*- theta 1) when theta 1 lies in the second quadrant, (c) the angle ( theta 1-180*) when theta 1 lies in the third quadrant, and (d) the angle (360*- theta 1) when theta 1 lies in the fourth quadrant.

Claim 25

The combination set forth in claim 15 in which said reference voltage Er is a sinusoidal alternating voltage and said output signals Es and Ec are sinusoidal alternating voltages variable in amplitude and phase polarity relative to said reference voltage, and wherein said changeable resistances Ra, Rb and Rc each comprise a plurality of individual resistors each in series with a field effect transistor, the combination further including means for turning on a particular one of the transistors in the resistances Ra and Rb as the angle theta 1 takes on corresponding particular values, and means for turning on a particular one of the transistors in the two resistances Rc as the angle theta 2 takes on corresponding particular values.

Claim 26

The combination set forth in claim 15 further characterized by means for representing by digital signals the changeable numbers m and n which constitute higher and lower order portions of a composite changeable number mn, said angles theta 1 and theta 2 being equal to m Alpha and n Beta respectively as m and n take on different values where Alpha is a predetermined angle and Beta is a submultiple of the angle Alpha , and wherein said means for changing the value of the resistance Ra is responsive to the digital signals representing the number m, said means for changing the value of the resistance Rb is responsive to the digital signals representing the number m, and said means for changing the values of the two resistances Rc are responsive to the digital signals representing the number n.

Claim 27

The combination set forth in claim 19 further characterized in that said number mn may be either positive or negative and including meAns for producing N+ and N- signals when such number is respectively positive or negative, and means responsive to the N- signal for reversing the effective polarity of said second input signals for said first and second amplifiers compared to their polarities when the signal N+ exists.

Claim 28

The combination set forth in claim 20 further characterized by means responsive to the N- signal for reversing the effective polarity of said first input signal for said first amplifier compared to its effective polarity when the signal N- exists.

Claim 29

In a digital-to-analog converter for producing two AC output signals Es and Ec which in amplitude are proportional to the sine and cosine of a changeable number mn having higher and lower order portions m and n, the combination comprising first and second signal combining operational amplifiers each having the same high gain and a negative feedback resistor Rf, and respectively producing AC output signals designatable Es and Ec, a first plurality of resistors Ra0, Ra1, Ra2...Rax which in value are sized to make the ratios (Rf/Ra0), (Rf/Ra1), (Rf/Ra2)...Rf/Rax) equal to sin m Alpha , as m takes on different values and where Alpha is a predetermined angle, a second plurality of resistors Rb0, Rb1, Rb2...Rbx which in value are sized to make the ratios (Rf/Rb0), (Rf/Rb1), (Rf/Rb2)...Rf/Rbx) equal to cos m Alpha as m takes on different values, third and fourth identical pluralities of resistors Rc0, Rc1, Rc2...Rcx which in value are sized to make the ratios (Rf/Rc0), (Rf/Rc1), (Rf/Rc2)...Rf/Rcx) equal to tan n Beta as n takes on different values and where Beta is a predetermined submultiple of the angle Alpha , means for producing digital signals representing the changeable values of the numbers m and n, a source of reference voltage Er, means responsive to the digital signals representing m for selectively connecting that one of said first plurality of resistors which corresponds to the value of m between said source and an additive input of said first amplifier, means responsive to the digital signals representing m for selectively connecting that one of said second plurality of resistors which corresponds to the value of m between said source and an additive input of said second amplifier, means responsive to the digital signals representing n for connecting that one of said third plurality of resistors which corresponds to the value of n between the output of said first amplifier and a subtractive input of said second amplifier, and means responsive to the digital signals representing n for connecting that one of said fourth plurality of resistors which corresponds to the value of n between the output of said second amplifier and an additive input of said first amplifier.

Claim 30

In a digital-to-analog converter for producing two AC output signals Es and Ec which in amplitude are proportional to the sine and cosine of a changeable number mn having higher and lower order portions m and n, the combination comprising first and second signal combining operational amplifiers each having the same high gain and a negative feedback resistor Rf, and respectively producing AC output signals designatable Es and Ec, a first plurality of resistors Ra0, Ra1, Ra2...Rax which in value are sized to make the ratios (Rf/Ra0), (Rf/Ra1), (Rf/Ra2)...Rf/Rax) equal to sin m Alpha , as m takes on different values and where Alpha is a predetermined angle, a second plurality of resistors Rb0, Rb1, Rb2...Rbx which in value are sized to make the ratios (Rf/Rb0), (Rf/Rb1), (Rf/Rb2)...Rf/Rbx) equal to cos m Alpha as m takes on different values, third and fourth identical pluralities of resistors Rc0, Rc1, Rc2...Rcx which in value are sized to make the ratios (Rf/Rc0), (Rf/Rc1), (Rf/Rc2)...Rf/Rcx) equal to tan n Beta as n takes on different values and where Beta is a predetermined submultiple of the angle Alpha , means for producing digital signals representing the changeable values of the numbers m and n, a source of reference voltage Er, means responsive to the digital signals representing m for selectively connecting that one of said first plurality of resistors which corresponds to the value of m between said source and an additive input of said first amplifier, means responsive to the digital signals representing m for selectively connecting that one of said second plurality of resistors which corresponds to the value of m between said source and an additive input of said second amplifier, means responsive to the digital signals representing n for connecting that one of said third plurality of resistors which corresponds to the value of n between the output of said first amplifier and a subtractive input of said second amplifier, and means responsive to the digital signals representing n for connecting that one of said fourth plurality of resistors which corresponds to the value of n between the output of said second amplifier and an additive input of said first amplifier.

Claim 31

The combination set forth in claim 22 further characterized by means for reversing the effective polarity with which signals are applied through said first plurality of resistors to an input of said first amplifier when the angle represented by m Alpha lies in the third or fourth quadrants, as contrasted to the first or second quadrants; and means for reversing the effective polarity with which signals are applied through said second plurality of resistors to said second amplifier when the angle m Alpha lies in the second or third quadrants, as contrasted to the first or fourth quadrants.

Claim 32

The combination set forth in claim 22 further characterized in that the four named means for selectively connecting one of each of the four pluralities of resistors includes field effect transistors in series with each individual resistor and selectively turned on or off by control voltages derived from the number-representing signals.