Switching arrangement for the transformation of digital angles into analog sine-and/or cosine values

Claim 2

A switching arrangement for generating analog approximations of trigonometric functions in response to digital representations of angle, said arrangement including a constant amplitude reference source, and a converter output for supplying an analog output, and further comprising: a. first digital-to-analog converter circuitry interposed between said constant amplitude reference source and said converter output and responsive to input digital angle values at least in the range of 0° to 45° to provide analog approximations of at least one trigonometric function selected from the sine function and the cosine function at said converter output, said first converter circuitry including a first resistance network comprising a first set of n individual resistors having respective resistance values selected to be functions of successive powers of 2, b. a digital control register having a series of register stages for registering a digital angle value and including at least n register stages sufficient to represent digital angle values in a range of 0° to 45° with such n register stages representing respective angle values which are functions of successive powers of 2, c. a first switching circuit connected with said first resistance network and operable for connecting said individual resistors in respective first circuit configurations to approximate successive values of the trigonometric function, said first switching circuit being coupled with said n register stages of said digital control register and being responsive to respective digital angle values therein to connect said resistors in respective corresponding circuit configurations to approximate the trigonometric function corresponding to the respective digital angle values, d. a correcting circuit interposed between said constant amplitude reference source and said converter output and comprising second digital-to-analog converter circuitry including a second resistance network with a second set of resistors having values which are functions of successive powers of 2, and e. a second switching circuit connected with said second resistance network and being operable for connecting said second resistance network in respective second circuit configurations to generate a correction function, said second switching circuit being connected with register stages of said digital control register and controlling the second resistance network to provide a correction function having maxima at odd multiples of 45° and minima at even multiples of 45° and having respective values in each of the respective second circuit configurations to modify the analog output at said converter output to more closely approximate the trigonometric function.

Claim 3

A switching arrangement in accordance with claim 1 characterized in that said correcting circuit is connected between said constant amplitude reference source and said first resistance network and produces a voltage at the input of the first resistance network which serves to precompensate for errors of the first resistance network in approximating the trigonometric function.

Claim 4

A switching arrangement in accordance with claim 1 characterized in that the correcting circuit is connected between said first resistance network and said converter output and provides post-compensation for errors of the first resistance network in approximating the trigonometric function.

Claim 5

A switching arrangement in accordance with claim 1 characterized in that a single common control register controls both said first switching circuit and said second switching circuit.

Claim 6

A switching arrangement according to claim 1 with said first digital-to-analog converter circuitry including two of said first resistance networks controlled by said first switching circuit, said first switching circuit being responsive to respective digital angle values to connect the resistors of one of said first resistance networks in accordance with the direct value of the angle digits and to connect the other of the first resistance networks in accordance with the complement of the digits of the registered digital angle value, and a switching register responsive to the quadrant of the digital angle value for selectively inverting the control of said first switching circuit from said digital control register in the case of angle value from 90° to 180° and from 270° to 360°.

Claim 7

A switching arrangement according to claim 5 characterized in that a further switching register is interposed between the control register and the second switching circuit for carrying out an inversion of the output from said digital control register to said second switching circuit in the case of angle values between 45° and 90°, 135° and 180°, 225° and 270°, and 315° and 360°.

Claim 8

A switching arrangement according to claim 1 with said first set of individual resistors having respective resistance values related in accordance with successive terms of a geometrical series.

Claim 9

A switching arrangement in accordance with claim 1 with said first digital-to-analog converter circuitry comprising two of said first resistance networks, said first switching circuit controlling the circuit configurations of one of said first resistance networks in accordance with a plural order binary signal generated as a function of the registered digital angle value, and controlling the other of said first resistance networks in accordance with the complement of said plural order binary signal whereby the output of one of said first resistance networks approximates a sine function while the output of the other of said first resistance networks approximates the cosine function of the same angle, said correcting circuit being responsive to a plural order binary signal representing angle values between 0 and 22.5°, and having two of said second resistance networks, said second switching circuit operating one of said resistance networks in accordance with the direct value of the plural order binary signal and operating the other of said second resistance networks in accordance with the complement of the plural order binary signal, and an inverter circuit interposed between said plural order binary signal and said second switching circuit and responsive to the stage of said digital control register representing an angle of 45° to invert said plural order binary signal at 90° intervals over the range of said digital control register.

Claim 10

A switching arrangement in accordance with claim 1 with said first digital-to-analog circuitry comprising two of said first resistance networks to provide two sets of n individual resistors, each set having respective resistance values selected to be functions of successive powers of 2, the first switching circuit being connected with both of said first resistance networks and controlling the circuit configurations of the respective first resistance networks to approximate values of the sine and cosine functions respectively, of the digital angle value registered in said digital control register.

Claim 11

A switching arrangement in accordance with claim 9 with said correcting circuit being connected between said constant amplitude reference source and each of said first resistance networks to produce an input analog signal common to both of said first resistance networks which serves to precompensate for errors of the first resistance networks in approximating the sine and cosine functions, respectively.

Claim 12

A switching arrangement according to claim 10 with a single common digital control register controlling both said first switching circuit and said second switching circuit to generate precompensated sine and cosine functions based on the angle value registered by said single common digital control register.

Claim 13

A switching arrangement according to claim 9 with said correcting circuit comprising two second resistance networks connected between the respective first resistance networks and the respective converter outputs to provide postcompensation for the errors of the respective first resistance networks in approximating the sine and cosine functions respectively, each of said second resistance networks providing a correction function having maxima at odd multiples of 45° and minima at even multiples of 45°.

Claim 14

A switching arrangement for generating analog approximations of trigonometric functions in response to digital representations of angle, said arrangement including a constant amplitude reference source and a pair of converter outputs for supplying analog outputs, and further comprising: a. first digital-to-analog converter circuitry interposed between said constant amplitude reference source and said converter outputs, said first converter circuitry including respective resistance network means for generating sine and cosine approximations respectively, and comprising a set of n individual resistor means having respective resistance values selected to generate sine and cosine approximations for digital angle values corresponding to successive powers ot 2. b. a digital control register having a series of register stages for registering a digital angle value and including at least n register stages corresponding to successive powers of 2 and sufficient to represent digital angle values in a range of 0° to 45°, c. a first switching circuit connected with said resistance network means and operable for connecting said individual resistor means in respective circuit configurations to generate approximations of the sine and cosine functions at the respective converter outputs, said first switching circuit being coupled with said n register stages of said digital control register and being responsive to respective digital angle values therein to connect said resistor means in respective corresponding circuit configurations to generate sine and cosine approximations corresponding to the respective digital angle values, d. a common correcting circuit connected between said constant amplitude reference source and said first converter circuitry and comprising second digital-to-analog converter circuitry having a common output connected via the respective resistance network means with the respective converter outputs, the second digital-to-analog converter circuitry comprising a common resistance network with a single set of resistors having values selected to approximate respective different common corrections needed at respective digital angle values corresponding to successive powers of 2 such that the sine and cosine functions are substantially more closely approximated at said converter outputs, and e. a second switching circuit connected with said common resistance network and operable for connecting said common resistance network in respective circuit configurations, said second switching circuit being connected to the outputs of the digital control register so as to generate a correction function at the common output of said second digital-to-analog converter circuit having maxima at odd multiples of 45° and minima at even multiples of 45°, and so as to systematically vary said correction function for each incremental angle value over the range of such respective digital angle values corresponding to successive powers of 2.

Claim 15

A switching arrangement for generating analog approximations of trigonometric functions in response to digital representations of angle, said arrangement including a constant amplitude reference source and a pair of converter outputs for supplying analog outputs, and further comprising: a. first digital-to-analog converter circuitry interposed between said constant amplitude reference source and said converter outputs, said first converter circuitry including respective resistance network means for generating sine and cosine approximations respectively, and comprising a set of n individual resistor means having respective resistance values selected to generate sine and cosine approximations for digital angle values corresponding to successive powers ot 2. b. a digital control register having a series of register stages for registering a digital angle value and including at least n register stages corresponding to successive powers of 2 and sufficient to represent digital angle values in a range of 0° to 45°, c. a first switching circuit connected with said resistance network means and operable for connecting said individual resistor means in respective circuit configurations to generate approximations of the sine and cosine functions at the respective converter outputs, said first switching circuit being coupled with said n register stages of said digital control register and being responsive to respective digital angle values therein to connect said resistor means in respective corresponding circuit configurations to generate sine and cosine approximations corresponding to the respective digital angle values, d. a common correcting circuit connected between said constant amplitude reference source and said first converter circuitry and comprising second digital-to-analog converter circuitry having a common output connected via the respective resistance network means with the respective converter outputs, the second digital-to-analog converter circuitry comprising a common resistance network with a single set of resistors having values selected to approximate respective different common corrections needed at respective digital angle values corresponding to successive powers of 2 such that the sine and cosine functions are substantially more closely approximated at said converter outputs, and e. a second switching circuit connected with said common resistance network and operable for connecting said common resistance network in respective circuit configurations, said second switching circuit being connected to the outputs of the digital control register so as to generate a correction function at the common output of said second digital-to-analog converter circuit having maxima at odd multiples of 45° and minima at even multiples of 45°, and so as to systematically vary said correction function for each incremental angle value over the range of such respective digital angle values corresponding to successive powers of 2.