Patent GB-843565-A (GB)
Title: Improvements in digital to analog converter of angular values
Inventor: TRIPP ROBERT WASHBURN
IPC: H03M1/00
Filed: 1958-02-10
Abstract: 843,565. Electric selective signalling systems. INDUCTOSYN Ltd. Feb. 10, 1958, No. 4302/58. Class 40 (1). [Also in Group XXXVI] In apparatus for converting digital representations of angular values to voltage analogues representing trigonometrical functions of the angles, there are two pairs of lines L1, L2 and L3, L4 which supply trigonometrical values sin # and cos # of an angle " # " and a switch 1 for interchanging the connection of the pairs with reversal of the lines of a pair in steps, thereby giving output signals having values corresponding to the sine and cosine functions of angle # plus a multiple of 90 degrees according to the selected step. The invention is an improvement in the converter described in Specification 807,219 in which angle values, represented on record cards, are converted to voltages representing the sine and cosine of the sums of these angles, for use in a servo system for machine tool control. To find the sine and cosine of the sum of two angles a, b, these equations are used: sin (a + b) = sin a cos b + cos a sin b cos (a + b) = cos a cos b - sin a sin b For convenience of circuitry the following expressions are derived by division by cos b which give proportional values suitable for use in a resolver: tan b cos a + sin a and cos a - tan b sin a In the apparatus shown angle values are given e.g. from a record reader, the first indicating that the required position lies in one of four quadrants, the second indicating that it lies in one of ten 9-degree steps and the third indicating that it lies in one of ten 0.9-degree steps. The second and third angles are combined by transformers 10 and 12 and the first is used to modify the signals produced thereby by means of switch 1. Transformer 2 has a reference voltage applied to its primary and its secondary has ten tappings producing sine and cosine values of angles between 0 and 90 degrees in steps of 9 degrees. Terminals 6 and 7 are selected by a stepping switch controlled by the input record to apply the sine and cosine values of the appropriate angle a to primary windings 9 and 11 of transformers 10 and 12. Each transformer has two secondary windings, one (13 or 14) having, say, a unity ratio and the other (16 or 29) having tappings to represent the tangent of the selected multiple of 0.9 degree, angle b. Connections are made so that the sin a value from winding 13 is added to the product of the cos a and tan b in winding 15. This sum, representing sin (a + b), is applied between lines L1 and L2. Between lines L3 and L4 are a winding 14, producing a cos a value, and a tapped winding 16 producing sin a tan b, the values being subtractively added to represent cos (a + b). The wipers 18, 19 of step switch 24 are positioned by the record reader to select the value for angle b. With switch 1 in the position shown, the sine value from lines L1 and L2 passes to the output line 20 and the cosine value from lines L3, L4 passes to line 21 without change. If switch 1 rotates one step clockwise from the position shown, this adds 90 degrees to the angle (a + b) selected by the second and third stages. The sine of an angle (# + 90 degrees) has the same value as cos # and cos (# + 90 degrees) equals minus sin #. The cosine value on lines L3 and L4 now passes to line 20 as sin (a + b + c) and the sine value from lines L1 and L2 passes to cosine leads 21 with reversal of sign. Similar changes are made in the third and fourth position of the switch 1 to represent angles in the third and fourth quadrant of a circle. Specification 807,218 also is referred to.