Digital Resolver Theory and Application

This paper describes a real time digital computing machine for calculation of coordinate transfor-mation and other trigonometric equations. It has same functions as servo computer with analog resolvers has and is more accurate, faster and of smaller size.<BR>When rotation angle in a plane is given, it is decomposed into many rotation steps in which'vector components transformation can be performed easily and each successive step is determined so as to reduce remaining error angle. When two components of a vector are given, its magnitude and argument are obtained by the almost same process, minimizing the remaining quadrature component. Resultant transformations are<BR>x'=x cosφ+ysinφ<BR>y'=-xsinφ+ysinφ or R=√x²+y²<BR>θ=tan^-1y/x<BR>In the rotation process, at first, multiple right angle transformations, number of which is determined from the bit pattern of φ or x and y, make remaining error angle within ± 45°. Then, ±sin^-12^-n or ±tan-12-n are next sequences of rotations, in which component transform arithmetic is of the form a±2^-mb, where a and b are results of the immediate previous arithmetic step. The functions of cascading analog resolvers are replaced by programming the time sharing use of this machine, which are possible by connecting the sequencer outputs to the control gate inputs. The machine, including the programming unit, are composed of four electromagnetic delay lines, two full adders and about ten control flip-flops and mean transformation time is about 0. 7 ms, using 1 Mc clock.<BR>In the paper some logical design techniques and circuits are given and three examples of the application are also described.