Synthesis of Vector Networks

The convenience of vector notation in formulating physical geometrical problems results principally because the significance of the problem can be isolated from the analysis used in its solution. When analog computer techniques are employed in problems of this nature, the advantages of the vector methods frequently are lost because the computer inherently is more adaptable to solving problems described in the algebraic field of real numbers rather than in a vector space, and vector equations must be reduced to their scalar counterparts before a network for solving the equations may be synthesized. To facilitate treatment of problems of this type, a method is presented for synthesizing networks directly from the vector notation. This method will simplify synthesis and analysis of the networks by drawing a closer analogy between the mathematics and the electronics. The application of transformations and operators represents two areas in which the pertinent aspects of the method can be illustrated. This is accomplished by presenting first the basic mathematical background, followed by the network aspects of the problem, and finally, by the illustrative examples. The more extensive problems usually encountered, for example, in airborne fire-control systems, then may be synthesized by proper application of the elementary ``vector networks.´´