Continuous, Full-Circle Arctangent Circuit

Abstract

A circuit generates an analog voltage proportional to an angle, in response to two sinusoidal input voltages having magnitudes proportional to the sine and cosine of the angle, respectively. That is to say, given input voltages proportional to sin(Omega(t))sin(Theta) and sin(Omega(t))cos(Theta) [where Theta denotes the angle, mega denotes 2(pi) x a carrier frequency, and t denotes time], the circuit generates a steady voltage proportional to Theta. The output voltage varies continuously from its minimum to its maximum value as Theta varies from -180deg to 180deg. While the circuit could accept input modulated sine and cosine signals from any source, it must be noted that such signals are typical of the outputs of shaft-angle resolvers in electromagnetic actuators used to measure and control shaft angles for diverse purposes like aiming scientific instruments and adjusting valve openings. In effect, the circuit is an analog computer that calculates the arctangent of the ratio between the sine and cosine signals. The full-circle angular range of this arctangent circuit stands in contrast to the range of prior analog arctangent circuits, which is from slightly greater than -90deg to slightly less than +90deg. Moreover, for applications in which continuous variation of output is preferred to discrete increments of output, this circuit offers a clear advantage over resolver- to-digital integrated circuits.