A new low cost converter topology is proposed for sinusoidal position encoders. The converter enables determination of the angle from the sine and cosine signals of the encoder. When used with resolvers, the implementation of the present scheme takes advantage of the available excitation signal used to operate the device. This trigonometric reference signal is optimally used to generate an analogue signal equivalent to a digital look-up table (LUT). This enables determination of the mechanical angle without using LUT, A/D, and D/A converters. The scheme is optimized in order to achieve highest possible precision. Beside simplicity of its implementation, the proposed converter offers the advantage of robustness to amplitude fluctuation of the transducer excitation signal. The converter was implemented using ordinary low-cost analog components. The theory of operation, computer simulation, and experimental results are given.