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The angle-to-amplitude converter is the building block that enables a DDS to produce a sinusoidal output. Like the accumulator, it is a digital circuit. The input and output buses of the angle-to-amplitude converter are generally of differing widths. Analog Devices’ denotes the input bus width as P bits and the output bus width as D bits. Typically, the output bus width coincides with the number of bits associated with the resolution of the DAC. That is, a DDS designed with a 10-bit DAC for example will normally have an angle-to-amplitude converter with a 10-bit output bus. The input bus of the angle-to-amplitude converter is usually three or more bits wider than its output bus. The reason for this will be explained in this product training module. The essential characteristic of the angle-to-amplitude converter is that it interprets the binary number, x, represented by its P-bit input bus as a fraction, namely x divided by 2 to the P, which occupies a range from 0 to slightly less than 1. Furthermore, it considers this fraction to represent the equivalent fraction of one full cycle of a sinusoid. That is, when x is 0 the angle-to-amplitude converter considers this to represent 0 degrees (or 0 radians). Similarly, when x is the maximum value of 2 to the P minus 1, the angle-to-amplitude converter considers this to represent slightly less than 360 degrees (or 2-pi radians). Intermediate values of x represent other angles proportionally. Most importantly, the angle-to-amplitude converter produces a digital output value, y, representing the amplitude of a sinusoid for the interpreted angle of the input value, x. Since y occupies a D-bit bus, the smallest y value is 0 and the largest y value is 2 to the D minus 1. In this way, 0 coincides with the bottom of the output sinusoid and 2 to the D minus 1 with the top of the sinusoid.
