ID 683406
Date 11/06/2017
Public

## 3.1.3. CORDIC Architecture

The CORDIC algorithm, which can calculate trigonometric functions such as sine and cosine, provides a high-performance solution for very-high precision oscillators in systems where internal memory is at a premium.

The CORDIC algorithm is based on the concept of complex phasor rotation by multiplication of the phase angle by successively smaller constants. In digital hardware, the multiplication is by powers of two only. Therefore, the algorithm can be implemented efficiently by a series of simple binary shift and additions/subtractions.

In an NCO, the CORDIC algorithm computes the sine and cosine of an input phase value by iteratively shifting the phase angle to approximate the cartesian coordinate values for the input angle. At the end of the CORDIC iteration, the x and y coordinates for a given angle represent the cosine and sine of that angle, respectively.

Figure 10. CORDIC Rotation for Sine & Cosine Calculation

With the NCO MegaCore function, you can select parallel (unrolled) or serial (iterative) CORDIC architectures:

• You an use the parallel CORDIC architecture to create a very high-performance, high-precision oscillator—implemented entirely in logic elements—with a throughput of one output sample per clock cycle. With this architecture, there is a new output value every clock cycle.
• The serial CORDIC architecture uses fewer resources than the parallel CORDIC architecture. However, its throughput is reduced by a factor equal to the magnitude precision. For example, if you select a magnitude precision of N bits in the NCO MegaCore function, the output sample rate and the Nyquist frequency is reduced by a factor of N. This architecture is implemented entirely in logic elements and is useful if your design requires low frequency, high precision waveforms. With this architecture, the adder stages are stored internally and a new output value is produced every N clock cycles.