Editing Numerically controlled oscillator (section)

==Operation==

An NCO generally consists of two parts: 
*A ''phase accumulator'' (PA), which adds to the value held at its output a frequency control value at each clock sample.
*A ''phase-to-amplitude converter'' (PAC), which uses the phase accumulator output word (phase word) usually as an index into a waveform [[look-up table]] (LUT) to provide a corresponding amplitude sample. Sometimes [[linear interpolation|interpolation]] is used with the look-up table to provide better accuracy and reduce phase error noise. Other methods of converting phase to amplitude, including mathematical algorithms such as [[power series]] can be used, particularly in a software NCO.

[[Image:Generic NCO.png|frame|Figure 1: Numerically controlled oscillator with optional quadrature output]]

When clocked, the phase accumulator (PA) creates a [[modulo operation|modulo]]-2<sup>N</sup> [[sawtooth wave]]form which is then converted by the phase-to-amplitude converter (PAC) to a sampled sinusoid, where N is the number of bits carried in the phase accumulator. N sets the NCO frequency resolution and is normally much larger than the number of bits defining the memory space of the PAC [[look-up table]]. If the PAC capacity is 2<sup>M</sup>, the PA output word must be truncated to M bits as shown in Figure 1. However, the truncated bits can be used for interpolation. The truncation of the phase output word does not affect the frequency accuracy but produces a time-varying periodic phase error which is a primary source of spurious products. Another spurious product generation mechanism is finite word length effects of the PAC output (amplitude) word.<ref name="kroupa">{{cite book |last=Kroupa |first=V. F. |title=Direct Digital Frequency Synthesizers |publisher=IEEE Press |year=1999 |isbn=0-7803-3438-8}}</ref>

The frequency accuracy relative to the clock frequency is limited only by the precision of the arithmetic used to compute the phase.<ref name="kroupa"/> NCOs are phase- and frequency-agile, and can be trivially modified to produce a [[phase modulation|phase-modulated]] or [[frequency modulation|frequency-modulated]] output by summation at the appropriate node, or provide [[quadrature phase|quadrature]] outputs as shown in the figure.