Numerically Controlled Oscillator - Operation

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 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.

When clocked, the phase accumulator (PA) creates a modulo-2N sawtooth waveform 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 2M, 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.

The frequency accuracy relative to the clock frequency is limited only by the precision of the arithmetic used to compute the phase. NCOs are phase- and frequency-agile, and can be trivially modified to produce phase-modulated or frequency-modulated by summation at the appropriate node, or provide quadrature outputs as shown in the figure.