Numerically controlled oscillator: Difference between revisions

Revision as of 03:42, 3 November 2014

Revision as of 17:14, 7 November 2014

Line 1:

A '''numerically controlled oscillator''' ('''NCO''') is a digital [[signal generator]] which creates a [[Synchronous circuit|synchronous]] (i.e. clocked), discrete-time, discrete-valued representation of a [[waveform]], usually [[sinusoidal]].<ref name="IEEE">{{ cite book | author last= Radatz, |first=J. | title = The IEEE Standard Dictionary of Electrical and Electronics Terms | publisher = IEEE Standards Office | ___location = New York, NY | year = 1997 |isbn=}}</ref> NCOs are often used in conjunction with a [[digital-to-analog converter]] (DAC) at the output to create a [[direct digital synthesizer]] (DDS).{{#tag:ref|While some authors use the terms DDS and NCO interchangeably,<ref name="latticeSC" /> by convention an NCO refers to the digital (i.e. the discrete-time, discrete amplitude) portion of a DDS<ref name="IEEE"/>}}

Numerically controlled oscillators offer several advantages over other types of oscillators in terms of agility, accuracy, stability and reliability.<ref name="latticeSC">{{ cite web | title = Numerically Controlled Oscillator | url = http://www.latticesemi.com/products/intellectualproperty/ipcores/numericallycontrolledosci/index.cfm | publisher = Lattice Semiconductor Corporation | year = 2009 }}</ref> NCOs are used in many communications systems including digital up/down converters used in 3G wireless and software radio systems, digital PLLs, radar systems, drivers for optical or acoustic transmissions, and multilevel [[Frequency-shift keying|FSK]]/[[Phase-shift keying|PSK]] modulators/demodulators.<ref name="latticeSC"/>

Line 11:

[[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^N [[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^M, 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 | author 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.