Direct digital synthesis (DDS) is a method employed by

frequency synthesizer A frequency synthesizer is an electronic circuit that generates a range of frequencies from a single reference frequency. Frequency synthesizers are used in many modern devices such as radio receivers, televisions, mobile telephones, radioteleph ...

s used for creating arbitrary

waveform In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electro ...

s from a single, fixed-frequency reference clock. DDS is used in applications such as signal generation,

local oscillator In electronics, a local oscillator (LO) is an electronic oscillator used with a mixer to change the frequency of a signal. This frequency conversion process, also called heterodyning, produces the sum and difference frequencies from the frequenc ...

s in communication systems,

function generator In electrical engineering, a function generator is usually a piece of electronic test equipment or software used to generate different types of electrical waveforms over a wide range of frequencies. Some of the most common waveforms produced ...

s, mixers,

modulator In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...

s, sound synthesizers and as part of a digital

phase-locked loop A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. There are several different types; the simplest is an electronic circuit consisting of a ...

Overview

Direct digital synthesizer block diagram

A basic Direct Digital Synthesizer consists of a frequency reference (often a

crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...

SAW A saw is a tool consisting of a tough blade, wire, or chain with a hard toothed edge. It is used to cut through material, very often wood, though sometimes metal or stone. The cut is made by placing the toothed edge against the material and mov ...

oscillator), a

numerically controlled oscillator A numerically-controlled oscillator (NCO) is a digital signal generator which creates a synchronous (i.e. clocked), discrete-time, discrete-valued representation of a waveform, usually sinusoidal. NCOs are often used in conjunction with a digit ...

(NCO) and a

digital-to-analog converter In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function. There are several DAC archit ...

(DAC) as shown in Figure 1. The reference oscillator provides a stable time base for the system and determines the frequency accuracy of the DDS. It provides the clock to the ''NCO'', which produces at its output a discrete-time, quantized version of the desired output waveform (often a sinusoid) whose period is controlled by the digital word contained in the ''Frequency Control Register''. The sampled, digital waveform is converted to an analog waveform by the ''DAC''. The output reconstruction filter rejects the spectral replicas produced by the

zero-order hold The zero-order hold (ZOH) is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter (DAC). That is, it describes the effect of converting a discrete-time signal to a continuous-time sign ...

inherent in the analog conversion process.

Performance

A DDS has many advantages over its analog counterpart, the

(PLL), including much better frequency agility, improved phase noise, and precise control of the output phase across frequency switching transitions. Disadvantages include spurious responses mainly due to truncation effects in the NCO, crossing spurs resulting from high order (>1) Nyquist images, and a higher noise floor at large frequency offsets due mainly to the

. Because a DDS is a sampled system, in addition to the desired waveform at output frequency F_out, Nyquist images are also generated (the primary image is at F_clk-F_out, where F_clk is the reference clock frequency). In order to reject these undesired images, a DDS is generally used in conjunction with an analog reconstruction lowpass filter as shown in Figure 1.Kroupa,Venceslav F.,''Direct Digital Frequency Synthesizers'', IEEE Press, 1999,

Frequency agility

The output frequency of a DDS is determined by the value stored in the frequency control register (FCR) (see Fig.1), which in turn controls the NCO's phase accumulator step size. Because the NCO operates in the discrete-time domain, it changes frequency instantaneously at the clock edge coincident with a change in the value stored in the FCR. The DDS output frequency settling time is determined mainly by the phase response of the reconstruction filter. An ideal reconstruction filter with a linear phase response (meaning the output is simply a delayed version of the input signal) would allow instantaneous frequency response at its output because a linear system can not create frequencies not present at its input.

Phase noise and jitter

The superior close-in phase noise performance of a DDS stems from the fact that it is a feed-forward system. In a traditional

phase locked loop A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. There are several different types; the simplest is an electronic circuit consisting of a ...

(PLL), the

frequency divider A frequency divider, also called a clock divider or scaler or prescaler, is a circuit that takes an input signal of a frequency, f_, and generates an output signal of a frequency: : f_ = \frac where n is an integer. Phase-locked loop frequency ...

in the feedback path acts to multiply the phase noise of the reference oscillator and, within the PLL loop bandwidth, impresses this excess noise onto the VCO output. A DDS, on the other hand, reduces the reference clock phase noise by the ratio

f_/f_o

because the fractional division of the clock derives its output. Reference clock

jitter In electronics and telecommunications, jitter is the deviation from true periodicity of a presumably periodic signal, often in relation to a reference clock signal. In clock recovery applications it is called timing jitter. Jitter is a significa ...

translates directly to the output, but this jitter is a smaller percentage of the output period (by the ratio above). Since the maximum output frequency is limited to

f_/2

, the output phase noise at close-in offsets is always at least 6dB below the reference clock phase noise. At offsets far removed from the carrier, the phase-noise floor of a DDS is determined by the power sum of the DAC quantization noise floor and the reference clock phase noise floor.

References

External links and further reading

Tutorial on Digital Signal Synthesis
(From Analog Devices) *L. Cordesses
"Direct Digital Synthesis: A Tool for Periodic Wave Generation (Part 1)"
''IEEE Signal Processing Magazine, DSP Tips & Tricks column'', pp. 50–54, Vol. 21, No. 4 July 2004. *L. Cordesses
Direct Digital Synthesis: A Tool for Periodic Wave Generation (Part 2)
''IEEE Signal Processing Magazine, DSP Tips & Tricks column'', pp. 110–117, Vol. 21, No. 5, Sep. 2004. * {{DEFAULTSORT:Direct Digital Synthesizer Digital signal processing Electronic oscillators