|Título/s:||Arbitrary function generator using Direct Digital Synthesis|
|Autor/es:||Iuzzolino, Ricardo; Adad, Walter F.|
|Institución:||INTI-Física y Metrología. Buenos Aires, AR|
|Palabras clave:||Generadores de señales; Técnicas digitales; Mediciones; Frecuencia; Modulación; Distorsión; Convertidores digital-analógico|
|Notas:||Fuente: IEEE, de acuerdo a su política de copywright: "Los autores / empleadores pueden reproducir o autorizar a terceros a reproducir la Obra, material extraído literalmente de la Obra o trabajos derivados para el uso personal del autor o para uso de la empresa, siempre que se indique la fuente y el aviso de copyright de IEEE, no deben usarse las copias de ninguna manera que implique el respaldo de IEEE de un producto o servicio de cualquier empleador y las copias en sí no se ofrecen para la venta"|
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Arbitrary function generator using Direct Digital Synthesis
Walter F. Adad* and Ricardo J. Iuzzolino*
*Instituto Nacional de Tecnología Industrial, Buenos Aires, Argentina
Abstract — This paper describes the development of an
arbitrary function generator based on Direct Digital Synthesis
(DDS) technique. This signal generator is capable of generating
single-tone sinusoidal (THD < -80 dBc), two-tone sinusoidal,
square wave, triangular and sawtooth waveforms in the
frequency range from 0 to 10 kHz. The frequency stability
achieved is 3.9 µHz (τ = 2 s) and the amplitude stability is 2.0 µV
(τ = 2 s).
Index Terms — Measurement, frequency measurement,
amplitude modulation, signal generators, distortion.
This work extends the facilities and performance analysis of
the system described in . This new system can be used not
only for ADC characterization as indicated in  but also in
other areas, such as time and frequency measurements,
calibration of sound level meters and calibration of
In comparison with phase locked loop (PLL), this method
allows to synthesize precise frequencies using low-cost
commercial devices (e.g. with a 48-bit DDS a frequency
resolution of 1.421 nHz can be achieved). Furthermore, this
technique has a low transient time to the output frequency and
few space requirements (commercial devices have small
II. THEORY OF OPERATION OF DIRECT DIGITAL SYNTHESIS
DDS technology consists in using digital signal processing
to generate signals at different frequencies selectable by
software from a reference clock.
A simplified block diagram of a DDS is shown in Fig. 1.
The block diagram consists of four blocks: a reference clock, a
phase accumulator, a look-up table and a digital-to-analog
(D/A) converter. The theory of operation can be summarized
as follow: the phase accumulator sums at each clock pulse the
tuning word. Thus, its output is a digital ramp (binary code).
The look-up table converts the phase accumulator output in a
digital sine. Finally, the D/A converter transforms the digital
sine into an analog signal.
The relationship between the tuning word, the clock
reference, the number of bits of the DDS and the frequency of
the output signal is shown in (1), as proposed in ,
f? ? M ???????N ,
where f? is the output frequency, M is the tuning word, f?????
is the reference clock frequency and N is the phase
Fig. 1. Simplified block diagram of a DDS
III. SYSTEM DESCRIPTION
Figure 2 shows a simplified block diagram of the developed
system. The reference clock can be either internal or external
set by a clock selector, which is controlled by a
microcontroller. The clock provider block delivers the clock
signal to the system and to an output for synchronization with
The generation of a two-tone sinusoidal signal was done
combining the output of two AD9852 (A and B in Fig. 2).
Single-tone sinusoidal was obtained by the AD9852-A.
Because the AD9852 is only capable to synthesize sine and
square waveforms, a third DDS (AD9834) was used to
generate triangular and sawtooth waveforms.
Phase accumulator truncation  and the DDS internal D/A
converter  contribute to the total harmonic distortion
(THD). To minimize their effects, the output signal of the
AD9852 was filtered by a third order Butterworth lowpass
passive filter. To reduce the system noise the filters were
made with passive components, as suggested in . Besides,
the Butterworth topology was used because of the flatness
characteristic in the passband, hence the signal amplitude is
attenuated by the same gain deviation in the frequency band of
The amplitude of the output signal of the DDS device is
limited to 1 V. To amplify the signals and not to degrade the
THD of the system, low distortions programmable gain
amplifiers (PGA) AD8250 were employed to remove spurious
frequencies generated by the PGAs, their output were also
filtered by the same filter topologies as in the case of the DDS
Finally, to combine the outputs of the AD9852-A and
AD9852-B to generate the two-tone signal, an adder and a
multiplier circuits have been designed.
622978-1-4673-0442-9/12/$31.00 2012 IEEE
The hardware was mounted in a two-layer PCB which was
toughly designed in order to avoid interference between
Some modifications were done to the system presented in
. One of them was the inclusion of optocouplers to
minimize noise between the microcontroller and the AD9852.
Other important modification in order to avoid crosstalk
between channels was to buffer the filtered output of the
A. Frequency and Amplitude Stability
To determine the frequency and amplitude stability the
system was programmed to generate a sinusoidal waveform
with nominal frequency of 62.5 Hz and nominal rms
amplitude of 0.23 V. The stability was obtained computing the
Allan variance on the measured data. The results are shown in
table 1 for an observation time τ = 2 s.
Table 1. Frequency and amplitude stability (τ = 2 s) of the arbitrary
function generator output.
62.539086 Hz 3.9 µHz 0.227902 V 2.0 µV
DDS technique is based on digital signal processing, thus it
does not introduce instability to the output frequency. As a
consequence, the contribution to the instability in frequency
depends on the reference clock.
B. Total Harmonic Distortion
The measured and simulated THD results listed in table 2
show that the designed system can achieve a THD of
Table 2. Total harmonic distortion of the system.
-80.37 dBc -80.62 dBc
The designed arbitrary function generator can achieve a
THD < -80 dBc, a frequency stability of 3.9 µHz and an
amplitude stability of 2.0 µV when generating single-tone
sinusoidal. This device can be used in measurement schemes
which require alternating signals as source.
Measurements of the total system performance will be
included at the full paper.
The authors would like to thank A. Tonina, M. Real, M.
Bierzychudek and L. Di Lillo for the valuables comments
made this work possible.
 W. Adad and R. Iuzzolino, “Low distortion signal generator
based on direct digital synthesis for ADC characterization”,
SEMETRO IX Conf. Digest, September 2011.
 Analog Devices, Inc. “A technical tutorial on Digital
 A. Torosyan and A. Willson, “Analysis of the output spectrum
for direct digital synthesizers in the presence of phase truncation
and finite arithmetic precision”, 2001.
 D. Buchanan, "AN-237: Choosing DACs for Direct Digital
Synthesis", Analog Devices, Inc.
 K. Lacanette, “A basic introduction to filters – active, passive
and switched capacitor NI”, Application Note AN-779, 1991.
Fig. 2. Simplified block diagram of the complete system