Centrad GF266 Manuel D'instructions page 22

For a given delta, the number of points per period is equal to 2
228/269 = 997901.3 points
The frequency difference corresponding to 1 delta is Fdiff = FMCLK/2
If FMCLK = 50MHz and n = 228, then Fdiff = 0.186Hz
This number also corresponds to the smallest frequency which can be generated.
Block diagram (Fig. 4)
f
M C L K
D e l t a
D e l t a
R e g i s t e r
Signal reconstruction steps (Fig. 5)
Phase
Accumulator
In a Mathematical Theory of Communication (1949), Claude Elwood Shannon states that the digital representation
of a sine wave signal requires at least 2 samples per period. This means that 2 points are theoretically sufficient to
reconstruct a sine wave.
In DDS, for the sine wave, the DAC output is connected to a 7-pole elliptic filter the purpose of which is to filter and
smooth the signal. Its inertia compensates the reduction in the number of points proportional to the delta and therefore
to frequency (NbrPoints = 2
To maintain a constant level over the entire range, the maximum frequency is limited, in general to fMCLK / 3.
DDS capabilities
This system offers a very wide frequency range without the need for switching capacitors as is almost always the
case with conventional analogue systems. DDS also allows frequency to be changed almost instantaneously (in 1
or a few fMCLK clock cycles) with phase continuity, which is impossible in PLL-based systems, which require a lock-
in time.
In contrast with analogue systems, this process provides excellent accuracy and stability, whatever the generated
frequency.
The digital technique is more flexible than the analogue technique; the functions can easily be nested.
For example, this process makes it possible to implement modulation schemes, such as FSK and PSK, that are quite
complicated to implement using conventional generators :
- For FSK: the delta register shown in the block diagram (see above) is duplicated. The two registers, loaded with
the deltas corresponding to frequencies F1 and F2, are switched at the modulating frequency.
- For PSK: 2 registers loaded with the numbers corresponding to be switched F1 and F2 are sequentially added to
the phase register (Accumulator) at the modulating frequency.
Summary of signal characteristics
The sine wave is a waveform into which all the other waveforms can be decomposed.
The signals can be characterized by their spectral properties (Fourier transform).
A perfect sine wave consists of a single frequency (spectral purity).
The other basic signals decompose into a fundamental frequency (waveform repetition frequency) and multiples of
this frequency, called harmonics.
The signal shapes closely depend on the amplitude and phase distribution of harmonics with reference to the
fundamental (line spectrum).
n
2
A c c u m u l a t o r
Phase-to-amplitude
conversion by the
ROM
n /∆).
n
/∆. In the previous example:
n
Fig. 4
i
2
R O M
Fig. 5
Dac
Output
- 22 -
j
2 V
D A C
o u t
Filtred
output