Digital Frequency Synthesis Demystified by Bar-Giora Goldberg

By Bar-Giora Goldberg

As within the first variation of this booklet, my objective is to offer to the clothier a accomplished overview of electronic suggestions in glossy frequency synthesis layout. The textual content in particular addresses sensible designers, and an try has been made to method thesubject heuristically, through the use of intuitive factors and together with many layout examples. now not some time past, frequency synthesis used to be thought of a novelty. It was once utilized in the extra complicated and critical purposes.

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This is referred to as the Nyquist frequency(half the sampling rate). In DDS, the procedure of the signal sampling is reversed. And the process is therefore reversed. Suppose that, instead of sampling a sine wave, we generated its samples. (All can be calculated since the waveform is known; the sine is a perfectly known wave- Introduction to Frequency Synthesis 29 Figure 1-14 DDS block diagram and waveforms. ) Then according to the theorem it will be possible to reconstruct the sine wave signal perfectly.

34 Chapter One It is important to note that the aliasing frequencies are always generated. 1Fck ! Close to the Nyquist frequency, these frequencies that cannot be filtered are spurious signals (there is a limit to the sharpness of the filter). In few applications (this represents a rarity in DDS applications), the aliasing frequencies are controlled (to generate the in-band signal) rather than the fundamental output (see Chap. 4). The resolution or the smallest frequency increment or step size is given by Fck /ACM, where ACM is the maximum number of states the accumulator produces.

To generate the amplitude of the output waveform, it is necessary to transform the phase ␸(t) to sin[␸(t)], and this is usually done by using a read-only memory (ROM), since the transformation is nonlinear and ROM (or RAM) is a convenient tool. The output of the ROM is thus the digital representation of the sine wave signal amplitude, (digital) samples, and the DAC converts it to an analog sine wave. The LPF removes all the aliasing frequencies and causes the signal to appear smooth, as shown in Fig.

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