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DDS output spectrum analysis under phase truncation condition In DDS design, due to the limitation of volume and cost, and in order to save the ROM capacity, people hope to cut the phase accumulation as much as possible without introducing too much spurious. Low effective bit. For a bit accumulator whose number of bits is N, the ROM's capacity is much less than 2N, because when this ROM is addressed, the low B bit of the accumulator output is rounded off, and only the high NB bit of its output is used to address the ROM. This produces a phase error <1> in the DDS.
It is assumed that the digital-to-analog converter has ideal performance and does not consider amplitude quantization errors. Let the number of bits of the phase accumulator be N=12. When the frequency control words K, 255 (000011111111, in binary form) and the accumulator discards the number of bits B=4 (off the last 4 bits of 1111), the computer simulation output Spectrum as shown.
When the number of bits rounded down by the accumulator is increased to B = 5 (the last 5 bits are rounded down to 11111), the computer simulation output spectrum is as shown. DDS output spectrum (N=12, B=4, K=255) (N=12, B=4, K=255) DDS output spectrum (N=12, B=4, K=255) (N=12, B=4, K=255) DDS output spectrum without phase truncation error (N=12, B=4, K=256) (N=12, B=4, K=256) As can be seen, with With the increase of the phase accumulator bits, the spectral spurious level of the DDS output increases.
The phase truncation error is one of the three main sources of DDS spurs, but when the truncated low-B bits are all zero, no phase truncation will result and therefore no error will occur at this frequency control word K value. Given N=12, B=4, K=256 (000100000000), the output spectrum of the DDS when there is no phase truncation error. Compared with the two, the frequency control word K has a difference of only 1, but there is a qualitative difference between the spurs.
When the frequency setting data is K, the reference frequency is fr, and the number of phase accumulator bits is N, the signal frequency output by the DDS is fout=(frK)/2N. Although theoretically, the output frequency of the DDS can be from DC to fr/2. However, considering the steepness of the edge of the filter and the spectral purity of the output signal, the actual output frequency is usually from DC to 0.4fr<1>.