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AD1896 Datasheet(PDF) 18 Page - Analog Devices |
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AD1896 Datasheet(HTML) 18 Page - Analog Devices |
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18 / 28 page  REV. A AD1896 –18– ASRC FUNCTIONAL OVERVIEW THEORY OF OPERATION Asynchronous sample rate conversion is converting data from one clock source at some sample rate to another clock source at the same or a different sample rate. The simplest approach to an asynchronous sample rate conversion is the use of a zero-order hold between the two samplers shown in Figure 4. In an asyn- chronous system, T2 is never equal to T1 nor is the ratio between T2 and T1 rational. As a result, samples at fS_OUT will be repeated or dropped producing an error in the resampling process. The frequency domain shows the wide side lobes that result from this error when the sampling of fS_OUT is convolved with the attenuated images from the sin(x)/x nature of the zero-order hold. The images at fS_IN, dc signal images, of the zero-order hold are infinitely attenuated. Since the ratio of T2 to T1 is an irrational number, the error resulting from the resampling at fS_OUT can never be eliminated. However, the error can be sig- nificantly reduced through interpolation of the input data at fS_IN. The AD1896 is conceptually interpolated by a factor of 2 20. ZERO-ORDER HOLD IN OUT fS_IN = 1/T1 fS_OUT = 1/T2 ORIGINAL SIGNAL SAMPLED AT fS_IN SIN(X)/X OF ZERO-ORDER HOLD SPECTRUM OF ZERO-ORDER HOLD OUTPUT SPECTRUM OF fS_OUT SAMPLING fS_OUT 2 fS_OUT FREQUENCY RESPONSE OF fS_OUT CONVOLVED WITH ZERO-ORDER HOLD SPECTRUM Figure 4. Zero-Order Hold Being Used by fS_OUT to Resample Data from fS_IN THE CONCEPTUAL HIGH INTERPOLATION MODEL Interpolation of the input data by a factor of 2 20 involves placing (2 20 – 1) samples between each f S_IN sample. Figure 5 shows both the time domain and the frequency domain of interpolation by a factor of 2 20. Conceptually, interpolation by 220 would involve the steps of zero-stuffing (2 20 – 1) number of samples between each fS_IN sample and convolving this interpolated signal with a digital low-pass filter to suppress the images. In the time domain, it can be seen that fS_OUT selects the closest fS_IN ¥ 220 sample from the zero-order hold as opposed to the nearest fS_IN sample in the case of no interpolation. This significantly reduces the resampling error. IN OUT fS_IN fS_OUT TIME DOMAIN OF fS_IN SAMPLES TIME DOMAIN OUTPUT OF THE LOW-PASS FILTER TIME DOMAIN OF fS_OUT RESAMPLING TIME DOMAIN OF THE ZERO-ORDER HOLD OUTPUT INTERPOLATE BY N LOW-PASS FILTER ZERO-ORDER HOLD Figure 5. Time Domain of the Interpolation and Resampling In the frequency domain shown in Figure 6, the interpolation expands the frequency axis of the zero-order hold. The images from the interpolation can be sufficiently attenuated by a good low-pass filter. The images from the zero-order hold are now pushed by a factor of 2 20 closer to the infinite attenuation point of the zero-order hold, which is fS_IN ¥ 220. The images at the zero-order hold are the determining factor for the fidelity of the output at fS_OUT. The worst-case images can be computed from the zero-order hold frequency response, maximum image = sin ( p ¥ F/fS_INTERP)/(p ¥ F/fS_INTERP). F is the frequency of the worst-case image that would be 2 20 ¥ fS_IN ± fS_IN/2 , and fS_INTERP is fS_IN ¥ 220. The following worst-case images would appear for fS_IN = 192 kHz: Image at fS_INTERP – 96 kHz = –125.1 dB Image at fS_INTERP + 96 kHz = –125.1 dB |
Similar Part No. - AD1896_15 |
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Similar Description - AD1896_15 |
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