AD1896_15 Datasheet, PDF (18/28 Pages) Analog Devices – 192 kHz Stereo Asynchronous Sample Rate Converter

AD1896
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 f_{S_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 f_{S_OUT} is convolved with the
attenuated images from the sin(x)/x nature of the zero-order
hold. The images at f_{S_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
f_{S_OUT} can never be eliminated. However, the error can be sig-
nificantly reduced through interpolation of the input data at
f_{S_IN}. The AD1896 is conceptually interpolated by a factor of 2²⁰.
between each f_{S_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 f_{S_OUT} selects the closest f_{S_IN} Â¥ 2²⁰
sample from the zero-order hold as opposed to the nearest f_{S_IN}
sample in the case of no interpolation. This significantly reduces
the resampling error.
IN
f_{S_IN}
INTERPOLATE
BY N
LOW-PASS
FILTER
ZERO-ORDER
HOLD
OUT
f_{S_OUT}
TIME DOMAIN OF f_{S_IN} SAMPLES
TIME DOMAIN OUTPUT OF THE LOW-PASS FILTER
IN
f_{S_IN} = 1/T1
ZERO-ORDER
HOLD
OUT
f_{S_OUT} = 1/T2
ORIGINAL SIGNAL
TIME DOMAIN OF f_{S_OUT} RESAMPLING
SAMPLED AT f_{S_IN}
SIN(X)/X OF ZERO-ORDER HOLD
SPECTRUM OF ZERO-ORDER HOLD OUTPUT
SPECTRUM OF f_{S_OUT} SAMPLING
f_{S_OUT}
2 ؋ f_{S_OUT}
FREQUENCY RESPONSE OF f_{S_OUT} CONVOLVED WITH ZERO-ORDER
HOLD SPECTRUM
Figure 4. Zero-Order Hold Being Used by f_{S_OUT} to
Resample Data from f_{S_IN}
THE CONCEPTUAL HIGH INTERPOLATION MODEL
Interpolation of the input data by a factor of 2²⁰ involves placing
(2²⁰ – 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 2²⁰. Conceptually, interpolation by 2²⁰ would
involve the steps of zero-stuffing (2²⁰ – 1) number of samples
TIME DOMAIN OF THE ZERO-ORDER HOLD OUTPUT
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 2²⁰ closer to the infinite attenuation point
of the zero-order hold, which is f_{S_IN} Â¥ 2²⁰. The images at the
zero-order hold are the determining factor for the fidelity of the
output at f_{S_OUT}. The worst-case images can be computed from
the zero-order hold frequency response, maximum image =
sin (p ¥ F/f_{S_INTERP})/(p ¥ F/f_{S_INTERP}). F is the frequency of the
worst-case image that would be 2²⁰ Â¥ f_{S_IN} ± f_{S_IN}/2 , and
f_{S_INTERP} is f_{S_IN} Â¥ 2²⁰.
The following worst-case images would appear for f_{S_IN} =
192 kHz:
Image at f_{S_INTERP} – 96 kHz = –125.1 dB
Image at f_{S_INTERP} + 96 kHz = –125.1 dB
–18–
REV. A