AD7821
lem of antialiasing filter design, the sampling rate is usually set
much greater than the Nyquist criterion. The maximum sam-
pling rate (f
MAX
) for the AD7821 in the WR-RD mode,
(t
RD
< t
INTL
) can be calculated as follows:
f
MAX
=
f
MAX
=
t
WR
1
+
t
RD
+
t
RI
+
t
P
INTERMODULATION DISTORTION
For intermodulation distortion (IMD), an FFT plot consisting
of very low distortion sine waves at two frequencies is generated
by sampling an analog input applied to the ADC. Figure 9
shows a 2048 point plot for IMD.
1
0.25E
−
6
+
0.25E
−
6
+
0.15E
−
6
+
0.35E
−
6
t
WR
= Write Pulse Width
t
RD
= Delay Time between
WR
and
RD
Pulses
t
RI
=
RD
to
INT
Delay
t
P
= Delay Time between Conversions
This permits a maximum sampling rate for the AD7821 of
1 MHz, which is much greater than the Nyquist criterion for
sampling a 100 kHz analog input signal.
DIGITAL SIGNAL PROCESSING APPLICATIONS
In Digital Signal Processing (DSP) application areas like voice
recognition, echo cancellation and adaptive filtering, the dy-
namic characteristics (Signal-to-Noise Ratio, Harmonic Distor-
tion, Intermodulation Distortion) of an ADC are critical. Since
the AD7821 is a very fast ADC with a built-in track-and-hold
function, it is specified dynamically as well as with standard dc
specifications (Total Unadjusted Error, etc.).
SIGNAL-TO-NOISE RATIO AND DISTORTION
Figure 9. FFT Plot for IMD
HISTOGRAM PLOT
The dynamic performance of the AD7821 is evaluated by apply-
ing a very low distortion sine wave signal to the analog input
(V
IN
) which is then sampled at a 512 kHz sampling rate. A Fast
Fourier Transform (FFT) plot is then generated from which
Signal-to-Noise Ratio (SNR) and harmonic distortion data are
obtained.
Figure 8 shows a 2048 point FFT plot of the AD7821 with an
input signal of 100.25 kHz. The SNR is 49.1 dB. It should be
noted that the harmonics are taken into account when calculat-
ing the SNR. The theoretical relationship between SNR and
resolution (N) is expressed by the following equation:
SNR = (6.02 N +
1.76)
dB . . . . . . . . . . . . . . . . . . . . .
(1)
When a sine wave of specified frequency is applied to the V
IN
in-
put of the AD7821 and several thousand samples are taken, it is
possible to plot a histogram showing the frequency of occur-
rence of each of the 256 ADC codes. A perfect ADC produces a
probability density function described by the equation:
P(V
)
=
1
π(
A
−
V
2
)
1/2
2
where
A
is the peak amplitude of the sine wave and
P(V)
is the
probability of occurrence at a voltage V.
If a particular step is wider than the ideal 1 LSB width, then the
code associated with that step will accumulate more counts than
for the code for an ideal step. Likewise, a step narrower than the
ideal width will have fewer counts. Missing codes are easily seen
because a missing code means zero counts for a particular code.
The absence of large spikes in the plot indicates small differen-
tial nonlinearity.
Figure 10 shows a histogram plot for the AD7821, which corre-
sponds very well with the ideal shape. The plot indicates very
small differential nonlinearity and no missing codes for an input
frequency of 100.25 kHz.
Figure 8. AD7821 FFT Plot
EFFECTIVE NUMBER OF BITS
By working backwards from Equation (1) it is possible to get a
measure of ADC performance expressed in effective number of
bits (N). A plot of the effective number of bits versus input fre-
quency is given in the Typical Performance Characteristics sec-
tion. The effective number of bits typically falls between 7.7 and
7.9, corresponding to SNR figures of 48.1 and 49.7 dB.
Figure 10. AD7821 Histogram Plot
–8–
REV. A
AD [ ANALOG DEVICES ]
