AD7870A
Effective Number of Bits
it is the ratio of the rms sum of the individual distortion prod-
ucts to the rms amplitude of the fundamental expressed in dBs.
In this case, the input consists of two, equal amplitude, low dis-
tortion sine waves. Figure 13 shows a typical IMD plot for the
AD7870A.
The formula given in (1) relates the SNR to the number of bits.
Rewriting the formula, as in (2), it is possible to obtain a mea-
sure of performance expressed in effective number of bits (N).
SNR –1.76
N =
(2)
6.02
The effective number of bits for a device can be calculated di-
rectly from its measured SNR.
Figure 12 shows a typical plot of effective number of bits versus
frequency for an AD7870AJN, with a sampling frequency of
100 kHz. The effective number of bits typically falls between
11.7 and 11.85 corresponding to SNR figures of 72.2 dB and
73.1 dB.
Figure 12. Effective Number of Bits vs. Frequency
Harmonic Distortion
Figure 13. IMD Plot
Harmonic distortion is the ratio of the rms sum of harmonics to
the fundamental. For the AD7870A, total harmonic distortion
(THD) is defined as
Peak Harmonic or Spurious Noise
Peak harmonic or spurious noise is defined as the ratio of the
rms value of the next largest component in the ADC output
spectrum (up to FS/2 and excluding dc) to the rms value of the
fundamental. Normally, the value of this specification will be
determined by the largest harmonic in the spectrum, but for
parts where the harmonics are buried in the noise floor the peak
will be a noise peak.
2
V22 +V32 +V42 +V52 +V6
THD = 20 log
V1
where V1 is the rms amplitude of the fundamental and V2, V3,
V4, V5 and V6 are the rms amplitudes of the second through the
sixth harmonic. The THD is also derived from the FFT plot of
the ADC output spectrum.
AC Linearity Plot
When a sine wave of specified frequency is applied to the VIN
input of the AD7870A, and several million samples are taken, a
histogram showing the frequency of occurrence of each of the
4096 ADC codes can be generated. From this histogram data it
is possible to generate an ac integral linearity plot as shown in
Figure 14. This shows very good integral linearity performance
from the AD7870A at an input frequency of 25 kHz. The ab-
sence of large spikes in the plot shows good differential linearity.
Simplified versions of the formulae used are outlined below.
Intermodulation Distortion
With inputs consisting of sine waves at two frequencies, fa and
fb, any active device with nonlinearities will create distortion
products at sum and difference frequencies of mfa + nfb where
m, n = 0, 1, 2, 3, etc. Intermodulation terms are those for
which neither m nor n are equal to zero. For example, the sec-
ond order terms include (fa + fb) and (fa – fb), while the third
order terms include (2fa + fb), (2fa – fb), (fa + 2fb) and (fa –
2fb). Using the CCIF standard, where two input frequencies
near the top end of the input bandwidth are used, the second
and third order terms are of different significance. The second
order terms are usually distanced in frequency from the original
sine waves while the third order terms are usually at a frequency
close to the input frequencies. As a result, the second and third
order terms are specified separately. The calculation of the in-
termodulation distortion is as per the THD specification where
V(i )–V(o)
V( fs)–V(o)
INL(i )=
× 4096 – i
where INL(i) is the integral linearity at code i. V(fs) and V(o)
are the estimated full-scale and offset transitions and V(i) is the
estimated transition for the ith code.
REV. 0
–10–
ADI [ ADI ]
