AD7874
Total Harmonic Distortion (THD)
Peak Harmonic or Spurious Noise
Total Harmonic Distortion (THD) is the ratio of the rms sum
of harmonics to the rms value of the fundamental. For the
AD7874, THD is defined as
V
2
+
V
3
+
V
4
+
V
5
+
V
6
THD
=
20 log
V
1
2
2
2
2
2
where
V
1
is the rms amplitude of the fundamental and
V
2
,
V
3
,
V
4
,
V
5
and
V
6
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.
Intermodulation Distortion
Harmonic or Spurious Noise is defined as the ratio of the rms
value of the next largest component in the ADC output spec-
trum (up to fs/2 and excluding dc) to the rms value of the fun-
damental. 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.
AC Linearity Plot
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 or n are equal to zero. For example, the second
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 intermodu-
lation distortion is as per the THD specification where it is the
ratio of the rms sum of the individual distortion products to the
rms amplitude of the fundamental expressed in dBs. In this case,
the input consists of two, equal amplitude, low distortion sine
waves. Figure 10 shows a typical IMD plot for the AD7874.
When a sine wave of specified frequency is applied to the V
IN
in-
put of the AD7874 and several million samples are taken, a his-
togram 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 Fig-
ure 11. This shows very good integral linearity performance
from the AD7874 at an input frequency of 10 kHz. The absence
of large spikes in the plot shows good differential linearity. Sim-
plified versions of the formulae used are outlined below.
(V (i )
−
V
(o))
⋅
4096
INL(i
)
=
−
i
V
(
fs)
−
V
(o)
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 es-
timated transition for the i
th
code.
V(i),
the estimated code transition point is derived as follows:
V
(i )
= −
A
⋅
Cos
[
π ⋅
cum(i
)
]
N
where
A
is the peak signal amplitude,
N
is the number of histo-
gram samples
and cum(i
)
=
∑
V
(n)occurrences
n
=o
i
Figure 11. AD7874 AC INL Plot
Figure 10. AD7874 IMD Plot
REV. C
–9–
AD [ ANALOG DEVICES ]
