19
LTC1285/LTC1288
APPLICATION INFORMATION
WUU
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Figure 12. Effective Bits and S/(N + D) vs Input Frequency
Signal-to-Noise Ratio
T
he Signal-to-Noise plus Distortion Ratio (S/N + D) is the
ratio between the RMS amplitude of the fundamental
input frequency to the RMS amplitude of all other fre-
quency components at the ADC’s output. The output is
band limited to frequencies above DC and below one half
the sampling frequency. Figure 12 shows a typical spec-
tral content with a 7.5kHz sampling rate.
INPUT FREQUENCY (kHz)
1
0
EFFECTIVE NUMBER OF BITS (ENOBs)
S/(N + D) (dB)
3
5
7
10
10 100
LTC1285/88 • TPC12
1
4
6
9
12
11
8
62
56
74
68
50
2
T
A
= 25°C
V
CC
= 2.7V
f
CLK
= 120kHz
THD =
++++
20log
VVV V
V
2
2
3
2
4
2
N
2
1
...
where V
1
is the RMS amplitude of the fundamental fre-
quency and V
2
through V
N
are the amplitudes of the
second through the N
th
harmonics. The typical THD speci-
fication in the Dynamic Accuracy table includes the 2nd
through 5th harmonics. With a 1kHz input signal, the
LTC1285/LTC1288 have typical THD of 80dB with
V
CC
= 2.7V.
Intermodulation Distortion
If the ADC input signal consists of more than one spectral
component, the ADC transfer function nonlinearity can
produce intermodulation distortion (IMD) in addition
to THD. IMD is the change in one sinusoidal input
caused by the presence of another sinusoidal input at a
different frequency.
If two pure sine waves of frequencies f
a
and f
b
are applied
to the ADC input, nonlinearities in the ADC transfer func-
tion can create distortion products at sum and difference
frequencies of mf
a
± nf
b
, where m and n = 0, 1, 2, 3, etc.
For example, the 2nd order IMD terms include (f
a
+ f
b
) and
(f
a
– f
b
) while 3rd order IMD terms include (2f
a
+ f
b
),
(2f
a
– f
b
), (f
a
+ 2f
b
), and (f
a
– 2f
b
). If the two input sine
waves are equal in magnitudes, the value (in dB) of the 2nd
order IMD products can be expressed by the following
formula:
IMD f f
mplitude f f
ab
ab
±
()
=
±
()
20log
a
amplitude at f
a
For input frequencies of 2.05kHz and 3.05kHz, the IMD of
the LTC1285/LTC1288 is 72dB with a 2.7V supply.
Peak Harmonic or Spurious Noise
The peak harmonic or spurious noise is the largest spec-
tral component excluding the input signal and DC. This
value is expressed in dBs relative to the RMS value of a full-
scale input signal.
Effective Number of Bits
The Effective Number of Bits (ENOBs) is a measurement of
the resolution of an ADC and is directly related to S/(N+D)
by the equation:
ENOB = [S/(N + D) – 1.76]/6.02
where S/(N + D) is expressed in dB. At the maximum
sampling rate of 7.5kHz with a 2.7V supply, the LTC1285
maintains above 10.7 ENOBs at 10kHz input frequency.
Above 10kHz the ENOBs gradually decline, as shown in
Figure 12, due to increasing second harmonic distortion.
The noise floor remains low.
Total Harmonic Distortion
Total Harmonic Distortion (THD) is the ratio of the RMS
sum of all harmonics of the input signal to the fundamental
itself. The out-of-band harmonics alias into the frequency
band between DC and half of the sampling frequency. THD
is defined as:
