9
LTC1409
APPLICATIONS INFORMATION
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Signal-to-Noise Ratio
The 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 frequency
components at the A/D output. The output is band limited
to frequencies from above DC and below half the sampling
frequency. Figure 2 shows a typical spectral content with
an 800kHz sampling rate and a 100kHz input. The dynamic
performance is excellent for input frequencies up to and
beyond the Nyquist limit of 400kHz.
Effective Number of Bits
The Effective Number of Bits (ENOBs) is a measurement of
the resolution of an ADC and is directly related to the
S/(N + D) by the equation:
N = [S/(N + D) – 1.76]/6.02
where N is the effective number of bits of resolution and
S/(N + D) is expressed in dB. At the maximum sampling
rate of 800kHz the LTC1409 maintains near ideal ENOBs
up to the Nyquist input frequency of 400kHz. Refer to
Figure 3.
THD
VVV Vn
V
=
+++…
20 Log
234
1
222 2
where V1 is the RMS amplitude of the fundamental fre-
quency and V2 through Vn are the amplitudes of the
second through Nth harmonics. THD vs input frequency is
shown in Figure 4. The LTC1409 has good distortion
performance up to the Nyquist frequency and beyond.
INPUT FREQUENCY (Hz)
EFFECTIVE BITS
12
11
10
9
8
7
6
5
4
3
2
1
0
1k 100k 1M 10M
LTC1409 • F03
10k
f
SAMPLE
= 800kHz
Figure 3. Effective Bits and Signal/(Noise +
Distortion) vs Input Frequency
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 the sampling frequency. THD is
expressed as:
Figure 4. Distortion vs Input Frequency
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 fa and fb are applied
to the ADC input, nonlinearities in the DC transfer function
can create distortion products at the sum and difference
frequencies of mfa + –nfb, where m and n = 0, 1, 2, 3, etc.
For example, the 2nd order IMD terms include (fa + fb). If
the two input sine waves are equal in magnitude, the value
(in decibels) of the 2nd order IMD products can be
expressed by the following formula:
IMD fa fb+
()
=20 Log
Amplitude at (fa + fb)
Amplitude at fa
Peak Harmonic or Spurious Noise
The peak harmonic or spurious noise is the largest spec-
tral component excluding the input signal and DC. This
INPUT FREQUENCY (Hz)
AMPLITUDE (dB BELOW THE FUNDAMENTAL)
0
–10
–20
–30
–40
–50
–60
–70
–80
–90
–100
1k 100k 1M 10M
LTC1409 • F04
10k
THD
3RD
2ND
