AD7871/AD7872
DYNAMIC SPECIFICATIONS
The AD7871/AD7872 is specified and tested for dynamic per-
formance specifications as well as traditional dc specifications
such as Integral and Differential Nonlinearity. These ac specifi-
cations are required for signal processing applications such as
Speech Recognition, Spectrum Analysis and High Speed
Modems. These applications require information on the effects
on the spectral content of the input signal. Hence, the param-
eters for which the AD7871/AD7872 is specified include SNR,
Harmonic Distortion, Intermodulation Distortion and Peak
Harmonics. These terms are discussed in more detail in the fol-
lowing sections.
Signal-to-Noise Ratio (SNR)
SNR is the measured signal-to-noise ratio at the output of the
ADC. The signal is the rms magnitude of the fundamental.
Noise is the rms sum of all the nonfundamental signals up to
half the sampling frequency (fs/2) excluding dc. SNR is depen-
dent upon the number of quantization levels used in the digiti-
zation process; the more levels, the smaller the quantization
noise. The theoretical signal to noise ratio for a sine wave input
is given by:
SNR(dB) = (6.02N + 1.76)
(1)
where N is the number of bits in the ADC. Thus for an ideal
14-bit converter, SNR = 86 dB.
The output spectrum from the ADC is evaluated by applying a
sine wave signal of very low distortion to the VIN input, which is
sampled at an 83 kHz sampling rate. A Fast Fourier Transform
(FFT) plot is generated from which the SNR data can be ob-
tained. Figure 13 shows a typical 2048 point FFT plot of the
AD7871/AD7872, with an input signal of 10 kHz and a sam-
pling frequency of 83 kHz. The SNR obtained from this graph
is
80 dB. It should be noted that the harmonics are included when
calculating the SNR.
Effective Number of Bits
The formula given in Equation 1 relates the SNR to the number
of bits. Rewriting the formula, as in Equation 2, it is possible to
get a measure of performance expressed in effective number of
bits (N).
N
=
SNR –1.76
6.02
(2)
The effective number of bits for a device can be calculated di-
rectly from its measured SNR. Figure 14 shows a typical plot of
effective number of bits versus frequency for the AD7871/
AD7872 with a sampling frequency of 60 kHz.
Figure 14. Effective Number of Bits vs. Frequency
Harmonic Distortion
Harmonic Distortion is the ratio of the rms sum of harmonics to
the fundamental. For the AD7871/AD7872, Total Harmonic
Distortion (THD) is defined as
THD(dB) = 20 log √V22+V32+V42+V52+V62
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. Figure 15 shows how the THD var-
ies with input frequency.
Figure 13. Fast Fourier Transform Plot
Figure 15. Total Harmonic Distortion vs. Frequency
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 second or-
der terms include (fa+fb) and (fa–fb), while the third order
terms include (2fa+fb), (2fa–fb), (fa+2fb) and (fa–2fb).
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REV. D