AD7886
–9–
REV. B
AD7886 DYNAMIC SPECIFICATIONS
The AD7886 is specified for dynamic performance specifica-
tions as well as traditional dc specifications such as integral and
differential nonlinearity. These ac specifications are required for
signal processing applications such as speech recognition, spec-
trum analysis and high speed modems. These applications require
information on the ADC’s effect on the spectral content of the
input signal. Hence, the parameters for which the AD7886 is
specified include SNR, harmonic distortion, intermodulation
distortion and peak harmonics. These terms are discussed in
more detail in the following 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 de-
pendent upon the number of quantization levels used in the
digitization process; the more levels, the smaller the quantiza-
tion noise. The theoretical signal to noise ratio for a sine wave
input is given by
SNR = (6.02N + 1.76) dB (1)
where N is the number of bits. Thus, for an ideal 12-bit con-
verter, SNR = 74 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 a 750 kHz sampling rate. A Fast Fourier Trans-
form (FFT) plot is generated from which the SNR data can be
obtained. Figure 12 shows a typical 2048 point FFT plot with
an input signal of 100 kHz and a sampling frequency of 750 kHz.
Figure 12. AD7886 FFT Plot
The SNR obtained from this graph is 68 dB. It should be noted
that the harmonics are taken into account 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
obtain a measure of performance expressed in effective num-
ber 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 13 shows a typical plot of effective number of bits versus
frequency for a sampling frequency of 750 kHz. Input frequency
range for this particular graph was limited by the test equipment
to FS/4. The effective number of bits typically falls between
10.9 and 11.2, corresponding to SNR figures of 67.38 dB and
69.18 dB.
12
11.5
11
10.5
10
0
FS/4
INPUT FREQUENCY
EFFECTIVE NUMBER OF BITS
SAMPLING FREQUENCY = 750kHz
T = 25 C
A
Figure 13. Effective Number of Bits vs. Frequency
Total Harmonic Distortion (THD)
THD is the ratio of the rms sum of harmonics to the fundamen-
tal. For the AD7886, THD is defined as
THD =20 log
V
2
2
+V
3
2
+V
4
2
+V
5
2
+V
6
2
V
1
(3)
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 (IMD)
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).
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 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 14 shows a typical IMD plot for the AD7886.
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
