AD7870A

–10–

REV. 0

Effective Number of Bits

The formula given in (1) relates the SNR to the number of bits.

Rewriting the formula, as in (2), it is possible to obtain a mea-

sure 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 12 shows a typical plot of effective number of bits versus

frequency for an AD7870AJN, with a sampling frequency of

100 kHz. The effective number of bits typically falls between

11.7 and 11.85 corresponding to SNR figures of 72.2 dB and

73.1 dB.

Figure 12. Effective Number of Bits vs. Frequency

Harmonic Distortion

Harmonic distortion is the ratio of the rms sum of harmonics to

the fundamental. For the AD7870A, total harmonic distortion

(THD) is defined as

THD

= 20 log

3

4

5

6

2

sixth harmonic. The THD is also derived from the FFT plot of

the ADC output spectrum.

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 sec-

ond 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 in-

termodulation distortion is as per the THD specification where

it is the ratio of the rms sum of the individual distortion prod-

ucts to the rms amplitude of the fundamental expressed in dBs.

In this case, the input consists of two, equal amplitude, low dis-

tortion sine waves. Figure 13 shows a typical IMD plot for the

AD7870A.

Figure 13. IMD Plot

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

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

input of the AD7870A, and several million samples are taken, a

histogram 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

Figure 14. This shows very good integral linearity performance

from the AD7870A at an input frequency of 25 kHz. The ab-

sence of large spikes in the plot shows good differential linearity.

Simplified versions of the formulae used are outlined below.

INL(i )

=

V (i )–V (o)

V ( fs)–V (o)

× 4096











 – i

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