AD7875LP datasheet(12/20 Pages) AD

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REV. B

AD7870/AD7875/AD7876

–12–

Figure 15. IMD Plot

AC Linearity Plot

When a sine wave of specified frequency is applied to the VIN

input of the AD7870/AD7875 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 16. This shows very good integral linearity per-

formance from the AD7870/AD7875 at an input frequency of

25 kHz. The absence of large spikes in the plot shows good dif-

ferential 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

estimated transition for the i

th code.

V(i) the estimated code transition point is derived as follows:

V(i) = –A • Cos

π⋅ cum(i )

[]

where A is the peak signal amplitude,

N is the number of histogram samples

and cum(i) =

Σi

n=0

V(n) occurrences

Figure 16. AC INL Plot

Figure 14 shows a typical plot of effective number of bits versus

frequency for an AD7870KN/AD7875KN with a sampling fre-

quency of 100 kHz. The effective number of bits typically falls

between 11.7 and 11.85 corresponding to SNR figures of 72.2

and 73.1 dB.

Figure 14. Effective Number of Bits vs. Frequency

Total Harmonic Distortion (THD)

THD is the ratio of the rms sum of harmonics to the rms value

of the fundamental. For the AD7870/AD7875, THD is defined

THD = 20 log

V 22 +V32 +V42 +V5

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.

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).

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 as 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 15 shows a typical IMD plot for the AD7870/

AD7875.

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.

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