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AD7874 Total Harmonic Distortion (THD)

Peak Harmonic or Spurious Noise

Total Harmonic Distortion (THD) is the ratio of the rms sum of harmonics to the rms value of the fundamental. For the AD7874, THD is defined as

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.


THD = 20 log




V 2 + V 3 + V 4 + V5 + V 6 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. 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 or n are equal to zero. For example, the second 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 intermodulation 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 10 shows a typical IMD plot for the AD7874.

AC Linearity Plot

When a sine wave of specified frequency is applied to the VIN input of the AD7874 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 11. This shows very good integral linearity performance from the AD7874 at an input frequency of 10 kHz. The absence of large spikes in the plot shows good differential linearity. Simplified versions of the formulae used are outlined below.  (V (i ) − V (o)) ⋅ 4096  INL(i ) =  −i V ( fs) − V (o)  

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 ith code. V(i), the estimated code transition point is derived as follows: V (i ) = − A ⋅ Cos

[ π ⋅ cum(i )] N

where A is the peak signal amplitude, N is the number of histogram samples i

and cum(i ) =

∑ V (n)occurrences n =o

Figure 11. AD7874 AC INL Plot

Figure 10. AD7874 IMD Plot



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