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AD7872JR Datasheet(PDF) 10 Page - Analog Devices |
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AD7872JR Datasheet(HTML) 10 Page - Analog Devices |
10 / 16 page AD7871/AD7872 –10– REV. D 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 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 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). 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. Figure 13. Fast Fourier Transform Plot √V 2 2+V 3 2+V 4 2+V 5 2+V 6 2 V1 |
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