Analysis of the pros and cons of ADC input noise (Part 2)

There are two basic limitations to maximizing SFDR for high speed ADCs: the first is the distortion introduced by the front-end amplifier and sample-and-hold circuit; the second is the distortion caused by the nonlinearity of the actual transfer function of the encoder portion of the ADC.

The key to improving SFDR is to minimize the above two nonlinearities.

It is futile to significantly reduce the inherent distortion introduced by the ADC front end by working externally to the ADC. However, the differential nonlinearity of the ADC encoder transfer function can be reduced by properly utilizing dither (i.e., external noise, which is summed with the analog input signal to the ADC).

Under certain conditions, dithering can improve the SFDR of an ADC (References 2-5). For example, even in an ideal ADC, the quantization noise has some correlation with the input signal, which can degrade the SFDR of the ADC, especially when the input signal is a divisor of the sampling frequency. Adding broadband noise (with an amplitude of about ? LSB rms) to the input signal tends to randomize the quantization noise, reducing its effect (see Figure 5A). However, in most systems, there is enough noise on top of the signal that the addition of dither noise is unnecessary. The input-referred noise of the ADC may also be sufficient to have the same effect. Increasing the broadband rms noise level by more than about 1 LSB will proportionally degrade the ADC SNR without further improvement in performance.

There are other schemes that use larger amounts of dither noise to randomize the ADC's transfer function. Figure 5B also shows a dither noise source consisting of a pseudo-random number generator driving a DAC. This signal is subtracted from the ADC input signal and digitally added to the ADC output without causing a significant degradation in SNR performance. This technique has an inherent disadvantage in that the allowable input signal swing decreases as the amplitude of the dither signal increases. The reason for reducing the signal amplitude is to prevent overdriving the ADC. It should be noted that this scheme does not significantly improve the distortion generated by the ADC front end, only the distortion caused by the nonlinearity of the ADC encoder transfer function.

Figure 5: Using dither to randomize the ADC transfer function

Another method that is easier to implement, especially in wideband receivers, is to inject a narrowband perturbation signal outside the target frequency band of the signal, as shown in Figure 6. Generally speaking, signal components will not be located in the frequency range close to DC, so this low frequency region is often used for this perturbation signal. The perturbation signal may also be located slightly below fs/2. The perturbation signal only occupies a small bandwidth relative to the signal bandwidth (hundreds of kHz bandwidth is usually sufficient), so the SNR performance will not be as significantly degraded as with wideband perturbations.

Figure 6: Injecting out-of-band dither to improve ADC SFDR

A sub-stage pipeline ADC, such as the AD6645 14-bit, 105 MSPS ADC shown in Figure 7, has very small differential nonlinearity errors at specific code transition points within the ADC range. The AD6645 consists of a 5-bit ADC1, a 5-bit ADC2, and a 6-bit ADC3. Significant DNL errors occur only at the ADC1 transition points, with very small DNL errors at the second and third ADC stages. ADC1 has 25 = 32 relevant decision points, occurring every 68.75 mV (29 = 512 LSBs) (2.2 V full-scale input range). Figure 8 shows these nonlinearity errors in an exaggerated form.

Figure 7: Simplified block diagram of the AD6645 14-bit 105 MSPS ADC

Figure 8: AD6645 classification point DNL error (exaggerated display)

For analog inputs up to approximately 200 MHz, the distortion components introduced by the AD6645 front end are negligible compared to the distortion introduced by the encoder. That said, the static nonlinearity of the AD6645 transfer function is the primary limitation on SFDR performance.

The goal is to choose the appropriate amount of out-of-band dither so that the effects of these small DNL errors are randomized across the entire input range of the ADC, thereby reducing the average DNL error. This can be determined experimentally, and a peak-to-peak dither noise that covers approximately two ADC1 transitions provides the best improvement in DNL. Higher amounts of noise do not significantly improve DNL. The two ADC1 transitions cover 1024 LSB peak-to-peak, or approximately 155 LSB rms (peak-to-peak Gaussian noise divided by 6.6 to get the rms value).

The first graph in Figure 9 shows the unperturbed DNL over a small portion of the input signal range. The horizontal axis is zoomed in to show two classification points that are 68.75 mV (512 LSBs) apart. The second graph shows the DNL after adding a 155 LSB rms perturbation, which equates to approximately –20.6 dBm. Note the dramatic improvement in DNL.

Figure 9: AD6645 DNL without and with perturbation

Perturbation noise can be generated in a number of ways. Noise diodes can be used, but simply amplifying the input voltage noise of a wideband bipolar op amp is a more economical solution, and this approach is described in detail in references 3, 4, and 5 and will not be repeated here.

The dramatic improvement in SFDR achieved with out-of-band dither is shown in the deep (1,048,576 point) FFT of Figure 10, where the AD6645 samples a –35 dBm, 30.5 MHz signal at 80 MSPS. Note that the SFDR is approximately 92 dBFS without dither and approximately 108 dBFS with dither, a 16 dB improvement!

Figure 10: AD6645 FFT plots without and with perturbation

The AD6645 ADC was introduced by Analog Devices in 2000 and until recently represented the ultimate in SFDR performance. Since its introduction, advances in both process technology and circuit design have driven ADCs to higher performance, such as the AD9444 (14-bit, 80 MSPS), AD9445 (14-bit, 105/125 MSPS), and AD9446 (16-bit, 80/100 MSPS), which have very high SFDR (typically greater than 90 dBc for a 70 MHz full-scale input signal) and low DNL.

Under certain input signal conditions, adding appropriate out-of-band disturbance signals can also improve SFDR performance.

Figure 11 shows the AD9444 (14-bit, 80MSPS) FFT with and without dither. Adding dither improves the SFDR by 25 dB under these input conditions. The data shown was obtained using the ADIsimADC program and the AD9444 model.

Figure 11: 14-bit, 80MSPS ADC AD9444, fs = 80MSPS, fin = 30.5MHz, signal amplitude = –40dBFS

While the results shown in Figures 10 and 11 are quite striking, one should not assume that adding out-of-band noise dither will necessarily improve the SFDR of an ADC, or that it will work under all conditions. As mentioned earlier, dither will not improve the linearity of the ADC’s ​​front-end circuitry. Even with a nearly ideal front end, the effect of dither will be highly dependent on the amplitude of the input signal and the amplitude of the dither signal itself. For example, when the signal approaches the full-scale input range of the ADC, the integral nonlinearity of the transfer function may become the limiting factor in determining the SFDR, and dither will not help. Be sure to study the data sheet carefully, as in some cases data with and without dither may be given, along with amplitude and bandwidth recommendations. Dither may be a built-in feature of newer generation IF sampling ADCs.

Conclusion

In this article, we have shown that all ADCs have a certain amount of input-referred noise. In precision, low-frequency measurement applications, digitally averaging the ADC output data can reduce this noise at the expense of a slower sampling rate and additional hardware. This averaging method actually improves the resolution of the ADC, but it does not reduce integral nonlinearity errors.