**Noise and temperature drift**

Once the drive capability has been determined, we must ensure that the noise from the reference circuit does not affect the ADC’s performance. To preserve the signal-to-noise ratio (SNR) and other specifications, we must keep the noise contribution from the reference to a fraction (ideally 20% or less) of the ADC noise. The AD7980 specifies 91-dB SNR with a 5-V reference. Converting to rms gives:

Thus, the reference circuit should have less than 10 µV rms noise to have minimal impact on the SNR. The noise specification for references and op amps is typically split into two parts: low-frequency (1/f) noise and wideband noise. Combining the two will give the total noise contribution of the reference circuit. Figure 7 shows a typical noise vs. frequency plot for the ADR431 2.5-V reference.

**Figure 7**

The ADR435 compensates its internal op amp to drive large capacitive loads and avoid noise peaking, making it very attractive for use with ADCs. This is explained in greater detail in the data sheet. With a 10 µF capacitor, it specifies 8 µV p-p 1/f (0.1 Hz to 10 Hz) noise and 115 nV/√Hz wideband noise spectral density. The estimated noise bandwidth is 3 kHz. To convert the 1/f noise from peak-to-peak to rms, divide by 6.6 to get

Next, calculate the wideband noise contribution using the estimated bandwidth with a 10 µF capacitor. The effective bandwidth will be given by:

Use this effective bandwidth to calculate the rms wideband noise:

The total rms noise is the root sum square of the low-frequency noise and the wideband noise:

This is less than 10 µV rms, so it won’t significantly impact the ADC’s SNR. These calculations can be used to estimate the noise contribution of the reference to determine its suitability, but this will need to be verified on the bench with real hardware.

The same analysis can be used to calculate the noise contribution if a buffer is used after the reference. The AD8031, for example, has 15 nV/√Hz noise spectral density. With a 10-µF capacitor on its output, its measured bandwidth is reduced to about 16 kHz. Using this bandwidth and noise density, and ignoring the 1/f noise, the noise contribution will be 2.4 µV rms. The reference buffer noise can be root sum squared with the reference noise to arrive at a total noise estimate. Generally the reference buffer should have a noise density much less than that of the reference.

When using a reference buffer, it is possible to band limit the noise from the reference even further by adding an RC filter with a very low cutoff frequency to the output of the reference, as shown in Figure 8. This can be useful, considering the reference is usually the dominant source of noise.

**Figure 8**

Some other important considerations for choosing a reference are initial accuracy and temperature drift. The initial accuracy is specified in percent or mV. Many systems allow for calibration, so initial accuracy is not as important as drift, which is typically specified in ppm/^{o} C or µV/^{o} C. Most good references have less than 10 ppm/^{o} C drift, and the ADR45xx family drives drift down to a couple of ppm/^{o} C. This drift must be incorporated into the system’s error budget.

@Alan: This is such a nice series of post. Thanks.

“To convert the 1/f noise from peak-to-peak to rms, divide by 6.6 to get…”I though that Vrms=Vp2p/(2√2), why is a factor of 6.6 used instead of 2√2?

@amrulah: Thank you for helping me to clarify on this formula. Even I was thinking the other way round.

“The effective bandwidth will be given by:

The equation you are using is valid if you are considering a sine wave signal. 1/f noise is random so to convert from pk-pk to rms you use a statistical number thats based on a gaussian noise distribution. Its explained better here but 6.6 is a standard number thats used. Sorry this should have been explained better, see page 5 of this app note.

http://www.analog.com/static/imported-files/tutorials/MT-048.pdf

The pi/2 factor is to convert the 3dB BW of the reference to an effective noise BW. This is an approximation and assumes the BW rolloff is first order. See this app note for a better explanation.

http://www.analog.com/static/imported-files/tutorials/MT-048.pdf

Alan: Thanks for the Appnote pdf, its nice.

Please correct me if I go wrong . Nominally 2√2*rms= Vp-p, but if we consider another dimension of time, then rms noise will increase as mentioned in table on page 5 of the pdf. To consider the effect of the time-bound random noise, a factor of 6.6 (more margin) is considered.

Thanks.

@amrutah : Your welcome. You are correct. The 2√2*rms= Vp-p applies to a sinusoidal waveform. The 6.6 factor is for a gaussian random noise distribution.