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Hello, and welcome to the TI Precision Lab covering noise calculations for ADC systems. Overall, this video will walk through how to predict the overall system noise for a data converter, amplifier, and reference. You'll use SPICE and data sheet specifications to do this analysis. Finally, we will see how measured results match the predicted noise closely.

In this section, we will do a calculation to find the total noise for this signal chain. In this example, the amplifier, data converter, and reference will all contribute some noise. The data converter's noise is defined by the signal-to-noise ratio. But the amplifier and reference noise are normally calculated or simulated in volts RMS.

In order to combine the noise from all three components, we need to translate the ADC noise into volts RMS. The equation on the top is the general equation for S and R. Solve this equation for ADC noise, denoted as Vn ADC. Then add all three noise components as the square root sum of the squares. Finally, it is useful to translate the total noise back to a signal-to-noise ratio, as this will directly relate to our measured results.

One way to get the total integrated RMS noise for a reference is to do a simulation. To do this from TINA SPICE, you first select Noise Analysis. Enter a frequency range that allows the integrated noise to converge to a final value. For most references, 1 megahertz or less should be sufficient.

The total noise is the integrated RMS noise at the output of the reference. In this case, the integrated noise is about 6.31 microvolts RMS. The total integrated noise in RMS is read where the total noise plot flattens out at high frequency to a consistent value. For this device, the data sheet also provides a typical total integrated noise spec for a 22 microfarad capacitor of 5 microvolts RMS. So the simulation and data sheet specification are reasonably close.

The noise for the amplifier configuration can also be simulated using TINA SPICE. Before running the noise analysis, it is useful to test the operation of the amplifier. In this case, the amplifier input is set to volts. So the output should be the gain times the input, or 11 times 0.1 volts, which is equal to 1.1 volts. Doing a DC analysis, calculate nodal voltages, confirms that the output is 1.1 volts, and the circuit is functioning properly.

A common mistake here is to ground the input. With 0 volts in, the amplifier's output will try to drive to ground, which is not a linear operating condition. Noise simulations require linear operation to function properly. Note that to do a noise analysis, an AC source must be connected to the op amp circuit. The VM source for this circuit needs to be an AC voltage source with a DC value of 0.1 volts.

Once linear operation of the amplifier is confirmed, Run Analysis, Noise Analysis. Enter a frequency range that will allow the noise to converge to a final value. Normally, this is about a decade beyond the bandwidth of the amplifier. In this example, the amplifier's bandwidth is 20 megahertz, so we try 100 megahertz for the maximum frequency.

You can see, over at the right, the spectral density and integrated noise curves. Notice that the integrated noise converges at 128.78 microvolts. This is the total RMS noise that we will use in the final calculation. If you are not familiar with noise simulation, you can learn more about this in the TI Precision Labs Op Amps videos. A link is given at the bottom of this page for your reference.

Here, we do the total noise calculation for the signal chain. First, we need to translate the ADC SNR specification to an RMS noise voltage. The equation given for the ADC noise requires the full-scale RMS input voltage. The full-scale range is 5 volts for this converter. The full skill range corresponds to the peak-to-peak input. To convert this to RMS, m-s we divide by 2 and multiply by 0.707.

For this example, the RMS input is calculated as 0.5 times 5 volts times 0.707, or 1.767 volts. The data sheet's typical SNR for this device is 93 db. Applying all these factors to the noise equation yields a total noise of 39.6 microvolts RMS for this device. Next, we combine the ADC, amplifier, and reference noise, using the square root sum of the squares. In this example, the total noise is 134 microvolts RMS.

Finally if we use the calculated total noise in the SNR equation, we can calculate a modified SNR for the example that includes the amplifier and reference noise. In this example, the modified SNR is 82.4 db. Plus, the ADC SNR was degraded from 93 db to 82.4 db by the amplifier and reference noise. Note that the reference noise was negligible in this case.

The Analog Engineer's Calculator, introduced in other Precision Labs videos, has a tool that will automatically do the calculation from the previous slide. First, enter the amplifier RMS noise. Second, enter the ADC data sheet information. And finally, press OK, and the results are displayed to the right. Notice that these numbers match the calculation in the previous slide. The URL where you can download this calculator is at the bottom of the page.

Here, we measure the noise for the example from the previous slide. One way to measure noise is to look at the histogram for a precision DC input signal. Ideally, this histogram should have one code bin that corresponds to the input voltage. In reality, however, most converters will have a Gaussian distribution of output codes that correspond to the output noise.

The standard deviation of this distribution is equal to the total RMS noise. In this measurement example, the standard deviation, or sigma, for the distribution is 1.70 codes. We can convert this to a noise voltage by multiplying the standard deviation by the LSB width. In this example, the noise is calculated to be 1.78 times 76.29 microvolts, which is equal to 136 microvolts RMS. The measured noise of 136 microvolts compares very well with the calculated 134 microvolts from the previous slide.

One way to reduce noise is to optimize the signal chain by choosing low-noise amplifiers and carefully selecting components to minimize noise. However, once the signal chain is optimized you may want to further reduce the noise. Averaging is another approach for reducing total noise.

This example shows real-world measured noise from the previous example. For a random uncorrelated Gaussian noise distribution, the total noise after averaging is the noise before averaging divided by the square root of the number of averages.

The example calculation here shows the effect of averaging by a factor of 10 on the previous example. The average noise is taking the 1.8 codes of un-averaged noise and dividing by the square root of 10, which yields 0.57 codes of RMS noise after averaging. A 10-point rolling average was done on the ADC data, and the standard deviation of the average data was calculated to be 0.59. So the effect of averaging on the actual measured data very closely matched the predicted noise by dividing by the square root of n.

Then a similar experiment was done with a 100-point rolling average, and both the calculated and measured average correspond quite well, reducing the noise to about 120 codes RMS. Be careful, as continuing to average the noise will not necessarily result in noise reduction. Averaging assumes a Gaussian uncorrelated distribution, and some forms of extrinsic noise will not meet this criteria. Furthermore, there are practical limits on how low the noise can go. It cannot be averaged below one LSB bit width.

That concludes this video. Thank you for watching. Please try the quiz to check your understanding of this video's content.