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# Why isn't noise performance improved from averaging?

Episode 6. Introducing points and notes of when improving noise performance by averaging ADC outputs.

This is a story that young A, who works in a fictional motor company deepens the knowledge of ADCs with a senior colleague K, and his boss, M, manager.

Young A

K-san, I averaged the ADC outputs, but noise measurements do not improve.

Senior K

What are you doing, specifically?

Young A

Using an ADC with 1 MSPS, (sampling rate 1 MHz), I averaged the ADC output twice since the noise was disturbing. This is the block diagram. (Figure 1)

Senior K

...I see, I guess you have a naive idea that noise gets better by averaging the output!

Young A

Oh? Am I wrong!?

Senior K

This is a case by case basis. Have you ever drawn an averaging chart on the frequency axis?

Young A

Frequency axis? How does it relate to averaging?

Senior K

Averaging is a type of digital filter.

Young A

Really?

Senior K

When thinking about noise, you always have to consider the frequency axis. The spectrum of noise and the filter characteristic that suppresses noise are considered.

Young A

I understand the analog low pass filter, (LPF), but I do not know about the digital filter well...

Senior K

Then here is a question, how much does noise improve by averaging the data string at ADC output?

Young A

I have heard it can improve about 3 dB by averaging twice.

Senior K

What is the basis?

Young A

By averaging twice, noise power is reduced to half. And it will be represented as the square root of one half in the effective value, so it is 3 dB.

Senior K

There is one important assumption for this. Understand?

Young A

No, I don't.

Senior K

Noise spectrum has no frequency dependence, assuming flat frequency.

Young A

Meaning white noise? I thought that the noise is usually white.

Senior K

What matters is that even if the noise was white at the beginning, it will not be white noise if band limitation is applied.

Young A

Can you make it more specific?

Senior K

There is an LPF at the input stage of the ADC. You know that the LPF reduces high frequency noise. Then the LPF characteristics will be reflected on the output noise spectrum.

Young A

I see.

Senior K

Then the same question again. What is the effect on noise when you average the ADC output twice?

Young A

Well, 3 dB improvement, correct? Because the noise is not white noise? So what type of noise does averaging reduce?

Senior K

Let's imagine. A 1 MSPS ADC samples 1V DC voltage. What happens when you average the output 2 times?

Young A

It's easy, 1V average is 1V.

Senior K

Correct. Then, if it is a sine wave of 500 kHz at ± 1V, what happens when it is averaged twice?

Young A

Well. Let me draw it in a figure. .... Oh, it is 0V. (Figure 2)

Senior K

Yes, the 500 kHz waveform disappears when it is averaged twice. The DC component remains intact, and the 500 kHz component disappears. That means it depends on the frequency of the LPF. The characteristics will be like this. (Figure 3)

Young A

I didn't know that the averaging can also be expressed as a filter on the frequency axis. The cutoff frequency of -3 dB attenuation is about 250 kHz.

Senior K

The cutoff frequency is about a level that is quarter of the sampling rate when averaging the ouptut twice. What matters is that, "the cutoff frequency of averaging is standardized by the sampling rate of the ADC.

Young A

That was close. I was just about to remember, "averaging twice results 250kHz on the LPF"

Senior K

So, lets start from the beginning.

Young A

Where were we?

Senior K

"Why isn't noise improved by averaging twice with a 1 MSPS ADC?" According to what you learn, what type of filter will it be?

Young A

When the 1 MSPS ADC output is averaged twice, the cutoff frequency of the digital filter is around 250 kHz.

Senior K

So what is the cutoff frequency of the LPF at the input stage of the ADC in Figure 1?

Young A

It is about 100 kHz... I see! So this is why noise isn't improved.

Senior K

Let's summarize it.

Young A

Averaging is a kind of digital filter, and the cutoff frequency by the digital filter is standardized from the sampling rate of the ADC. The effectiveness of the digital filter depends on whether the noise that can be reduced by the cutoff frequency remains in the output of the ADC. If the LPF at input stage of the ADC has reduced the noise, it is not improved even if the ADC output is averaged.

Senior K

Perfect ! .. I wanted to say.

Young A

No. I tried quite hard though..

Senior K

It is case by case since the ADC itself also has noise.

Young A

I see. The noise of the ADC itself can be reduced from averaging.

Senior K

Averaging is effective if the noise of the ADC is large enough that it cannot be ignored comparing with the noise before the ADC.