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# What are advantages of oversampling?

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

I do not understand oversampling very well, do you? After all, how is it beneficial?

Expert M Manager

In order to understand the effectiveness of oversampling, you must first understand the Nyquist theorem.

Young A

The Nyquist theorem? I know it. The waveform can be reproduced only up to half of the sampling frequency.

Senior K

Yes. In extreme terms, if you input a 1 MHz signal to the SAR type ADC sampling at 1 MHz, the result will be a DC component.

Young A

It is folding.

Expert M Manager

Similarly, an input signal of 600 kHz is converted to 400 kHz at the output of the ADC, and a 900 kHz signal becomes 100 kHz. All frequency components input to the ADC are converted in the range from DC to 500 kHz by A/D conversion. (Figure 1)

Young A

My understanding is unclear.

Senior K

So why do you need a low pass filter, (LPF), before the ADC?

Young A

This is because, the higher frequency component will be folded back more likely than the Nyquist frequency of the ADC. It is necessary to reduce the high frequency component with the LPF at the input stage of the ADC.

Senior K

Yes, that is the purpose of the anti-aliasing filter.

Young A

What, anti ...?

Senior K

An LPF placed at the input stage of the ADC is called an anti-aliasing filter. Then, what cutoff frequency do you think is good?

Young A

Probably, near the Nyquist frequency.

Senior K

It depends on the noise design whether you don't want folding in high frequency noise, but basically it is correct.

Expert M Manager

This is the so-called "Nyquist ADC". Will this be different from, "oversampling ADC"?

Young A

Huh? I didn't know there is such a name. What does oversampling ADC mean?

Senior K

Simply, it is a ADC that executes a lot of A/D conversions, processes these conversion data with built-in digital filter, and ultimately lowers the output data rate. A typical oversampling type is the ΔΣ ADC.

Young A

There it is, delta-sigma. I do not understand it well.

Senior K

Here, this is a difference. (Figure 2)

Young A

I see, there is a difference in the output data rate relative to the sampling rate.

Senior K

The ratio between the sampling rate and the output data rate is called a decimation ratio or an oversampling ratio. It can also be abbreviated as OSR.

Young A

I often hear OSR. Now, I understand.

Senior K

Then I have a question, when the output data rates are aligned as shown in Figure 2, what happens to each Nyquist frequency in two ADCs with 1 MHz output, for example?

Young A

Well, since the sampling data and data output corresponds 1:1 with the Nyquist ADC, it is 500 kHz, half of 1 MHz. What about oversampling ADC? In Figure 2, since OSR = 6, it seems to be sampling at 6 MHz. The Nyquist frequency will be 3 MHz.

Senior K

If it is an oversampling type, the Nyquist frequency will be much higher, won't be?

Young A

Does that mean you can increase the LPF cutoff frequency or lower the LPF order?

Senior K

Young A

Hmm… But if the cutoff frequency is increased, the noise at the input stage of the LPF will not be reduced, so will the noise characteristics deteriorate?

Expert M Manager

You understand a lot. Yes, noise that can not be reduced by the LPF is input to the ADC. Then, what is the filter characteristic of the ADC itself?

Young A

Well, it's determined from Full Power Bandwidth, isn't it?

Senior K

That's right with a SAR type Nyquist ADC. In the case of the oversampling ADC, the characteristics of the digital filter are dominant. (Figure 3)

Young A

Oh, I see. It is about what you were talking, processing with the built-in digital filter.

Senior K

The digital filter characteristics depend on the product. You should check it on the datasheet.

Young A

We found that the LPF cutoff frequency can be set higher with the oversampling ADC, but what is it that makes us happy after all?

Senior K

We'll see in the next episode!