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# What is 16-bit precision while the output is 1 bit?

Episode 10. Introducing a 1-bit output delta-sigma modulator.

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

Look at this data sheet of an ADC called the AK9223MK. While it says 16-bit precision, in fact, it only has a 1 bit output.

Senior K

Let's see ... Well, it's a delta-sigma modulator.

Young A

It is actually false advertising. I will call them up.

Senior K

Stop it. You will just expose ignorance.

Young A

Well, then why is 1 bit 16-bit?

Senior K

Take a careful look, "delta-sigma type modulator", right? It is not a "delta-sigma type ADC"

Young A

No way! It is on the introduction page of the ADC. ... What is a modulator?

Senior K

Modulator means a device used to modulate an electromagnetic wave.

Meaning, a delta-sigma type modulator is not a delta-sigma A/D converter.

Young A

It's just paraphrasing, isn't it? ...

Senior K

Applying a digital filter to the ΔΣ-modulated data sequence will result in a ΔΣ ADC. Therefore, "delta-sigma type ADC" = "delta-sigma type modulator" + "digital filter". (Figure 1)

Young A

In other words, when using the delta-sigma modulator, does the user have to prepare a digital filter as well? It is troublesome. I wish it could also have a digital filter.

Senior K

There are some benefits to this configuration. First, users can arbitrarily build digital filters. The output rate you want is quite different from user to user. Secondly, if two or more digital filters are prepared, each filter output can be obtained.

Young A

When do you want to have more than two outputs?

Senior K

For example, you can select slow data output with high precision, or low accuracy with fast data output. In order to detect faults, low precision may be required, so you may want fast data. With a modulator, it is easy to get output data from two digital filters in parallel. (Figure 2)

Young A

I see. The versatility is expanded when you change the digital filter at the output stage.

Young A

By the way it is a fundamental question, but why can you get a 16 bit precision signal from a 1 bit data string?

Senior K

It's not precise, but I'll briefly explain the concept. Imagine that the resolution in the voltage axis direction is given in the time axis direction. For example, in this case, to express 0.25, four data points of 0, 1, 0, 0 are averaged.

Young A

In order to represent one 16-bit data in the voltage axis direction, does it mean that a lot of data strings are required in the time axis direction? Well, it's 16th power of 2, so ... 65536 data? What?

Senior K

If you are just averaging, it will be so. But the quantization noise is modulated to the high frequency band in delta-sigma modulator. So the number of required data points will be drastically reduced if you choose a digital filter properly. This AK9223MK guarantees the characteristics of its datasheet when using about 768, (= 256 × 3), points of data.

Young A

Wow. After all, does it all depend on oversampling and noise shaping?

... Well, 256 is OSR, isn't it? Why is it three times the number of data points?

Senior K

With a 3rd order SINC filter, we need triple the data amount than OSR. Since the AK9223MK performs internal delta-sigma modulation in the second order, a third order or higher SINC filter is often used.

Senior K

For motor current detection, "Isolated Delta-sigma Modulator", with the insulation function added to this 1-bit output delta-sigma modulator is prevalent. It is often called, "isolated ADC", but it is actually a modulator.

Young A

I often hear the isolated ADC, but I do not know what it is exactly.

Senior K

In the isolated ADC, there is a delta-sigma modulator which receives an analog input from the primary voltage stage. 1 bit data is output on the secondary voltage stage after 1 bit data string is galvanically isolated by the built-in photocoupler.

Senior K

Well, it is a product that integrates 1 bit output delta-sigma modulator at the preceding stage of a photocoupler.

(Figure 3)

Senior K

In motor current detection, this combination of an isolated ADC and a shunt resistor is mainstream, but there are cases you want to increase responsiveness more.

Young A

Certainly, it is kind of a trend to speed up detection of motor current. Well, if it is delta-sigma type, the delay of the digital filter is large so it is not suitable for high speed.

Senior K

AKM proposes a new solution for motor current detection with a combination of a current sensor and a ZDS-NS ADC.

Young A

Oh, now you will tell me, "How to use ZDS-NS ADC", won't you!?

Senior K

We'll see in the next episode!