[Go, Tanepenz! ~Support Diary for Young Analog FAEs~] Episode 4: What is an Anti-aliasing Filter? ~A Discussion of Analog Filters You Must Consider Before an ADC~

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Design Analog Devices

I joined Macnica as a new graduate and am currently working as a junior semiconductor FAE (Field Application Engineer). I only began seriously studying the analog field after joining the company, and I have encountered many situations when proposing AD converters where "they are being used according to the datasheet, but for some reason the expected accuracy is not being achieved."

One of the reasons I later understood was the importance of anti-aliasing filters. This time, I will introduce what I learned about anti-aliasing filters, starting from "why they are necessary."

What is aliasing?

To understand anti-aliasing filters, you first need to understand the phenomenon called "aliasing." AD converters convert a continuous analog signal into a digital signal by sampling it at a fixed interval. If the sampling frequency is insufficient, high-frequency components in the input signal may be observed as lower-frequency components that are not their true nature. This is called "aliasing."

Furthermore, the Nyquist theorem becomes important in this context. The phenomenon of aliasing can be explained by the Nyquist theorem. The Nyquist theorem was also discussed in the second article, so please refer to that as well.

Now, let's briefly review the Nyquist theorem.

The maximum frequency included in the input signal

\( f_{a(\mathrm{max})} \)

Therefore, the sampling frequency fs is,

\( f_s \geq 2f_{a(\mathrm{max})} \)

The following conditions must be met. In this case, if fn is half the sampling frequency,

\( f_N = \frac{f_s}{2} \)

This can be expressed as follows, and this point is called the Nyquist frequency.

If the input contains components exceeding the Nyquist frequency, these are aliased as low-frequency components after sampling. Because these aliased components become indistinguishable from the original signal during digital processing, they cannot be removed by subsequent digital filters.

Aliasing phenomenon in AD converters causing code reversal — Figure 1: Folding due to aliasing

Therefore, aliasing countermeasures must be implemented before conversion by the AD converter, that is, in the analog domain.

Figure 2: Anti-aliasing filter required for the analog input section of the AD converter

The concept of anti-aliasing filters

An "anti-aliasing filter" is used to prevent aliasing in AD converters. An anti-aliasing filter is a low-pass filter (LPF) placed before the AD converter, and its role is to attenuate high-frequency components that exceed the Nyquist frequency in advance.

Reduction of aliasing components by anti-aliasing filters — Figure 3: Reduction of aliasing components by anti-aliasing filter

The first thing to understand here is that in real-world filters, signals cannot be completely blocked at a certain frequency; rather, they have a characteristic where the signal gradually attenuates as the frequency increases beyond the cutoff frequency.

Therefore, in anti-aliasing filter design, the important approach is not to "cut everything above the Nyquist frequency," but rather to consider "how much attenuation should be ensured before reaching the Nyquist frequency."

As a practical guideline, ensuring an attenuation of approximately-40 dB around the Nyquist frequency, and aiming for even greater attenuation when higher precision is required, can be considered a good criterion for judgment.

The design procedure begins with the maximum frequency of the signal to be measured.

\( f_{a(\mathrm{max})} \)

Understand the sampling frequency of the AD converter and the Nyquist frequency

\( f_N = \frac{f_s}{2} \)

We will determine this. Then, we will set the cutoff frequency so that the following relationship is satisfied.

\( f_{a(\mathrm{max})} < f_c < f_N \)

Also, as an example RC Composed of 1 Next low-pass filter Considering this, the cutoff frequency is expressed by the following formula:

\( f_c = \frac{1}{2\pi RC} \)

Ensuring required accuracy through anti-aliasing filters. — Figure 4: Ensuring required accuracy with anti-aliasing filters.

Relaxation of filter design through oversampling

When considering anti-aliasing filter design, the relationship with oversampling is also an important point.

A first-order low-pass filter (LPF) exhibits a characteristic attenuation of-20 dB/dec in the region above the cutoff frequency (a 20 dB attenuation for every tenfold increase in frequency). This shows that to achieve a large attenuation with only a first-order LPF, the cutoff frequency must be set considerably lower than the Nyquist frequency. Therefore, in practice, it is common to design LPFs in combination with higher-order filters or oversampling. (For more on oversampling, please refer to the second article.) It is explained in detail there.

Setting a higher sampling frequency fs also increases the Nyquist frequency fn. This means that a wider margin (transition bandwidth) can be secured between the signal bandwidth and the Nyquist frequency. This increased margin makes the attenuation characteristics required for the anti-aliasing filter gentler, and as a result, aliasing can be sufficiently suppressed even with a low-order filter configuration.

Therefore, when actually designing, one has to consider the trade-off between "forcibly cutting through with a higher-order analog filter" or "creating a margin with oversampling." Oversampling is one effective way to alleviate the steepness required of anti-aliasing filters and make it easier to secure design margins.

Summary

Anti-aliasing filters play a crucial role before the AD converter in preventing aliasing, an error component that cannot be removed by digital processing.
When designing, it is important to clarify the relationship between the signal bandwidth, sampling frequency, and Nyquist frequency, and then design the circuit after considering the cutoff frequency and the required attenuation.

Furthermore, by combining this with oversampling, we can increase the flexibility in anti-aliasing filter design.