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This time, let's talk about an audio topic: Active Noise Cancellation, or ANC for short. In fact, Roy talked about "noise reduction" in his article "This Damn Noise" 5 years ago.
But at that time, it was just a little bit of water and a little mention, but the content of this issue is not simple, and it is mainly based on the output of dry goods. (Due to space limitations, this time we will only discuss headphones)
Basic concepts
Let me explain the basic concept of ANC in one sentence at the speed of light: it is a technology that uses inverted sound waves to cancel out ambient noise and make the listener feel quieter. The ideal ANC system, which usually includes a feedforward and feedback system, gives the impression of "sinking to the bottom of the ocean in a second".
Popular understanding: The "inverted sound wave" mentioned above is a "shadow clone" built by the engineer to cancel out the original noise, and ideally, after the two fight, they can die together (everything returns to tranquility).
Roy homemade
It's easier said than done. In the real world, the "ontology" is often more powerful than the "shadow clone", especially in a noisy environment, the "inverted sound wave" summoned by the engineer is usually implemented in the feedforward system, but it can generally only cancel out a part of the noise energy, and in order to kill as much noise as possible, it often needs more barriers: feedback systems.
Network screenshots, invasion and deletion
Unlike the "shadow clone" summoned by the "feedforward system", the "feedback system" is not so particular, and it doesn't care if it looks like noise, it is more like a "Hercules", and will use brute force to deal with the "residual noise" after being canceled by the "shadow clone". But it will be constrained by the acoustic design of the system, and a good acoustic design can make it exert more power. Poor acoustic design (secondary path) and brute force will result in acoustic noise due to insufficient phase margin.
It should be noted that the ANC's sphere of influence is constrained by the depth and width of noise reduction. The final result depends on the acoustic structure, electroacoustic device (Mic+Spkr), noise reduction chip (Codec+DSP), and the combination of "noise reduction depth/width" and "psychoacoustics".
So, you will see a lot of headphones that claim to have noise cancellation of 40dB, but the actual noise cancellation effect is not as good as the products that claim 30dB, and you will also see a lot of headphones, after the OTA upgrade, the stability is enhanced, but the noise cancellation performance will be weakened...
Actual combat to uncover the mystery of ANC
Next, let's take a basic hybrid ANC system as an example to talk about how designers summon noise "shadow clones" and "Hercules".
Figure 1
Based on first principles, we can simplify "how to build a basic ANC system" to: how to design FF Filter ("shadow clone") and FB Filter ("Hercules").
Of course, if you want to play cooler, you can also build multiple feedforward systems (multiple shadow clones), and even multiple feedback systems (multiple warriors), as well as a more intelligent adaptive noise cancellation system, which will not be repeated here.
Figure 2
For the sake of description, let's first unify the following terms:
FF Filter: A feedforward filter that mainly processes feedforward microphone signals.
FB Filter: Feedback filter, which mainly processes feedback microphone signals.
Primary Path (A2DRP): The acoustic path through which external noise travels into the ear.
Secondary Path (D2DRP): The acoustic path that occurs from the earphone's own horn to the ear.
A2FF:外部噪声到FF麦的频响。
A2FB：外部噪声到FB麦的频响。
Create a "shadow clone":
Step 0, as described in Figure 2, set up the device and turn on the microphone and speaker paths.
The first step is to make the loudspeaker in the anechoic chamber sound based on PC+AP and other equipment, and record the FF microphone and FB microphone at the same time, which can obtain:
(1) A2FF frequency response
② A2FB频响（≈A2DRP）
The primary path (i.e., P(z)) characteristics of the headset are: (2)/(1)
The second step is to let the headphones sound from their own speakers, and record the FB microphone at the same time, which can obtain:
③ D2FB频响（≈D2DRP），此即其次级路径 S(z)
At this point, we can finally create a noise "shadow clone":
FF Filter = (②/①)*③，（相位上也可视为：②-①+③）
The quality of the FF filter design will largely determine the noise reduction width, as well as the phase margin of the next-pass feedback filter, and if the acoustic margin is insufficient, the noise reduction depth will be constrained.
Summon Hercules:
The role of Hercules is to fight against the residual noise that survives from the "shadow clones", and is mainly responsible for suppressing the low frequencies. This step is easy to say and difficult to say.
As I just said, FB Filter is a strong man with infinite strength, but if you use brute force in the wrong situation, it will cause self-excitation and howling, which is unsafe.
Screenshot of the simulation
Since the delay of the FB feedback path is very low, it is enough to directly invert at the low frequency (to put it bluntly, it is multiplied by minus one), raise it, and then superimpose the noise. But be careful: don't be too arrogant when lifting up, because the amplitude is changing at the same time, the phase is also changing, and if you are not careful, the secondary path/feedback system may howl.
Good acoustic structure design, in the case of satisfying the FF Filter design is very powerful, it can also leave enough margin for FB Filter to do low-frequency inverted lifting. With this in mind, the system design is good enough.
The design of the FB filter determines the depth of noise reduction and the stability of the entire system. Many times the self-excitation howling is because the FB tune is more aggressive (Hercules pushes too hard), so that the pole is too close to the unit circle, and when the user uses it, a slight change in the acoustic path (such as shaking the head and squeezing the ear canal when wearing headphones) may cause the pole to escape outside the unit circle, isn't this self-exciting?
We also talked about this point in "Dry Goods Weekly: Easy to Understand "Op Amp Stability" and "Zero Pole Art" (Extra Part 4).
Summary & Bugs
Just talking about not practicing fake handles, the following is the common appearance of frequency response at each stage:
In summary, the minimalist expression of the whole system can be approximated as:
H(z)=P(z)*FF/(1+S(z)*FB)，其中P(z)为初级路径，S(z)为次级路径。
I don't know if you have noticed it, in fact, there is a bug in the above analysis process: that is, the primary and secondary paths we measured earlier are all using the effect of FB microphones, which approximates the effect of what is actually heard in the ear, which is inaccurate (think about why?). And thousands of people, the actual effect of DRP in different people is also very different.
This in itself is also a big problem in the ANC industry, but the top players still found some ways to directly turn the "shadow clone technique" into "filthy earth reincarnation".
Internet search, invasion and deletion
So far, only a few players have managed to solve this problem properly, and it is precisely because of this that their products have been able to maintain the commanding heights of technical products.
On the one hand, there is the dark abyss of involution, and on the other hand, there is the continuous realization of technological dividends.
It's exciting
End
Roy's personal opinion, for reference only