Limitations to the ANC performance
Ideal theory meets real world limitations.
The above mentioned ANC principles would work in a very broad frequency range if all conditions were ideal. In practice there are many factors limiting the ANC performance at higher frequencies.
Delay, digital domain
When processing signals in the digital domain, there will be some delay issues, which will disturb the ANC performance. Ideally the processing should be with zero delay, but this I not possible. Such a delay will degrade high-frequency ANC the most due the shorter wavelengths of the signal frequencies involved.
In the analog domain a significant limiting factor is the variance of the transfer function of the system in the ear of the user. This variance will increase at higher frequencies and course many and rapid phase shifts in the transfer function. Knowing that the basic ANC application is based on adding a noise signal in counter phase, many and rapid phase shifts will of course complicate the task significantly. In fact there is a huge risk at higher frequencies to increase the noise level due to this or even enter an unstable loop finding its own resonance frequency and turning into an oscillator.
For these reasons, the ANC performance is often by purpose band limited to around 1.2kHz. This also makes sense since the mechanical structure of the earphone/headphone gives a solid passive background noise attenuation above 1.2kHz making ANC obsolete over this frequency range.
Limitations to the elements in the ANC loop
There are three major elements in the ANC loop:
—The driver (receiver)
In the ideal world these elements would be total linear within a large dynamic range, have flat frequency and phase response and no internal noise. If this was the case, designing the ANC application would be a piece of cake. Unfortunately we have to face reality: A modern electret or MEMS microphone has quite a high dynamic range, a modest noise figure and a fairly flat frequency and phase response. The same goes for the ANC processor, which “only” adds some time delay as mentioned earlier. But when it comes to the receiver, the picture is a totally different one. Due to size constrains (especially in the in-ear earphones) a quite small receiver has to be chosen (Ø8mm – Ø15mm) and then some performance parameters become quite challenging.