Active Noise Cancellation
In head- and earphones
Working principles
Subtracting the noise
An ANC circuit is basically a loop controlled circuit where one or more microphones, an earphone (receiver) and an ANC controller circuit are involved.
An electrical signal (speech or music) is fed into the ANC controller circuit and an electrical noise signal is picked up by a microphone, phase shifted by 180 deg. and fed into the ANC controller circuit as well. The microphone is positioned in a place where best pickup of background noise can be achieved. By phase shifting this noise signal 180 deg., the background noise will ideally be cancelled out and only the pure speech or music signal will reach the earphone and thereby no noise will reach the listeners ear.
Three different topologies
– Feed forward, feedback and hybrid –
While the basic ANC concept is the same, it can be implemented in three different ways in earphones/headphones. Each principle has advantages as well as disadvantages as described below:
Feedforward
(microphone outside earcup)
In the feed-forward design the microphone is placed outside the ear cup. Here the microphone detects the noise before the listener does.
The ANC circuit processes the noise and makes the anti-noise signal before sending it to the earphone.
Advantage
Disadvantage
Feedback
(microphone inside earcup)
In the feedback design, the microphone is placed inside the ear cup and in front of the speaker “hearing” the resulting signal in exactly the same way as the listener does.
Advantage
Disadvantage
Hybrid
(microphone inside and outside earcup)
The Hybrid ANC design takes the best of both worlds in combining the feed-forward and the feedback ANC having microphones placed both outside and inside the ear cup.
Advantage
Disadvantage
LIMITATIONS TO THE ANC PERFORMANCE
– Ideal theory meets 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 is not possible. Such a delay will degrade high-frequency ANC the most due the shorter wavelengths of the signal frequencies involved.
Analog domain
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:
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 constraints (especially in the in-ear earphones) a quite small receiver has to be chosen (Ø8mm – Ø15mm) and then some performance parameters become quite challenging.
Primary parameter: Maximum Sound Pressure Level
If the ANC performance should be able to handle really high noise sound pressure levels up to ex. 140dB SPL (traffic noise, flight take offs, shouts, building construction machine activities etc.), the receiver should be able to handle these SPLs as well without significant distortion and knowing that the noise signal must be reproduced in counter phase according to ANC loop. This is only possible with a receiver allowing a very high stroke of the membrane without entering a compression mode. The smaller the receiver is in diameter, the harder the need will be for a high membrane stroke.
Secondary parameters
The following parameters for the receiver application are of secondary importance, because they are strongly related to the amount of filter orders available in the chosen ANC digital system. Almost all of the following parameters can be compensated for, by having unlimited access to the number of filters, but the tradeoff is the cost for the ANC circuit as well as an increased power consumption. Therefore a good engineering practice is to optimize the following parameters before relying on a higher number of ANC filter orders.
Damping Ratio
The Damping Ratio, ζ (zeta), for the whole receiver application should be tuned to around 0.7 for achieving best reproduction of the electrical signal into acoustic signal (best mirroring of electrical signal). The best mirroring of the electrical signal into an acoustic signal (reproduced by the receiver) is very important for assuring the highest linearity of the ANC loop and thereby best ANC performance. A Damping Ratio of around 0.7 is the best compromise between fast enough rise time and minimized post ringing at the system`s resonance frequency.
When looking at the Frequency domain, we normally express a Quality Factor (Q factor) for the resonance system. The relation between the damping ratio and quality factor is given by the equation (1)
ζ=1/(2*Q)
It can be calculated using equation 1, that a damping ratio around 0.7 will result in a Q factor of 0.7 (called critical damping). This means that in the frequency domain you would need a critical damped system for achieving best ANC conditions.
The total Q factor for the system is not the same as the total Q factor for the receiver involved. The receivers total Q factor must primarily be controlled by a very strong magnet system which will lower the Q factor down towards the desired value of 0.7, but normally this is not enough for reaching the critical damped factor of 0.7. The remaining lowering of the system Q factor will be done by mesh tuning on rear side of the receiver and/or mesh covering a rear vent in the earphone/headphone.
So when a Q factor of approx. 0.7 is tuned in, the Damping ratio will also be approx. 0.7 according to equation 1.
Phase response
The receivers phase response up to around 1.2 kHz must have minimum phase shifts with a smooth response for the ANC processor to be able to handle the signal. Therefore resonances in this frequency range must be kept at a minimum. Preferably only the mechanical resonance determined by the moving mass (coil & membrane) and the compliance of the membrane. This resonance is unavoidable in a moving coil receiver but must have as low a resonance frequency as possible for being positioned outside of the pass band.
It can be seen that a damping ratio of 0.7 (equation 1) will result in the most smooth phase response and thereby best ANC counter phase correction conditions.
The conclusion is that a system quality factor of 0.7 ensures the best conversion of the electrical signal to the acoustic signal out of the receiver, which is needed for best linearity of the system and the flattest phase response ensuring best counter phase conditions for the ANC loop.
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