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)
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 (see Fig 7).
Fig. 7: Phase and frequency response vs. Q factors
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.