by Chu Moy
Noise cancellation headphones (NCHs) supplement the acoustic isolation characteristic of headphones with active noise reduction. By their nature, headphones block out some degree of external noise because the earcups absorb it, but NCHs go a step further and diminish the noise that manages to get through. In industrial settings, NCHs protect the hearing of workers exposed to deafening levels of sound on a daily basis. In the field of communications, they can enhance the intelligibility of speech. The average consumer uses them for listening to music on airplanes, trains or other situations that suffer from constant noise pollution.
NCHs come in a variety of styles: circumaural, supra-aural and in-ear. In principle, all NCHs counteract noise by generating “anti-noise” to nullify it. However, noise cancellation technologies vary in sophistication. This article examines the theories and implementations of three type of NCHs: open loop, closed loop and adaptive. It follows the development of noise cancellation technologies in patent disclosures and technical papers. Many innovations are omitted due to space limitations, and the discussion is concerned only with those noise cancellation technologies that are relevant to headphones.
Noise reduction devices that are more advanced than simple earmuffs or earplugs go back many decades to the first half of the 20th century. The use of headphones in combination with electronic methods to handle noise emerged in the 1960s and 1970s. They first appeared as noise filtering headphones (figure 1), in which the electronics are bandpass filters and audio limiters that reduce noise by stripping the high and low frequencies in the audio signal and flattening the amplitudes before being output to the headphone transducer.
The headphone itself (an earmuff or hearing protector) blocked external noise with passive attenuation. The listener could activate an externally-mounted microphone to to hear speech and other sounds filtered for greater intelligibility in high noise environments. (See, e.g., Richard David Williams, “Hearing Protector,” US Patent No. 4064362, 12/20/77 and Gordon Kyle, “Ear Protection and Hearing Device,” US Patent No. 3,952,158, 4/20/76.) However, the drastic bandpass filtering in these devices does not clean up noise embedded in the passband, is unsuitable in high fidelity applications, and is further limited to the passive attenuation of the headphones as the sole means of reducing external noise. Noise suppression headphones evolved to noise cancellation technologies that actively nullify noise with anti-noise.
Anti-noise is simply an inverted version of the noise signal, so that when noise and anti-noise meet, they cancel each other. The effect is a manifestation of the Superposition Principle. When two identical soundwaves combine that are 180 degrees out of phase, the result is destructive interference (figure 2). If the anti-noise is not a perfect replica of the noise waveform or is not exactly 180 degrees out of phase, the destructive interference will weaken the noise, but not cancel it. (For more information about superposition and other acoustic principles, see The Elements of Musical Perception.) NCH headphones employ electronic circuits that are integrated with the headphone design to generate anti-noise. They are called active noise reduction (ANR) systems.
NCHs rely on the passive acoustic isolation of headphones as well as ANR to provide broadband noise reduction (figure 3). Closed-ear headphones can passively block high frequency noise down to about 500Hz. At high frequencies, a well-designed closed-ear headphone can reduce noise by nearly 30dB – the amount of attenuation being dependent upon the quality of the seal from the ear cushion around the ears, the construction of the earcups and the sound-absorbent materials used in the earcups. For example, NCHs that have supra-aural earpieces will have less passive noise reduction than closed-ear types.
Where passive attenuation begins to weaken in the low frequencies, ANR takes over. Electronic noise cancellation is less effective at high frequencies due to the limitations of ANR filters and headphone transducers to reproduce accurate high-frequency (complex) anti-noise. Not all applications require broadband noise attenuation, and some models of NCH reduce low frequency noise only.
ANR systems create anti-noise by first sampling the noise with a microphone. In an open-loop system, the microphone is positioned outside the earcup (figure 4). An inverting amplifier outputs the anti-noise signal which is then mixed with the desired audio signal before being played back in the headphone transducer. The anti-noise signal should attenuate the external noise, leaving the desired audio signal more intelligible. This design does not adapt to different users, who individually adjust the amount of anti-noise for optimal effect.
Open loop systems have the advantage of simplicity, but may not perform as well as other NCH types. Because the microphone is located outside the earcup, the sampled noise is not a perfect replica of the noise inside the earcup, which is altered by passing through the earcup as well as by internal reflections. Therefore, in some situations, the anti-noise signal may actually introduce noise inside the headphones.
On average, open-loop ANR can attenuate noise by 10 to 15dB. It is commonly found in NCHs for professionals and consumers in a variety of wear and transducer styles (circumaural, supra-aural, open-air, closed-ear, etc.). The open-air and supra-aural styles do not provide substantial passive attenuation, so higher frequency sounds (such as voice) will remain audible. The Build Your Own Noise Cancellation Headphones project by Jules Ryckebusch is an example of an open-loop system.
A more accurate anti-noise signal is possible if the microphone is placed inside the earcup in front of the transducer. Doing so electrically “closes” the ANR circuit because the microphone now samples both the sound emitted by the headphone transducer as well as the noise in the earcup. This signal is fed back to the desired audio signal input as an error correction for the noise. Hence, these NCHs are called closed-loop systems. The operation of closed-loop ANR is characterized by negative feedfack and is the province of automatic control theory.
Under control theory, noise (like amplifier distortion) is viewed as a non-linearity, which can be mitigated or eliminated by applying a correction signal to the system. The block diagram in figure 5 depicts a NCH with closed-loop ANR. A microphone mounted inside the earcup receives sound that is a mixture of the desired audio signal and noise. The first stage of the ANR removes the desired audio signal from the mixed signal and inverts it. The next stage compensates the inverted noise signal for stability in the closed-loop system (discussed below). The output stage remixes the anti-noise signal with the desired audio signal for playback in the headphone transducer. Because of the negative feedback, closed-loop systems may become unstable under certain conditions.
The amount of noise reduction in a closed-loop system can be calculated as Hc = Hc / (1 – Hc * Hf), where Hc is the transfer function of the earcup cavity and Hf is the transfer function of the feedback network of the ANR. The larger the value of Hf, the greater the noise reduction, assuming the feedback signal is 180 degrees out of phase with the noise in the earcup. The point of greatest attenuation is at the position of the microphone.
The stability of a negative feedback system can be determined from a Nyquist-Bode frequency domain analysis. Whereas the stability of an open-loop system is independent of gain, negative feedback systems have guaranteed stability only within the boundaries defined by the gain and phase margins. Outside those margins, the gain of the controller must be set below 1 to maintain system stability (figure 6).
In particular, closed-loop ANR systems are prone to oscillation due to excessive phase shift of the feedback signal caused by the time delay from the distance between the microphone and the transducer and by the inherent delays of the microphone and transducer. The phase shift from the first cause is minimized by placing the microphone as close as possible to the transducer. The second cause of phase shift is handled by applying a low pass filter to adjust the phase and high frequency content of the feedback signal, which, of course, also limits the operational range of the ANR to low frequencies. A high pass filter prevents oscillation due to violent movements of the listener’s head.
The design of the compensatory network should maximize open loop gain across a wide bandwith to extend the effectiveness of the ANR. The phase margin at the feedback cutoff frequency should be 30 degrees or more. If the attenuation is only 6dB per octave from the cutoff as suggested by Bode (so that the gain is 1 at approx. 2.5 octaves from the cutoff), the performance of the ANR is compromised in that region. Instead, a compensation network with regions of arbitrary slope (the slope at the cutoff is much high than that at the critical frequency where the gain drops to 1) can then be configured for maximum loop gain from about 40Hz to 2kHz (figure 7). (Amar Bose, “Headphoning,” US Patent No. 4,455,675 – 6/19/84.)
Closed-loop ANR headphones can provide up to 30dB of noise reduction across the audio spectrum when deployed in closed-ear headphones with superior passive attenuation (figure The most effective closed-ear NCHs tend to resemble “ear muff” hearing protectors and are often used in industrial or professional audio applications.
Adaptive Noise Reduction
The open-loop and closed-loop ANR discussed above employ analog filters to create anti-noise. Digital filters are more versatile and more easily configured than analog filters. Digital filters for noise cancellation are called adaptive filters and can correct for both phase and amplitude errors.
Figure 8 is an example of a NCH using adaptive noise reduction. A reference microphone at the top of the headband receives a noise signal. The adaptive filter attempts to predict the noise inside the earcup by passing the signal through a transfer function that models the headphone system. The inverse of the predicted noise is added to the desired audio signal and then sent to the headphone transducer. A second microphone inside the earcup measures the resulting sound and generates an error signal to converge the filter to zero (eliminate the noise seen by the error sensing microphone) for more accurate anti-noise.
The controller in an adaptive filter is typically a least means square (LMS) type, which is pre-trained offline (usually with white noise) for broadband operation. The disadvantage to LMS filters is that they must be retrained for changes in the feedback path (e.g., temperature changes, a different person wears the headphones). If the noise is narrow-band or a tone, the performance of the noise cancellation will degrade because LMS filters will try to adapt without converging. For narrow-band noise cancellation, the solution is to use an infinite impulse response (IIR) filter. An IIR is best to model the acoustic system and feedback path, because IIRs have a recursive characteristic to provide an infinite response and have feedforward and feedback sections to generate zeros and poles. A recursive LMS algorithm (made of two LMS filters) can optimally adapt the filter coefficients. (Larry J. Eriksson, “Active Sound Attenuation System with On-Line Adaptive Feedback Cancellation,” US Patent No. 4,677,677 – 6/30/87.)
The recursive LMS filter can adapt to changes in the feedback path without retraining by updating the filter coefficients with a time delay value, chosen for a specific region of frequency stability. The time delay value only partially simulates the transfer function between error microphone-headphone transducer, but is adequate to compensate for the phase shifts between from the transfer functions of the error mike and the speaker that cause instability in conventional adaptive filters. The adaptive filter must be stable in order to converge to its steady state solution. (Paul Feintuch, “Active Adaptive Noise Canceller without Training Mode,” US Patent No. 5,117,401 – 5/26/92.) If a single time delay results in a stable region that is too limited in bandwidth, the noise can be divided into two or more frequency bands and each band handled by a separate adaptive filter with different delays (figure 9). A single delay has a straight-line phase response which may be unable to stabilize the composite phase of a system. (Allen K. Lo, “Multiple Adaptive Filter Active Noise Canceller,” US Patent No. 5,425,105 – 6/13/95.)
Headphone Design for Active Noise Reduction
Headphone construction can be optimized for ANR (figure 10). The ear cushions should be compliant enough to effect a seal that prevents leaks and has sufficient high density and flow resistance to create an “ideal” cavity (rigid walls, constant pressure amplitude for wavelengths much larger than the distance across the cavity). The diaphragm should be small – less than 1/3 wavelength of the highest audio frequency to be reproduced. The volume parameter of the front cavity must balance two considerations: a small front cavity will minimize the sound pressure required to cancel low frequencies, but a large front cavity offers superior passive attenuation.
Passive attenuation in an earcup is a function of the front and rear cavity volumes and the driver compliance below the free air resonance. If the front cavity is kept small to maximize efficiency, then increasing the driver compliance can compensate for the reduction of passive attenuation. Efficiency is a major issue with portable NCHs which are battery-powered. (Amar Bose, “Headphoning,” US Patent No. 4,455,676 – 6/19/84.)
High compliance drivers are sensitive to overpressure, which can occur when the user moves or takes off the headphones – the pressure waves due to the movement can pull the voice coil outside the gap or distort the diaphragm. One solution is to add an excursion stop (a tiny barrier or mesh) in front of the diaphragm to prevent the voice coil from traveling too far. Forming grooves or indentations in the diaphragm can strengthen it and allow it to quickly recover when distorted. (Roman Sapiejewski, “High Compliance Headphone Driving,” US Patent No. 5,181,252 – 1/19/93.)
Another option is to stiffen the diaphragm by constructing it from different material laminates for greater strength and to prevent natural resonances. This method has the advantage of extending the operating range of the ANR without phase shifts because the system resonance frequency is raised when the diaphragm compliance is less than the compliance of the rear cavity. The fundamental resonance of the diaphragm can be dampened with a dampening disk positioned below the diaphragm. The tradeoff is reduced transducer sensitivity, but that may be restored by optimizing the voice coil paramaters (e.g., maximize the product of the specific conductivity and cross-sectional area of voice coil wire). (Volker Bartels, “Sound Reproduction Device with Active Noise Compensation,” US Patent No. 5,809,156 – 9/15/98.)
Bartels, Volker, “Headset with Active Noise Reduction System for Mobile Applications,” J. Audio Eng. Soc. April 1992, p. 277.
Bartels, Volker, “Sound Reproduction Device with Active Noise Compensation,” US Patent No. 5,809,156, 9/15/98.
Bose, Amar, “Headphoning,” US Patent No. 4,455,675, 6/19/84.
Eriksson, Larry J., “Active Sound Attenuation System with On-Line Adaptive Feedback Cancellation,” US Patent No. 4,677,677, 6/30/87.
Feintuch, Paul, “Active Adaptive Noise Canceller without Training Mode,” US Patent No. 5,117,401, 5/26/92.
Kyle, Gordon, “Ear Protection and Hearing Device,” US Patent No. 3,952,158, 4/20/76.
Lo, Allen K., “Multiple Adaptive Filter Active Noise Canceller,” US Patent No. 5,425,105, 6/13/95.
Sapiejewski, Roman, “High Compliance Headphone Driving,” US Patent No. 5,181,252, 1/19/93.
Williams, Richard David, “Hearing Protector,” US Patent No. 4064362, 12/20/77.
c. 2001 Chu Moy.