Moulton  Lectures

 

On

Electro-Acoustics

 

 

 

Presented by:

Dave L Moulton

 

 

 

 

Location:  Thales Acoustics Harrow UK

Date:  18-December-2002

 

Content

 

We now move onto a very significant subject which has made revolutionary in-roads into the design and performance of hearing protectors. My next few lectures will be focused on the theory behind Active Noise Reduction, commonly known as ANR.

 

This particular lecture will be a gentle introduction to the fundamental concepts of ANR as applied to a hearing protector. I will put together one of the simplest mathematical system models for a headset ANR system and derive a general expression for the closed loop response.

 

On with the Lecture

 

What is ANR?

Active Noise Reduction (ANR) is process for enhancing the natural attenuation performance of a device, in our case a headset, by electronic assistance.  The electronic assistance could be analogue or even a digital system which acts to introduce anti noise into the acoustic environment.

 

There are several ways of providing ANR into a headset, the most common two being the ‘Feedback’ and ‘Feedforward’ techniques.  Both methods involve the use of a sensing (monitor) microphone, multipole filter and earphone transducer. 

 

The general principal of both techniques is for the sensing microphone to detect the unwanted acoustic noise signal and pass it to the multi pole filter.  The filter inverts the signal which is then radiated out of the earphone into the earshell as acoustic anti-noise. The anti-noise will mix with the unwanted noise in the earcup and produce localized cancellation of the sound pressure.

 

Both techniques are shown in figure 10.1 below:

 

Figure 10.1

 

 

The feedforward technique has low frequency performance limitations when applied to a circum-aural hearing protector, although it is often employed in commercial lightweight supra-aural headphones.  For the purpose of this lecture and its applicability to real life products I will concentrate on the feedback technique

 

 In the case of a hearing protector with employs the feedback ANR technique the electronic assistance usually invokes the following process:

 

1.     A microphone located in the earshell detects the localised noise Sound Pressure Level.

2.     The output from the microphone is fed to an electronic circuit.

3.     The circuit processes the gain and phase characteristics of the noise signal and produces an anti phase version of the noise (anti-noise).

4.     The anti noise is radiated out of a transducer (Earphone) also located inside the earshell and in close proximity to the monitoring microphone.

5.     The radiated anti noise mixes with the original noise signal causing localised cancellation of the sound pressure.

 

The process is shown in figure 10.2 below:

 

The 5 steps that I have described above are very simplistic and also very Ideal.  The ideal case would be when the Anti-Noise perfectly cancels the original noise such that the voltage output from the microphone v_out reduces to zero.   As I will explain in later lecture, the reality is far from Ideal.

Figure 10.2

 

 

 

Why Do we Need ANR?

In previous lectures we have looked at the general characteristics of a simplistic hearing protector, and have also seen a presentation relating the mathematical model to real life measurements.  It should now be clear that all practical hearing protectors perform poorly at low frequencies (20Hz to 250Hz) relative to their high frequency performance (beyond 250Hz).  In fact the reality is that below 250Hz to achieve any more than a peak attenuation of 30dB is pushing the boundaries of passive hearing protector technology.  Whereas beyond 250Hz, 30dB to 40dB is achievable.  See graph 10.1 below:

 

 

Graph 10.1

 

There are certain environments where equipment and machinery generate significant amounts of acoustic noise in the 20Hz to 250Hz band. A very typical example of this is the noise levels generated inside main battle tanks and armoured troop carriers. In the military environment tank crews and infantry have to endure long periods of time within these noisy vehicles.  To give you an example of the sorts of Sound Pressure Levels that can be generated see Table 10.1 below:

 

Military Vehicle	Peak Sound Pressure level  dBLin	After Best Case Passive Atten’n 25dB at 200Hz 18dB at 125Hz	Resulting     A-weighted Sound Pressure Level  dBA
Challenger II (UK Tank)	130dB (at 200Hz)	105dB	95dB
Warrior  ( UK Troop Carrier)	125dB (at 125Hz)	107dB	91dB
M113 (US Troop Carrier)	127dB (125Hz)	109dB	93dB

 

Table 10.1

 

As can be seen from table 10.1 even when taking into account the A-weighting the levels are still far in excess of the recognised Health and Safety exposure limit.  (Leq = 85dBA for 8 hours).

 

Military Establishments around the world have recognised that prolonged exposure to excessive low frequency noise can result in mental Fatigue. In a military environment noise fatigue can reduce the effectiveness of infantry and tank crews, which can result in tactical errors and put lives at risk.

 

In order to address this problem ANR has been introduced into a range of military headsets around the world.  In particular the UK and US armies now have ANR headsets fitted in most of their tracked vehicles.  The UK MoD took the lead and where the first to equip all of its fleet of tracked vehicles with ANR headsets. In particular the Thales Acoustics Crewgard and Combat Headsets.  The US soon followed suit by supplying the BOSE CVC headset for Tank Crews and the Thales Slimgard II for Infantry Passengers. The French army have been a lot slower in fitting out their vehicles with the ANR headsets.

 

 

What are the Limitations?

All of these in-service headsets go a long way to addressing the low frequency attenuation problem.  However, they all have low frequency performance limits, typically the BOSE CVC and Thales Crewgard  have peak Active Attenuation performance levels of between 16dB to 20dB. 

You may ask yourself, what are the limiting factors to the ANR performance?  The answer to this question involves a lot of in depth technical analysis, to be covered in another lecture. However, I feel quite comfortable in mentioning one word that limits the performance of all ANR headsets and that is ‘Stability’.  Ideally we would like to have ANR headsets with 30 to 40dB of low frequency active attenuation, unfortunately the more attenuation you try and achieve the more critically stable the ANR system becomes. If you push the system too hard the end result can be the reverse affect known as enhancement and uncontrollable oscillations.

 

The stability of an ANR system within a headset can be a function of many parameters all of which determine the Open Loop and Closed Loop Electroacoustic Gain/Phase response of the headset. 

 

The Simple ANR Model

I will now derive and explain the simple ANR model. 

 

Firstly lets have another look at how we are trying to achieve ANR. To make life easier I will draw the ANR block without the surrounding earshell, I will also re-orientate the picture.

 

Figure 10.3

I will now represent the monitor microphone and the earphone transducer as Transfer Function Models. I will also represent the ANR circuit as a constant gain amplifier and a multi-pole filter. There is also a Transfer Function between the earphone and the microphone, largely made up of the earshell acoustics.  By the way, I will be operating in the S-domain when converting to these Models.  So lets start by summarising the individual Transfer Function elements.

 

Figure 10.4

 

I have purposely only represented the input and output variables on some of these blocks.  When the blocks are linked to form the model all of the input and output variables will make sense.  We must now represent what is happening to the acoustic pressures at the face of the microphone.  For this simple model we can assume that the sound pressure arriving from the earphone transducer simply adds to the un-wanted noise pressure.  In control systems it is standard practice to represent this model in the following way:

 

Figure 10.5

 

I can now bring all of these elements together and create a simple ANR control system model.

 

 

Figure 10.6

 

 

This model is very simple and very Ideal. Our main criteria is to ensure that the addition of the unwanted noise pressure P_o(s) and the anti-noise Pressure P_T (s)  result in a minimum pressure P_m(s) at the face of the microphone.  Thus we start with the defining equation:

 

 

Now for the fun part, I can simply work my way around the loop so that P_T(s)   can be expressed in terms of all the system transfer functions.  Figure 10.7 below shows the root around the loop.

 

 

Figure 10.7

 

I can now start putting the closed loop system equation together as follows:

 

Lets start with the defining equation and substitute for P_T(s) .

 

 

Now for some factorizing:

 

 

Arranging to shown the transfer function:

 

 

I will now simplify the expression even further by letting:

 

 

Thus:

 

This is the final form of the closed Loop transfer function.  To achieve maximum noise cancellation we need to make the modulus of the closed loop Transfer Function as small as possible.  Looking at equation [10.6] the ideal would be to let   G(s) = H(s)^-1 and then make the system gain k as large as possible:

 

Thus:

 

Leading to:

 

 

 

For large values of constant gain k the modulus of equation [10.8] simplifies to:

 

 

This is the absolute ideal situation, and it assumes that we can create a stable transfer function G(s).  The difficulties in realizing this ideal will be discussed in another lecture.

 

The Headset Transfer Function H(S)

Now lets move on to another very important aspect of the ANR model.  The Headset Transfer Function H(S), this is the staring point for all ANR system design, H(S) is the natural transfer function between the input to the earphone transducer and the output of the monitor microphone.  The Poles and Zeros of H(S) are very important since we need to know them to create the ideal function G(S).  Remembering that G(S) is the  inverse of H(S).  We can create G(S) by means of electronic circuits and digital filters.

 

Fortunately we can easily measure H(S) by means of a spectrum analyzer,  simply by injecting an input into the earphone and measuring the corresponding output from the microphone.  The analyzer should be able to produce the transfer function H(S) either as a Gain/Phase Plot or as an interpolation of Poles and Zeros.  Figure 10.8 below shows how H(S) can be obtained.

 

 

 

 

Figure 10.8

 

 

Note: In order to establish a realistic H(S) the following guidelines are important:

 

1.     The headset should be worn on a series of real heads while H(S) is being  measured. Significant variations in H(S) can occur between different test subjects.

 

2.     All of the Mechanics for the ANR housing should be included. 

 

3.     All representative elements intended for use inside the earshell should be included such as Foams, PECs, Transducers and other mechanical features.

 

4.     The headset should be worn fully sealed to the head, this also includes the ports for the test leads to the analyzer.  Although variations in H(S) due to leak paths can be useful to know.

 

5.     The analyzer should be able to present H(S) as a graphical Gain-Phase plot or more useful as an interpolated Pole-Zero Polynomial.

 

 

 

 

End of Lecture