A-level Physics Coursework - Microphones

Physics Research Brief Matt R****

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How does microphone design relate to application?

Microphones exist in a vast range of forms are used for a huge variety of applications. A microphone is any

device that acts as a transducer, converting sound/acoustic energy – in the form of longitudinal pressure

waves (usually travelling through the air) – into electrical energy (1) (2) (3) (4). I’m going to be researching the

general principles behind microphone function, and then focusing on how certain design specifics apply to

microphones intended for use on stage in live situations.

The majority of microphones fall into two main categories based on the means by which they function;

dynamic microphones, which operate on the principles of electromagnetic induction, and condenser

microphones which are based on electrostatics (1) (2) (3).

Dynamic microphones

The operation of a dynamic microphone is often considered analogous to a ‘loudspeaker in reverse’ (3). A

diaphragm is attached to a coil of wire which is then allowed to pass through the magnetic field of a fixed

magnet, inducing a voltage in the wire (3) (5). The magnet is always fixed and the coil attached to the

diaphragm due to the much greater mass of the magnet. Because of this, dynamic microphones are often

called ‘moving coil microphones’ (5).

Fig 1. Typical magnet assembly of a dynamic microphone

The shape of the magnet in a dynamic microphone is usually very similar to that found in a loudspeaker.

The path of the flux in this circular design travels through the base of the magnet then passes across the air

gap between the north and south poles. This creates a uniform field for the coil of wire to cut through. As

shown by Fleming’s right hand rule (figure 3), a conductor cutting through a magnetic field will have a

current induced perpendicular to the direction of the motion (6). The induced electromotive force (emf) is

dependent on the conductor having velocity through the field.

Fig 2. Fleming’s right hand rule of electromagnetic induction (7)

When the right hand rule is applied to a coil of wire, the induction of an emf depends on the changing flux

within the coil, causing the flux linkage to change; the flux linkage is equal to the product of the total

magnetic flux (the flux density multiplied by the area covered by the coil) and the number of turns in the

coil (8). Faraday’s law of electromagnetic induction, which states that the magnitude of the induced emf is

proportional to the rate of change of magnetic flux (9), can be expressed as the equation in figure 5.

coil


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Fig 3. Electromagnetic induction (9) (10) (8)

Where:

is induced electromotive force in volts (V)

is the number of turns in the coil

is the total flux in Webers (Wb)

is the magnetic flux density in Teslas (T)

is area covered by coil in square metres (m2)

When the coil is made to pass through the magnetic field (as a consequence of pressure waves in the air

interacting with the diaphragm it is attached to), the changing flux linked by the coil results in a varying

output voltage that reflects the displacement of the diaphragm – a representation of the sound captured

sound wave as an electrical signal.

Fig 4. Exposed capsule of a dynamic microphone

Dynamic microphones are usually very durable and can withstand sharp forces, exposure to moisture, etc.

The most delicate part of a dynamic microphone – the diaphragm, coil and suspension assembly – is

generally protected by a sturdy metal grill, whilst the rest of the magnet assembly and body are inherently

robust anyway.

Condenser microphones

Condenser microphones work in a very different way. The capsule of a condenser microphone consists of a

thin conductive membrane held in front of a metal backplate (5) (11).

Fig 5. Basic construction of a condenser capsule

The membrane itself is typically made of Mylar (PET, a plastic), but this is coated in an extremely thin layer

of metal to make it conductive (11) (5) (2). Gold is typically chosen due to its very high conductivity. The typical

thickness of a condenser microphone membrane is only 6 microns (6x10-6 metres) (2) (4).

membrane backplate

terminals


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Fig 6. A typical large-diaphragm condenser microphone

Condenser microphones are based on the same principles as a parallel plate capacitor; hence they are also

often called capacitor microphones (2) (5). The membrane acts as one plate of the capacitor, and the

backplate as the other (5).

Fig 7. Capacitance (10)

Where:

is capacitance in farads (F)

is charge in coulombs (C)

is potential difference in volts (V)

According to the relationship in figure 7, if Q is kept constant then the capacitance will be proportional to

the voltage. The capacitance of the arrangement also varies according to the distance between the two

plates (as shown in figure 8).

Fig 8. Varying capacitance with distance (12) (2) (13)

Where:

is the permittivity of free space (taken to be 8.85x10-12 C2N-1m-2) (10) (14)

is the area of the two overlapping plates in metres (m)

is the distance between the two plates in metres (m)

By combining these two relationships, a formula can be derived that relates the voltage across the plates to

the distance between them (figure 9). If the charge on the plates, the area they overlap and the value of

remain constant, then the voltage is proportional to the distance.

Fig 9. Relationship linking voltage and distance between plates

During use, a polarising voltage is applied to charge the plates; a high-value resistor (ranging between

100MΩ to 10GΩ, depending on the microphone (2) (1) (15)) is then employed in the circuit to maintain as

constant charge on the plates as possible, regardless of any fluctuations in the voltage or capacitance

across them (2). The model for the discharge of a capacitor shows how this would work (figure 10).


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Fig 10. Exponential discharge of a capacitor (10)

Where:

is the charge in coulombs (C) after time t

is the initial charge in coulombs (C)

is time elapsed in seconds (s)

RC is the time constant of the circuit with the units of seconds (s)

The RC time constant is the product of resistance and capacitance and has units of seconds; a higher value

of RC will result in a much slower discharge. The time constant can also be defined as the time taken for the

charge to drop by ⁄ its initial value; similar in meaning to a half-life (16).

Using this, a constant charge is maintained by ensuring that the value of RC in the circuit is very high; as a

result, the rapidly varying capacitance (that reflects the changing distance between the plates), only has a

negligible effect on the value of Q as the ‘response’ is greatly slowed by the resistance in the circuit. Q can

be considered as constant, and so it is the voltage that is affected by the changing capacitance.

Therefore, when the diaphragm is caused to move by the fluctuations of air pressure, the voltage of the

circuit will change; a compression will cause the distance between the plates to decrease and the voltage to

increase, whilst a rarefaction will do the opposite and cause the voltage to decrease. Like with the dynamic

microphone, the motion of the diaphragm is represented by the varying output voltage.

Fig 11. A typical large-diaphragm capsule

The typical distance between diaphragm and backplate of a condenser microphone is only around 2x10-5m,

whilst the peak displacement of the diaphragm usually only represents a variation of about ±5% from this

rest position; a movement of around 1x10-6m (2). This, combined with the very thin membrane, means that

the capsule construction is very delicate compared to the robustness of dynamic microphones.

Dust, moisture or other deposits (such as tar from cigarette smoke) on the membrane can severely change

the characteristics of the microphone. Condensation on the membrane also affects its conductive

properties (2). The membrane is also difficult to clean without causing damage or adding to the deposits.

The much less massive diaphragms of condenser microphones give them a lot of advantages over their

moving-coil counterparts including increased sensitivity and faster transient response.

As mentioned previously, the transverse compression waves that form sound consist of waves of pressure

differences in air. When these pressure waves reach the diaphragm of a microphone, they exert a force on

it. As shown by the relationship in figure 12, if the area remains constant (which the area of the

microphone diaphragm does) then the force exerted will be proportional to the pressure.


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Fig 12. Pressure (17)

When the force from the pressure wave is exerted on the membrane, this will cause the membrane to

accelerate (from F=ma (18)). The magnitude of this acceleration is inversely proportional to the mass of the

membrane (see figure 13); a more massive diaphragm will have a slower acceleration for the same force as

a lighter diaphragm.

Fig 13. Acceleration due to force (18)

The upshot of this is that a heavier diaphragm will take longer to ‘respond’ to a sudden change in pressure.

Much of the distinctive sound of a musical instrument comes from the ‘attack’ of its notes; the initial sharp

peak that defines the sharp pluck of a string, the hit of a drum, etc.

These attack phases of sounds are often referred to as transients, and it is desirable for a signal chain to be

able to keep them ‘intact’; to capture and reproduce them as accurately as possible to retain the crisp,

defined nature of the original sound.

Fig 14. Response to impulse for condenser (top) and dynamic (bottom) (19)

Figure 14 shows the response of two different microphones to the same impulse; a brief, sharp sound that

is meant to be as close as having no length in the time domain as possible (an ideal impulse would be

impossible to produce in reality).

The microphone represented by the top plot, a condenser, responds faster and reaches its peak a lot earlier

than the dynamic microphone. It also returns to a resting state a lot sooner; in almost half the time to the

dynamic microphone.

Polar patterns

The most basic type of microphone acts as a pressure transducer – the diaphragm is only open at one side

and so it responds to pressure changes around the microphone equally regardless of their direction (4).

Rather than sealing the capsule completely, a small vent leading into the space between the membrane

and backplate ensures that changes in atmospheric pressure do not affect its operation (2). This kind of

microphone exhibits an omnidirectional pattern, as shown in figure 15.


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Fig 15. An omnidirectional polar pattern (20)

In reality some of the pickup from behind is blocked by the body of the microphone and the polar pattern

will not be linear across the whole all frequencies (2), but nevertheless this pickup pattern does not give the

strong and controllable directional characteristics that are often wanted in a microphone.

Directional microphones are instead based on the idea of a pressure-gradient transducer; the diaphragm

responds to the difference in pressure on either side (1) (5) (2). A basic pressure-gradient transducer has the

diaphragm open on both sides (usually achieved by drilling holes in the backplate) and exhibits a figure-8

polar pattern.

Fig 16. A figure-8 polar pattern (21)

By modifying this design, a microphone can be produced that only picks up from one side of the diaphragm.

This is achieved through means of some specially designed vents and ports leading into the space behind

the diaphragm, often termed an ‘acoustic labyrinth’. Vents can be seen on the back of the microphone

capsule shown in figure 19. These delay the sound arriving at the rear of the diaphragm, resulting in the

effects shown by figures 17 and 18 (2).

Fig 17. Sound arriving from the front of the microphone

diaphragm rear port


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For sounds arriving from the front of the microphone, the delayed signal reaching the rear of the

diaphragm has negligible effect on the sound. However for sound arriving from the rear, the delay

introduced by the vents is designed to match the extra time it takes for the sound to reach the front of the

diaphragm, so they arrive at both sides of the diaphragm at the same time; it can be thought of that,

because they have arrived in opposite directions, they will be complete out of phase and destructively

interfere so the sound will not be picked up (19) (22) (2).

Fig 18. Sound arriving from the rear of the microphone

More correctly, returning to the concept of such a microphone being a pressure-gradient transducer, the

pressure change arrives at both sides of the diaphragm at the same time, so the difference in pressure on

either side of the diaphragm – the net pressure - is zero; the same force is exerted on either side with no

resultant force, so the diaphragm does not move.

Fig 19. Vents visible at the back of a microphone capsule

The most common polar pattern created by this kind of design is the cardioid pattern (figure 20), which

strongly rejects sound from the rear but not from the front or sides, useful for live microphones that do not

pick up sound from the audience, loudspeakers or onstage monitors.

Fig 20. A cardioid polar pattern (23)

a delay is introduced for sound arriving from rear sound reaches front and rear of diaphragm

simultaneously, but in antiphase


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Other patterns can be created by varying this effect or combining it with pressure transducer principles (2).

One of these is the hypercardioid pattern (figure 21) which has a narrower pattern of pickup from the front

of the microphone, rejects more sound from the sides, but has a small ‘lobe’ of pickup at the rear.

Fig 21. A hypercardioid polar pattern (24)

Some microphones incorporate two independent diaphragms and some accompanying circuitry which

allows them be combined in a variety of configurations, enabling them to be switched between a number

of different polar patterns.

Frequency Response

The frequency response of a microphone relates to its input-output characteristics over a range of

frequencies (25); for example, if presented with a sound consisting of tones of equal amplitude at 300 Hz and

1000 Hz, a microphone may exhibit a much greater response to the lower tone (the tone would have

greater amplitude in the output signal (26)).

A linear frequency response is often considered to be desirable as its output most closely matches the

original sound; the sound can be reproduced far more accurately. In reality a ‘flat’ frequency response

(referring to the flat, horizontal line of a plot of such a response) is impossible to achieve, but many

expensive specialist microphones close to it (27).

Fig 22. Frequency response of the microphone in figure 6 (28)

In other cases, a non-linear frequency response might be wanted to accentuate different frequencies in the

tone of an instrument or voice (26), for example a microphone with peaks in its response between around

40-120 Hz, and again about 2-4 kHz, in order to ‘compliment’ and enhance the sound of a kick drum.

A dynamic microphone diaphragm with no damping usually has a strong fundamental resonance between

400 and 800 Hz and a poor response either side of this peak (22). Through the use of damping and resonant


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chambers (such as Helmholtz resonators to extend the low-end frequency response), a much more linear

frequency response can be achieved and tailored to meet specific design criteria (2).

Condenser microphones naturally have a much more linear frequency response; however there are still

many design factors that can have an effect on it – for example, diaphragm tension and size (2). The size of

the diaphragm is very important for a condenser microphone; the membrane is fixed at the edges and

allowed to oscillate in response to sound waves reaching it, in contrast to a dynamic microphone where the

whole diaphragm and coil moves together.

This means that the membrane follows a similar pattern of resonant modes to the skin of a drum, which

likewise is a membrane under tension. Resonances above the fundamental will result in parts of the

membrane moving closer to the backplate and other parts moving away, affecting the capacitance change

due to distance and thus the output signal (2). Some of these are shown in figure 23.

Fig 23. Some of the possible resonant modes of a circular membrane (29)

Therefore it is important to ensure that these resonant modes do not interfere with the operation of the

microphone. As the diameter of a circular membrane increases, the frequencies of its resonances decrease.

If it is too large, these resonances will be in the audible range, and audibly alter the response of the

microphone. Condenser diaphragm diameters are conventionally measured in inches with the most

prevalent sizes being 1” and ½“, though some ¼” and ¾” microphones are also reasonably common.

For this reason, condenser microphones with smaller membranes generally have a much more accurate

high-end frequency response and are chosen where high-frequency detail is paramount, usually when

recording cymbals or orchestral music (30); a rule of thumb is to choose a microphone with a diaphragm

diameter half the shortest wavelength you want to accurately transduce. The distortion introduced by

these resonances in larger diaphragms can, at times, be less obvious and even complimentary to the sound;

they are often chosen for vocal recordings where these characteristics may flatter or enhance the voice.

Conclusion

Because they are used outside the controlled conditions found in a recording studio, ruggedness is a

primary concern for live microphones. Regardless of the live application in question, microphones are often

handled or stored in unfavourable ways due to the hassles of live operations, unsupervised use, or simply

because the microphones are being hand-held on stage. Those investing money in the microphones will

want to know that they will withstand common trials such as being dropped.

In this sense, my research has led me to conclude that dynamic microphones may be better suited for live

use, though condenser microphones may also be used where their characteristics (such as superior

transient response or flatted frequency response) would be advantageous but they are less likely to be

damaged – when secured to stands for drum overheads, for example.

Directionality is an important characteristic for live use. If the signal from the microphone is being amplified

(reproduced by loudspeakers), it is possible for a feedback loop to be formed; the characteristic squeal

produced when the amplified signal from a microphone is in turn picked back up by the microphone and


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amplified further. By exploiting the directional characteristics of certain microphones such that they pick up

less sound from surrounding loudspeakers, the chances of such loops developing can be greatly reduced.

Sound engineers dealing with multiple musicians will also habitually use the directionality of microphones

to “isolate” specific sound sources so have more control over the amplification of individual instruments.

For these reasons, I can conclude that microphones with cardioid and hypercardioid pickup patterns are

preferable when selecting for live use (1) (2).

In summary, my research has led me to determine that a cardioid dynamic microphone would probably be

the most appropriate type of microphone for a lot of live situations. To finish, this may explain why the

Shure SM58 and SM57 – two very similar cardioid dynamic microphones – are amongst the best-selling

microphones ever and are often considered to be the ‘industry standard’ for live microphones (31) (32).

Bibliography

1. Microphone. Wikipedia. [Online] [Cited: 4 March 2010.] http://en.wikipedia.org/wiki/Microphone.

2. Eargle, John. The Microphone Book. s.l. : Focal Press, 2004.

3. Storr, Wayne. Electronics Tutorial about Sound Transducers. Electronics-Tutorials. [Online] [Cited: 11 March 2010.]

http://www.electronics-tutorials.ws/io/io_8.html.

4. Williamson, R. A Professional Condenser Microphone. [Online] July 1963. [Cited: 17 March 2010.]

http://www.conditionedresponse.com/DIY/microphones/Rwillmic.pdf.

5. Microphone Design and Operation. Wikibooks. [Online] [Cited: 15 March 2010.]

http://en.wikibooks.org/wiki/Engineering_Acoustics/Microphone_Design_and_Operation.

6. Fleming's right hand rule. Wikipedia. [Online] [Cited: 6 March 2010.] http://en.wikipedia.org/wiki/Fleming's_right_hand_rule.

7. Maxim88. File:RightHandOutline.png. Wikipedia. [Online] 26 July 2006. [Cited: 17 March 2010.]

http://en.wikipedia.org/wiki/File:RightHandOutline.png.

8. Duffy, Andrew. Applications of electromagnetic induction. Physics lecture demonstrations at Boston University. [Online] 22 July

1999. [Cited: 14 March 2010.] http://physics.bu.edu/~duffy/py106/Electricgenerators.html.

9. Faraday's law of induction. Wikipedi. [Online] [Cited: 16 March 2010.] http://en.wikipedia.org/wiki/Faraday's_law_of_induction.

10. OCR. Data, Formulae and Relationships Booklet. 2009.

11. White, Paul. Capacitor Microphones Explained. Sound On Sound. February 1998.

12. Colwell, Catharine H. Parallel Plate Capacitors. PhysicsLAB. [Online] [Cited: 12 March 2010.]

http://dev.physicslab.org/Document.aspx?doctype=3&filename=DCcircuits_CapacitorProperties.xml.

13. Vawter, Dr. Richard. Parallel-Plate Capacitors. PhysicsNet. [Online] [Cited: 9 March 2010.]

http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Capacitors/ParallCap.html.

14. Nave, Rod. Electric Field. HyperPhysics, Department of Physics and Astronomy, Georgia State University. [Online] [Cited: 12

March 2010.] http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html#c4.

15. Erland, Jakob. DIY Tube Microphone. [Online] 5 May 2009. [Cited: 29 March 2010.] http://www.gyraf.dk/gy_pd/g7/gic.htm.

16. Storr, Wayne. Electronics Tutorial about the RC Time Constant. Electronics-Tutorials. [Online] [Cited: 14 March 2010.]

http://www.electronics-tutorials.ws/rc/rc_1.html.


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17. Pressure. HyperPhysics, Department of Physics and Astronomy, Georgia State University. [Online] [Cited: 16 March 2010.]

http://hyperphysics.phy-astr.gsu.edu/hbase/press.html.

18. Newton's Second Law. HyperPhysics, Department of Physics and Astronomy, Georgia State University. [Online] [Cited: 17 March

2010.] http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html#fma.

19. Boudreau, John and Waller, Rick. Microphone Techniques for Music. [Online] 2009. [Cited: 14 March 2010.]

http://shure.com/stellent/groups/public/@gms_gmi_web_ug/documents/web_resource/us_pro_micsmusicstudio_ea.pdf.

20. Galak76. File:Polar pattern omnidirectional.png. Wikipedia. [Online] 25 April 2007. [Cited: 14 March 2010.]

http://en.wikipedia.org/wiki/File:Polar_pattern_omnidirectional.png.

21. —. File:Polar pattern figure eight.png. Wikipedia. [Online] 25 April 2007. [Cited: 14 February 2010.]

http://en.wikipedia.org/wiki/File:Polar_pattern_figure_eight.png.

22. Center for Audio Recording Arts, School of Music, Georgia State University. Microphone Transducer Types and Design.

Introduction To Audio Recording. [Online] 29 November 2004. [Cited: 5 March 2010.]

http://cara.gsu.edu/courses/MI_3110/mic1/1.htm.

23. Galak76. File:Polar pattern cardioid.png. Wikipedia. [Online] 25 April 2007. [Cited: 14 March 2010.]

http://en.wikipedia.org/wiki/File:Polar_pattern_cardioid.png.

24. —. File:Polar pattern hypercardioid.png. Wikipedia. [Online] 25 April 2007. [Cited: 14 March 2010.]

http://en.wikipedia.org/wiki/File:Polar_pattern_hypercardioid.png.

25. Frequency response. Wikipedia. [Online] [Cited: 11 April 2010.] http://en.wikipedia.org/wiki/Frequency_response.

26. The Importance of Microphone Frequency Response. [Online] 12 February 2010. [Cited: 4 April 2010.]

http://www.behindthemixer.com/content/importance-microphone-frequency-response.

27. Microphone Frequency Response. MediaCollege.com. [Online] [Cited: 4 April 2010.]

http://www.mediacollege.com/audio/microphones/frequency-response.html.

28. Rode NT1000 Studio Condenser Microphone. zZounds.com. [Online] [Cited: 31 March 2010.] http://www.zzounds.com/item--

RODNT1000.

29. Vibrational Modes of Drums. Sound-Physics.com. [Online] [Cited: 1 April 2010.] http://www.sound-physics.com/Drum-

Vibrational-Modes/.

30. Kadis, Jay. Microphones, Music 192a. Center for Computer Research in Music and Acoustics. [Online] 2007. [Cited: 15 March

2010.] https://ccrma.stanford.edu/courses/192a/2-Microphones.pdf.

31. Shure SM58. Wikipedia. [Online] [Cited: 10 April 2010.] http://en.wikipedia.org/wiki/Shure_SM58.

32. Shure Incorporated. The History of Shure Incorporated. [Online] [Cited: 14 April 2010.]

http://www.shure.com/Corporate/CompanyOverview/History/index.htm.

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A-level Physics Coursework - Microphones