Acoustics

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Part XVII: Pressure-gradient microphones

5.6. Electromagnetic ribbon microphones

General features

The ribbon microphone has approximately the same sensitivity and impedance as a moving-coil microphone when used with a suitable impedance-matching transformer. Because of its figure 8 directivity pattern, it used to be extensively used in broadcast and public-address applications to eliminate unwanted sounds that are situated in space, relative to the microphone, about 90 degrees from those sounds that are wanted but fell from favor because the delicate ribbon material was too prone to damage. However, because newer more rugged materials have emerged, the ribbon microphone has seen a significant revival of interest in recent years. This has also been helped by the reduction in size and weight made possible by the introduction of neodymium magnets. The ribbon microphone is often preferred by singers to introduce a “throaty” or “bassy” quality into their voices. Similarly, it produces a rich, full sound when placed close to amplified instruments. A disadvantage of the ribbon microphone is that, unless elaborate wind screening is resorted to, it is often very noisy when used outdoors.

Construction

A typical form of a pressure-gradient microphone is that represented by Fig. 5.27. It consists of a ribbon with a very low resonant frequency hung in a slot in a baffle. A magnetic field transverses the slot so that a movement of the ribbon causes a potential difference to appear across its ends. In this way, the moving conductor also serves as the diaphragm. In modern design, the ribbon element might be 38-mm long, 3.5-mm wide, and 4-μm thick with a clearance of 0.25 mm at each side.

From Eq. (5.11) we see that the pressure difference acting to move the diaphragm is

{\tilde{p}}_{R} = {\tilde{f}}_{R} / S = \tilde{u} ω ρ_{0} Δ l \cos θ,

${\tilde{p}}_{R} = {\tilde{f}}_{R} / S = \tilde{u} ω ρ_{0} Δ l \cos θ,$

(5.56)

where

${\tilde{f}}_{R}$ ${\tilde{f}}_{R}$ is the net force acting to move the ribbon.
$\tilde{u}$ $\tilde{u}$ is the particle velocity in the wave in the direction of propagation of the wave.
Figure 5.27 Sketch of the ribbon and magnetic structure for a velocity microphone type KSM313 ©2012, Shure Incorporated. The lead-out wires are soldered to metal blocks, and these blocks are clamped against the ribbon by the rectangular plates and the hex-shaped screws that thread into the steel frame.
Courtesy of Shure Incorporated.
S is the effective area of ribbon.
Δl is the effective distance between the two sides.
θ is the angle the normal to the ribbon makes with the direction of travel of the wave.

This equation is valid as long as the height of the baffle is less than approximately one-half of the wavelength.

Analogous circuit

The equivalent circuit (impedance analogy) for this type of microphone is shown in Fig. 5.28. There

{\tilde{p}}_{R}

${\tilde{p}}_{R}$

is the pressure difference that would exist between the two sides of the ribbon if it were held rigid and no air could leak around it; Z _AA is the acoustic impedance of the medium viewed from one side of the ribbon;

{\tilde{U}}_{R} = S {\tilde{u}}_{R}

${\tilde{U}}_{R} = S {\tilde{u}}_{R}$

is the volume velocity of the ribbon;

{\tilde{u}}_{R}

${\tilde{u}}_{R}$

is the linear velocity of the ribbon; M _AR, C _AR, and R _AR are the acoustic constants of the ribbon itself (for example, M _AR = M _MR/S ², where M _MR is the mass of the ribbon); M _AS and R _AS are the acoustic mass and resistance, respectively, of the slots at either edge of the ribbon; and

{\tilde{U}}_{S}

${\tilde{U}}_{S}$

is the volume velocity of movement of the air through the slot on the two sides of the ribbon.

Over nearly all the frequency range, the radiation impedance Z _AA is a pure mass reactance corresponding to an acoustic mass M _AA (see Eq. (4.172)). In a properly designed microphone,

{\tilde{U}}_{S} < < {\tilde{U}}_{R}

${\tilde{U}}_{S} < < {\tilde{U}}_{R}$

. Also, the microphone is operated above the resonance frequency so that ωM _AR >> 1/(ωC _AR). Usually, also, ωM _AR >> R _AR. Hence, the circuit of Fig. 5.28 simplifies into a single acoustic mass of magnitude 2M _AA + M _AR.

When the admittance analogy is used and the electrical circuit is considered, we get the complete circuit of Fig. 5.29. Here, M _MA = M _AA S ², M _MR = M _AR S ², B is flux density, l is length of the ribbon, and

{\tilde{f}}_{R} = {\tilde{p}}_{R} S

${\tilde{f}}_{R} = {\tilde{p}}_{R} S$

Figure 5.28 Analogous acoustical circuit for a ribbon microphone (impedance analogy).

Figure 5.29 Simplified electromechanical analogous circuit for a ribbon microphone (admittance analogy).

Performance

The open-circuit voltage

{\tilde{e}}_{0}

${\tilde{e}}_{0}$

of the microphone is found from solution of Fig. 5.29 to be

{\tilde{e}}_{0} = \frac{B l {\tilde{f}}_{R}}{j ω (2 M_{M A} + M_{M R})} .

${\tilde{e}}_{0} = \frac{B l {\tilde{f}}_{R}}{j ω (2 M_{M A} + M_{M R})} .$

(5.57)

Substitution of Eq. (5.56) in Eq. (5.57) yields

| {\tilde{e}}_{0} | = | \tilde{u} | \frac{(B l) ρ_{0} Δ l}{2 M_{M A} + M_{M R}} S \cos θ .

$| {\tilde{e}}_{0} | = | \tilde{u} | \frac{(B l) ρ_{0} Δ l}{2 M_{M A} + M_{M R}} S \cos θ .$

(5.58)

The open-circuit voltage is directly proportional to the component of the particle velocity perpendicular to the plane of the ribbon. In a well-designed ribbon microphone, this relation holds true over the frequency range from 50 to 10,000 Hz. The lower resonance frequency is usually about 15–25 Hz. The effects of diffraction begin at frequencies of about 2000 Hz but are counterbalanced by appropriate shaping of the magnetic pole pieces.

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