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8.2 - DIRECTIVITY

8.2.1 - OMNIDIRECTIONAL DIRECTIVITY RESPONSE

The basic directivity pattern of a pressure microphone is omnidirectional, at least whilst the diameter of the diaphragm and body of the microphone are less than half the wavelength. At frequencies where the diaphragm diameter is greater than the half wavelength, two acoustic phenomena come into play, one when the sound wave arrives on the side of the diaphragm, we have a reduction in response due to pressure-summing across the diaphragm, the other is when the sound wave comes from behind the microphone, the response is reduced due to diffraction - the body of the microphone causing a shadow effect similar to the shadow behind the pole-pieces of a ribbon microphone as shown in section 4.2 (Pressure-gradient Acoustic Coupling) – No pressure-summing is perceptible at 90° to the directivity axis of the microphone, at frequencies where the half wavelength is greater than the diameter of the diaphragm, as shown in Figure 36.


Figure 36 - diameter of the diaphragm is smaller than the half wavelength

This does not mean that a reduction in level will not be measurable below the half- wavelength point, but simply that our perception of this attenuation is considerably more tolerant than the usual measurement of frequency response would seem to suggest – simply because our perception tends to integrate the response over a band of frequencies of about an octave. Added to this we will only be conscious of a change in response when the attenuation has reached a certain threshold value, which is around 2dB or 3dB overall attenuation in this octave band of frequencies. A reduction in level, due to summing of pressure across the diaphragm surface, begins to be perceptible, with respect to the on-axis response, when the half-wavelength is equal to the diaphragm diameter. In the example shown in Figure 37, the diaphragm is constrained to a piston-like movement by the rigidity of the voice coil and by the surrounding corrugations – the diaphragm will only be put into motion by the average pressure value over the surface of the diaphragm. Strictly speaking, pressure at the periphery of the diaphragm will have somewhat less effect than in the centre area - so the summation function is rather more complex.


Figure 37 - diameter of diaphragm is equal to the half wavelength

Considerably more reduction of level occurs at frequencies where the wavelength is much smaller than the microphone diameter, as shown in Figure 38.


Figure 38 - – Diameter of diaphragm is much greater than the half wavelength
This reduction in response is also a function of the angle of incidence of the sound wave as shown in Figure 39. In this example, at 20° there is no noticeable reduction in level, at 40° the reduction is just noticeable, and at 60° the reduction is very much in evidence.


Figure 39 - – Sound Wave a 20°, 40° & 60° to the microphone diaphragm
The same reasoning applies to the dimensions of a condenser pressure capsule or indeed any microphone capsule system using a diaphragm to pickup the acoustic signal. If we take as an example a quarter inch (6.35mm) condenser microphone capsule, there will be a marked level reduction due to pressure–summing at 90° from about 26.8kHz upwards – well outside the audible range.

λ / 2 = 6.35mm    λ *  f = 340m/s     f = 340 / (2 * 0.00635 ) = 26.77kHz

λ / 2 = 12.7mm (½ inch) pressure summing from 13.4kHz
λ / 2 = 15mm pressure summing from 11kHz
λ / 2 = 19mm (¾ inch) pressure summing from 9kHz
λ / 2 = 25.4mm (1 inch) pressure summing from 6.8kHz

These are the approximate frequency values where pressure summing begins to be noticeable (about 3dB to 5dB down on the frequency response curve).

These same values apply with respect to the shadow effect for sound waves coming from behind the microphone – a shadow zone will cause a noticeable drop in response when the body-diameter of the microphone is again near the half-wavelength value. In the tubular microphone construction the body diameter is perforce slightly larger than the diaphragm diameter, however the drop in response is sufficiently similar to the pressure-summing effect, for the two effects to be perceived as one and the same. But in fact as the angle of incidence of the sound wave changes from 90° to 180°, the reduction in level due to pressure-summing diminishes, whereas the reduction in level due to the shadow effect becomes dominant.

It is therefore only possible to maintain an omnidirectional directivity pattern throughout the whole of the audible frequency range with a diaphragm size of below 10mm - the body of the microphone must also be as near as possible this diameter in order to keep the shadow effect above the limit of the audible frequency range. In practice, most high quality studio condenser microphones of this type have a diaphragm diameter of about 12mm to 15mm, and a cylindrical body diameter of at least 20mm, with the result that some attenuation in the high frequencies is inevitable off-axis. When microphones are used at some distance from the sound source (more or less in the reverberant field), this frequency roll-off at high frequencies can give the impression of a general high frequency loss. It is common practice in this case to give some high frequency emphasis, so that the overall energy frequency response curve is flat – this is equivalent to saying that the Directivity Factor for an omnidirectional microphone will remain at ‘1’ for the whole frequency range, as shown in Figure 40.


Figure 40 - comparison between flat on-axis response (Schoeps MK2)
and high frequency emphasis producing overall flat energy response (Schoeps MK3)
© frequency response curves published by courtesy of Schoeps
The pressure-summing and acoustic shadow effects are not confined only to omnidirectional microphones, pressure-gradient directional microphones suffer from the same basic phenomena. However with careful design it is possible to integrate the drop in level at the higher frequencies on the side and back of the microphone, into the overall directivity response, so that the effect becomes much less noticeable. Figure 41 shows just such a design where the difference between the theoretical cardioid response (shown as dashed lines) and the measured directivity pattern is minimal, at least up to about 100° from the axis of the directivity pattern.

Figure 41 - comparison between measured directivity pattern
and the theoretical directivity for a cardioid microphone
(diameter of diaphragm Φ = 12mm,
diameter of microphone body Φ = 20mm)

These measurements have been made using a white noise source signal filtered into octave bands, each octave being centred on the frequency shown in each diagram. This measurement technique has been used so as to obtain a polar diagram tracing as near as possible to our perception of directivity in operational conditions.