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8.2 - DIRECTIVITY

8.2.3 - UNI-DIRECTIONAL: HYPOCARDIOID, CARDIOID, SUPERCARDIOID and HYPERCARDIOID

In between the omnidirectional and the bi-directional directivities lie the whole range of unidirectional microphone designs. Two design techniques may be used to produce a unidirectional directivity response:

An acoustic labyrinth in the path of the sound wave to the back of the diaphragm

The combined electrical response of two capsules (omni & bi, or two back to back cardioids)

Acoustic labyrinth design - In general most of the present day small diaphragm unidirectional microphones (hypocardioids, cardioid, supercardioid and hypercardioids) rely on the sound reaching the back of the diaphragm via some form of acoustic labyrinth - the different delay values introduced by this acoustic labyrinth will produce specific directivity patterns. Figure 43 shows a moving coil microphone capsule where a simple labyrinth path has been created so as to produce pressure-gradient acoustic coupling and unidirectional response.

Figure 43 – Moving Coil Microphone - Equivalent Path Length Difference
at Various Angles of Incidence

In Figure 43 the path lengths are approximately equivalent for sound coming from 135°. Equivalent path length difference is maximum at 0°, smaller at 90° and 180° and zero at 135°. As with the bi-directional microphone, the back lobe of this hypercardioid capsule will be opposite in polarity with respect to the front lobe.

The design of a condenser pressure-gradient capsule is perhaps even more simple – at least as a theoretical exercise! As shown in Figure 44 the length of the labyrinth can be adjusted to accommodate any desired directivity pattern from hypocardioid through cardioid to hypercardioid. The exact labyrinth design will depend on the desired extinction angle (as in the previous figure for a moving coil pressure-gradient capsule).


Figure 44 – Electrostatic Microphone - Design of Path Length Difference

The basic problem with this labyrinth approach to directivity as shown in Figure 44, is that the delay is inevitably frequency dependent - it is impossible to design an acoustic labyrinth system which produces the same delay throughout the whole of the audible spectrum. The result in the bass frequencies, is that there is a tendency for the directivity to become either omnidirectional or sometimes bi-directional (as in Figure 53 in section 8.2.6), whereas in the high frequencies range the directivity usually tends towards hypocardioid. Despite this fundamental limitation, the fact that the majority of professional-high quality-small diaphragm-unidirectional-condenser microphones use this technique, is proof of the effort that has gone into optimising microphone labyrinth design.

COMBINED ELECTRICAL RESPONSE OF TWO CAPSULES
Multiple directivity capsule design has produced some remarkable microphone designs over the years:

• The combination of an omnidirectional and bi-directional through a switchable matrix has been a design technique since the 1940s
• Back to back cardioids again through a switchable matrixing circuit has become more feasible with the present day trend towards miniaturization of microphone capsules
• Combining two diaphragms into one double diaphragm capsule is a solution that has been used for many years - the Neumann series U47, U67, U87/9 up to the present day digital D01 being one of the well known illustrations of this approach
• Mechanical labyrinth ‘switching’ has also been tried as a multiple directivity capsule design

However it must be said that some microphones using this combined capsule approach, have probably found favour with sound engineers, more as a result of the deviations from standard directivity and the characteristic sound that this produces, rather than the regularity of the standard directivity response. Indeed recent developments in design seem to suggest that different directivity patterns in different parts of the spectrum can have a considerable influence on our perception of timbre of the sound source. A patent by the company Schoeps - PolarFlex TM - has highlighted a design that allows the user to adjust the directivity pattern independently in the low, medium and high frequency ranges, thereby tailoring the directivity pattern to our perception of timbre in a specific sound recording situation.

Double diaphragm pressure-gradient microphones also behave rather differently to single diaphragm pressure-gradient microphones in proximity conditions, even when they have the same nominal directivity pattern^[8][9] - in some circumstances this could be the reason for user preference for this type of design. The matrixing of capsule directivities can be shown in two ways, one using the mathematical model for directivity as described later in this section, the other by a graphical representation as shown in Figure 45 and in Tables D & E .

In the graphical approach it is important to remember that an omnidirectional microphone will give the same positive nominal polarity no matter which the direction of the sound source. On the other hand a bi-directional microphone will give a positive nominal polarity in the front hemisphere, and a negative polarity in the back hemisphere.
Figure 45 – 0.5 * Omni + 0.5 * Bi = Cardioid

Simple addition of the amplitude of the omnidirectional and the bi-directional response will produce the cardioid directivity diagram as shown in Table D. Remember that the response at 180° with the ‘omni’ is positive, whereas the response of the back lobe of the ‘bi’ is negative, so the combined response is zero. Table D shows a graphical representation of the addition in different proportions (matrixing) of omnidirectional and bi-directional directivities.


Simple addition of polar patterns produced graphically must be with a linear response scale – the maximum response (on-axis) is ‘1’, the minimum response is ‘0’ in the centre - intermediate values at specific angles represent the ratio of the microphone response at that specific angle to the response on-axis . The last column in Table D shows each directivity pattern drawn with a logarithmic scale – from 0db to –25dB in the centre. The simple solution when the matrix is switched to 100% ‘omni’ or 100% ‘bi’ is not shown.

The same graphical addition method may be applied to derive the directivity patterns from two ‘back to back’ cardioids as shown in Table E.


The negative sign in the equation signifies that the polarity of the back cardioid is negative, or in other words the back cardioid is subtracted from the Front Cardioid in order to obtain Supercardioid, Hypercardioid and Bi-directional directivity patterns. This is a simple graphical way to derive the various directivity patterns. In the next section the same process is used but with the help of a simple mathematical model that represent the two constituent directivity patterns – omnidirectional and bi-directional.

[8] 1998 - "Understanding the Transfer Functions of Directional Condenser Microphones in Response to Different Sound Sources" by Guy Torio, Shure Inc. USA. 105th AES Convention, Los Angeles USA - Preprint 4800

[9] 2000 – "Unique Directional Properties of Dual-Diaphragm Microphones" by Guy Torio and Jeff Segota, Shure Inc, USA, 109th AES Convention, Los Angeles – Preprint 5179