## Directional Responses and Polar Diagrams of Microphones

By    Categories:

Microphones are designed to have a specific directional response pattern, described by a so-called ‘polar diagram’. The polar diagram is a form of two-dimensional contour map, showing the magnitude of the microphone’s output at different angles of incidence of a sound wave. The distance of the polar plot from the center of the graph (considered as the position of the microphone diaphragm) is usually calibrated in decibels, with a nominal 0 dB being marked for the response at zero degrees at 1 kHz. The further the plot is from the center, the greater the output of the microphone at that angle.

Omnidirectional pattern

Ideally, an omnidirectional or ‘omni’ microphone picks up sound equally from all directions. The omni polar response is shown in Figure 3.1 , and is achieved by leaving the microphone diaphragm open at the front, but completely enclosing it at the rear, so that it becomes a simple pressure transducer, responding only to the change of air pressure caused by the sound waves. This works extremely well at low and mid frequencies, but at high frequencies the dimensions of the microphone capsule itself begin to be comparable with the wavelength of the sound waves, and a shadowing effect causes high frequencies to be picked up rather less well to the rear and sides of the mic. A pressure increase also results for high-frequency sounds from the front. Coupled with this is the possibility for cancelations to arise when a high-frequency wave, whose wavelength is comparable with the diaphragm diameter, is incident from the side of the diaphragm. In such a case positive and negative peaks of the wave may result in opposing forces on the diaphragm.

FIGURE 3.1 Idealized polar diagram of an omnidirectional microphone.

Figure 3.2 shows the polar response plot which can be expected from a real omnidirectional microphone with a capsule half an inch (13 mm) in diameter. It is perfectly omnidirectional up to around 2 kHz, but then it begins to lose sensitivity at the rear; at 3 kHz its sensitivity at 180° will typically be 6 dB down compared with lower frequencies. Above 8 kHz, the 180° response could be as much as 15 dB down, and the response at 90° and 270° could show perhaps a 10 dB loss. As a consequence, sounds which are being picked up significantly off axis from the microphone will be reproduced with considerable treble loss, and will sound dull. It is at its best on axis and up to 45° either side of the front of the microphone.

FIGURE 3.2 Typical polar diagram of an omnidirectional microphone at a number of frequencies.

High-quality omnidirectional microphones are characterized by their wide, smooth frequency response extending both to the lowest bass frequencies and the high treble with minimum resonances or coloration. This is due to the fact that they are basically very simple in design, being just a capsule which is open at the front and completely enclosed at the rear. (In fact a very small opening is provided to the rear of the diaphragm in order to compensate for overall changes in atmospheric pressure which would otherwise distort the diaphragm.) The small tie-clip microphones which one sees in television work are usually omnidirectional electret types which are capable of very good performance. The smaller the dimensions of the mic, the better the polar response at high frequencies, and mics such as these have quarter-inch diaphragms which maintain a very good omnidirectional response right up to 10 kHz.

Omni microphones are usually the most immune to handling and wind noise of all the polar patterns, since they are only sensitive to absolute sound pressure. Patterns such as figure-eight (especially ribbons) and cardioid, described below, are much more susceptible to handling and wind noise than omnis because they are sensitive to the large pressure difference created across the capsule by low-frequency movements such as those caused by wind or unwanted diaphragm motion. A pressure-gradient microphone’s mechanical impedance (the diaphragm’s resistance to motion) is always lower at LF than that of a pressure (omni) microphone, and thus it is more susceptible to unwanted LF disturbances.

Figure-eight or bidirectional pattern

The figure-eight or bidirectional polar response is shown in Figure 3.3 . Such a microphone has an output proportional to the mathematical cosine of the angle of incidence. One can quickly draw a fi gure-eight plot on a piece of graph paper, using a protractor and a set of cosine tables or pocket calculator. Cos 0° = 1, showing a maximum response on the forward axis (this will be termed the 0 dB reference point). Cos 90° = 0, so at 90° off axis no sound is picked up. Cos 180° is −1, so the output produced by a sound which is picked up by the rear lobe of the microphone will be 180° out of phase compared with an identical sound picked up by the front lobe. The phase is indicated by the + and – signs on the polar diagram. At 45° off axis, the output of the microphone is 3 dB down (cos 45° represents 0.707 or 1/√2 times the maximum output) compared with the onaxis output.

FIGURE 3.3 Idealized polar diagram of a fi gure-eight microphone.

Traditionally the ribbon microphone has sported a figure-eight polar response, and the ribbon has been left completely open both to the front and to the rear. Such a diaphragm operates on the pressure- gradient principle, responding to the difference in pressure between the front and the rear of the microphone. Consider a sound reaching the mic from a direction 90° off axis to it. The sound pressure will be of equal magnitude on both sides of the diaphragm and so no movement will take place, giving no output. When a sound arrives from the 0° direction a phase difference arises between the front and rear of the ribbon, due to the small additional distance traveled by the wave. The resulting difference in pressure produces movement of the diaphragm and an output results.

At very low frequencies, wavelengths are very long and therefore the phase difference between front and rear of the mic is very small, causing a gradual reduction in output as the frequency gets lower. In ribbon microphones this is compensated for by putting the low-frequency resonance of the ribbon to good use, using it to prop up the bass response. Single-diaphragm capacitor mic designs which have a figure-eight polar response do not have this option, since the diaphragm resonance is at a very high frequency, and a gradual roll-off in the bass can be expected unless other means such as electronic frequency correction in the microphone design have been employed. Double-diaphragm switchable types which have a figure- eight capability achieve this by combining a pair of back-to-back cardioids (see next section) that are mutually out of phase.

Like the omni, the figure-eight can give very clear uncolored reproduction. The polar response tends to be very uniform at all frequencies, except for a slight narrowing above 10 kHz or so, but it is worth noting that a ribbon mic has a rather better polar response at high frequencies in the horizontal plane than in the vertical plane, due to the fact that the ribbon is long and thin. A high-frequency sound coming from a direction somewhat above the plane of the microphone will suffer partial cancelation, since at frequencies where the wavelength begins to be comparable with the length of the ribbon the wave arrives partially out of phase at the lower portion compared with the upper portion, therefore reducing the effective acoustical drive of the ribbon compared with mid frequencies. Ribbon figure-eight microphones should therefore be orientated either upright or upside-down with their stems vertical so as to obtain the best polar response in the horizontal plane, vertical polar response usually being less important.

Although the figure-eight picks up sound equally to the front and to the rear, it must be remembered that the rear pickup is out of phase with the front, and so correct orientation of the mic is required.

Cardioid or unidirectional pattern

The cardioid pattern is described mathematically as 1 + cos θ, where θ is the angle of incidence of the sound. Since the omni has a response of 1 (equal all round) and the figure-eight has a response represented by cos θ, the cardioid may be considered theoretically as a product of these two responses. Figure 3.4a illustrates its shape. Figure 3.4b shows an omni and a figure-eight superimposed, and one can see that adding the two produces the cardioid shape: at 0°, both polar responses are of equal amplitude and phase, and so they reinforce each other, giving a total output which is actually twice that of either separately. At 180°, however, the two are of equal amplitude but opposite phase, and so complete cancelation occurs and there is no output. At 90° there is no output from the figure-eight, but just the contribution from the omni, so the cardioid response is 6 dB down at 90°. It is 3 dB down at 65° off axis.

FIGURE 3.4 (a) Idealized polar diagram of a cardioid microphone. (b) A cardioid microphone can be seen to be the mathematical equivalent of an omni and a fi gure-eight response added together.

One or two early microphone designs actually housed a figure-eight and an omni together in the same casing, electrically combining their outputs to give a resulting cardioid response. This gave a rather bulky mic, and also the two diaphragms could not be placed close enough together to produce a good cardioid response at higher frequencies due to the fact that at these frequencies the wavelength of sound became comparable with the distance between the diaphragms. The designs did, however, obtain a cardioid from first principles. The BBC type 4033 was one such example.

The cardioid response is now obtained by leaving the diaphragm open at the front, but introducing various acoustic labyrinths at the rear which cause sound to reach the back of the diaphragm in various combinations of phase and amplitude to produce a resultant cardioid response. This is difficult to achieve at all frequencies simultaneously, and Figure 3.5 illustrates the polar pattern of a typical cardioid mic with a three-quarter-inch diaphragm. As can be seen, at mid frequencies the polar response is very good. At low frequencies it tends to degenerate towards omni, and at very high frequencies it becomes rather more directional than is desirable. Sound arriving from, say, 45° off axis will be reproduced with treble loss, and sounds arriving from the rear will not be completely attenuated, the low frequencies being picked up quite uniformly.

FIGURE 3.5 Typical polar diagram of a cardioid microphone at low, middle and high frequencies.

The above example is very typical of moving-coil cardioids, and they are in fact very useful for vocalists due to the narrow pickup at high frequencies helping to exclude off-axis sounds, and also the relative lack of pressure- gradient component at the bass end helping to combat bass tip-up. High-quality capacitor cardioids with half-inch diaphragms achieve a rather more ideal cardioid response. Owing to the presence of acoustic labyrinths, coloration of the sound is rather more likely, and it is not unusual to find that a relatively cheap electretomni will sound better than a fairly expensive cardioid.

Hypercardioid pattern

The hypercardioid, sometimes called ‘cottage loaf ’ because of its shape, is shown in Figure 3.6 . It is described mathematically by the formula 0.5 + cos θ, i.e. it is a combination of an omni attenuated by 6 dB, and a fi gureeight. Its response is in between the cardioid and fi gure-eight patterns, having a relatively small rear lobe which is out of phase with the front lobe. Its sensitivity is 3 dB down at 55° off axis. Like the cardioid, the polar response is obtained by introducing acoustic labyrinths to the rear of the diaphragm. Because of the large pressuregradient component it too is fairly susceptible to bass tip-up. Practical examples of hypercardioid microphones tend to have polar responses which are tolerably close to the ideal. The hypercardioid has the highest direct-to-reverberant ratio of the patterns described, which means that the ratio between the level of on-axis sound and the level of reflected sounds picked up from other angles is very high, and so it is good for excluding unwanted sounds such as excessive room ambience or unwanted noise.

FIGURE 3.6 Idealized polar diagram of a hypercardioid microphone.

Excerpt from Sound and Recording: Applications and Theory, 7th Edition by Francis Rumsey and Tim McCormick © 2014 Taylor & Francis Group. All Rights Reserved.

*