There are a lot of myths about directed long-range microphones. You can here like they can reach distances of 100, 200 and more meters, others say that this is a myth and these numbers are commercial purposes. Let us try mathematically find proof and see the real situation.
Introduction to long-range microphones
When talking about directed microphones, usually we have in mind that sound sources are in the open air, and there are no reverberation effects. So the only factor is the distance of the sound source object from the microphone. Along the distance, sound power drops significantly, and in longer ranges, it interferes with other sounds like wind and other noises in the atmosphere.
When the distance is about 100m sound pressure drops more than 40dB(comparing to a distance equal to 1m). If the sound level is 60dB then from 100m, you will hear 20dB. Sound level 20dB is less than other environmental noise, and many standard microphones are not sensitive enough for such sound level.
So we can say that directed microphones must have:
High sensitivity and selectivity from environment noises even if they have a higher level than real sound;
High directivity to for excluding noise signals that are higher than useful sound signal. Directivity means the ability to attenuate noise signals, that come from other directions than sound source object.
Practically speaking to comply with these requirements with one microphone is quite a difficult task. There were other solutions like the creation of low directive microphones with high sensitivity or highly directive microphones with low sensitivity. There are several constructions of directional microphones that help to solve different technical limitations.
Types of long-range directional microphones
There are four general types of directional microphones:
Flat with Phase grid;
Microphones with a running wave;
Parabolic directional microphones
Parabolic microphones have a parabolic shape that reflects incoming sound waves to one focal point where the microphone is located. The construction is one of the most known and commonly used directional microphones
The diameter of the parabolic mirror may reach from 200 to 500mm. The working principle is simple – sound waves incoming along direction axis are reflected towards the microphone in parabola focal point. At this point, sound level amplifies because of sound waves added with the same phase.
The bigger diameter of the mirror is the more significant amplification may be reached. Different sounds coming from different angles aren’t amplified much by this effect because of various phases of each reflection in the focal point. The parabolic microphone has high sensitivity, but the directivity isn’t very high.
Flat directed microphones with phase grid
Flat directed microphones are based on the idea of receiving sound from multiple points located in one plain surface, which is perpendicular to the incoming audio source.
The picture above isn’t an exact drawing of such a microphone, but it gives an idea of how it looks. Instead of waveguide holes are there can be microphones located. Signals can be summed electrically or waveguides where sound-waves are summed at one point and then converted to the electrical signal. Mechanical or electrical signals have to be in the same phase. If all sound signals entering waveguides are unidirectional, then they will have the same phase and summing them will give a maximal result. If sound direction isn’t perpendicular then it will have different phases in each hole and summing will weaken them. The more significant angle, the lower the noise level. One good advantage of flat microphones comparing to parabolic is that they are easier to hide because the flat surface can be a suitcase or even a wall.
Microphones with running wave
Microphones with running wave or so-called pipe microphones are different because it receives sound not perpendicularly but along wave direction.
The central part of this microphone is a waveguide pipe with diameter 10mm to 30mm with individual cells located along the pipeline. The sound incoming into each hole will be added with the same phase. If the sound is incoming with a different angle, then the phase in each hole will differ because of varying sound speed inside the pipe would result in losing its power.
Pipe length usually is from 15cm to 1m. The longer waveguide is the more significant sensitivity of the microphone.
Gradient directional Microphones
Gradient microphones are different from phased receivers, where same phase signals are added to get more sensitivity. Gradient microphones are based on a calculation by direction. But this method is limited by the sensitivity of discrete microphones. Estimation of signals also weakens signal but summing noises. But the main advantage is that this method allows constructing small sized directional microphones. Most straightforward gradient microphone is so-called first-order microphone:
This construction consists of two high sensitivity microphones near each other. Output signals of both microphones are subtracted from each other. And finally, the diagram cos(Q) is calculated where Q is the angle of the incoming wave. By this diagram, sounds can be filtered for one direction. Usually, there are 2nd and 3rd, and higher order gradient microphones with better characteristics.
Comparing long-range directional microphones
Directional microphones can be compared by working distance by common conditions. For an open area with independent noise direction working distance R is related with:
spectral SNR in the output of microphone (q);
spectral speech level (Ss);
spectral acoustic noise level (Sn);
where G – direction coefficient of microphone(dB), Sp – microphone sensitivity threshold(dB).
Coefficient G can be calculated by the formula:
Where Q- wave angle, φ– angle in polar coordinates.
L – length of the waveguide, l – sound wavelength. When L=l then for Running wave microphone:
For Flat microphone:
where S – aperture area, l- sound wavelength.
For gradient microphone:
n- order of microphone.
When G is known, then it is enough for calculating SNR value. But in most cases, this may end up with wrong results. This is why it is better to calculate relative non-absolute values of distance. Using this ideology, microphones can be compared with human ear. Then we can write:
R=R0 · 10 · 0.05·(G-G0)-0.005 · ΔSp;
Where R0 – a distance of hearing sound with the human ear, R- distance with a directional microphone, G0 – ear directional coefficient. ΔSp – sensitivity difference between ear and microphone.
In the diagram, we can see that when G=15dB(value for good microphone) then the distance is about three times bigger than the ear. Practically speaking if we compare human ear and directional microphone in the city (noisy area) then values would be like human ear can hear human speech at a distance about 2- 4m and directional microphone can from about 6 – 12m. Outside city where the noise level is low, the ear can hear at distance 10m while directional microphone from more than 30m.
Of course, there are more advanced methods like digital multichannel filtering and using high sensitivity sensors where the threshold may reach -15dB. Sensitivity can also be increased by increasing the size of antenna.
As we mentioned at the beginning calculation shows that reaching 100 or 200m distance with directional microphones is quite a difficult task. Typically there are directional microphones in the market that can effectively register human speech (76dB) at distances close to 50m.
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