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, other say that this is a myth and these numbers are commercial purposes. Lets try mathematically find a proof and see real situation.
Introduction to long range microphones
When talking about directed microphones usually we have in mind that sound sources are in open air, and there is no reverberation effects. So the only factor is distance of sound source object from microphone. Along the distance sound power drops significantly and ir longer ranges it interfere with other sounds like wind and other noises in atmosphere.
So when distance is about 100m sound pressure drops more than 40dB(comparing to distance equal to 1m). So if sound level is 60dB then from 100m you will hear 20dB. Sound level 20dB is less than other environmental noise and many common 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 highe level than real sound;
High directivity in order to able exclude noise signals that are higher than useful sound signal. Directivity means ability to attenuate noise signals, that come from other directions than sound source object.
Practically speaking to comply these requirements with one microphone is quite difficult task. There were other solutions like creation of low directive microphones with high sensitivity or highly directive microphones with low sensitivity. This is why there are several constructions of directional microphones.
Types directional microphones
There are four general types of direction microphones:
Flat with Phase grid;
Microphones with running wave;
Parabolic microphones have parabolic shape that reflects incoming sound waves to one focal point where microphone is located. This is one of most known and commonly used directional microphones
Diameter of parabolic mirror may reach from 200 to 500mm. Working principal is simple â€“ sound waves incoming along direction axis are reflected towards microphone in parabola focal point. At this point sound level â€œamplifiesâ€ because of sounds added with same phase. So the bigger diameter of mirror is the bigger amplification may be reached. Other sounds coming from different angles aren’t amplified much by this effect because of different phases of each reflections in focal point. Parabolic microphone has high sensitivity, but directivity isn’t very high.
Flat directed microphones
Flat directed microphones are based on idea of receiving sound from multiple points located in one plain surface which is perpendicular to incoming sound.
The picture above isn’t exact drawing of such microphone, but it gives an idea how does it look like. Where wave guide holes are there can also be microphones located where signals can be summed electrically or waveguides where sound-waves are summed at one point and then converted to electrical signal. Mechanical or electrical signals have to be same phase. If all sound signals entering waveguides are unidirectional then they will have same phase and summing will give maximal result. If sound direction isn’t perpendicular then it will have different phases in each hole and summing will weaken them. The bigger angle the lower 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 perpendiculary but along wave direction.
Main part of this microphone is a waveguide pipe with diameter 10 â€“ 30mm with special cells located over all length of pipe. It is obvious that that sound incoming into each hole will be added with same phase. If sound is incoming with different angle then the phase in each hole will differ because of different sound speed inside pipe would result in loosing its power.
Pipe length usually is from 15 – 230mm to 1m. The longer waveguide is the bigger sensitivity of microphone.
Gradient microphones are different from phased receivers, where same phase signals are added to get more sensitivity. Gradient microphones are based on calculation by direction. But this method is limited by sensitivity of discrete microphones. Calculation of signals also weakens signal but summing noises. But main advantage is that this method allows constructing small sized directional microphones. Simplest gradient microphone is so called first order microphone:
This construction consist 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 angle of 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 directional microphones
Directional microphones can be compared by working distance by common conditions. For 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 formula:
Where Q- wave angle, φ– angle in polar coordinates.
L – length of waveguide, l – sound wave length. When L=l then for Running wave microphone:
For Flat microphone:
where S – aperture area, l- sound wave length.
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 result in 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 – distance of hearing sound with human ear, R- distance with 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 distance is about 3 times bigger than ear. Practically speaking if we compare human ear and directional microphone in city (noisy area) then values would be like human ear can hear human speech at distance about 2- 4m and directional microphone can from about 6 – 12m. Outside city where noise level is low, 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 threshold may reach -15dB. Sensitivity can also be increased by increasing size of antenna.
As we mentioned at the beginning calculation shows that reaching 100 or 200 distance with directional microphones is quite difficult task. Normally there are directional microphones in market that can effectively register human speech (76dB) at distances about 50m.