Very low frequencyorVLFis theITUdesignation[1]forradio frequencies(RF) in the range of 3–30kHz,corresponding towavelengthsfrom 100 to 10 km, respectively. The band is also known as themyriameter bandormyriameter waveas the wavelengths range from one to tenmyriameters(an obsolete metric unit equal to 10 kilometers). Due to its limitedbandwidth,audio(voice) transmission is highly impractical in this band, and therefore only lowdata ratecoded signals are used. The VLF band is used for a fewradio navigationservices, governmenttime radio stations(broadcasting time signals to setradio clocks) and for secure military communication. Since VLF waves can penetrate at least 40 meters (131 ft) into saltwater, they are used formilitary communicationwithsubmarines.
Frequency range | 3–30kHz |
---|---|
Wavelength range | 100-10 km |
Propagation characteristics
editBecause of their long wavelengths, VLF radio waves candiffractaround large obstacles and so are not blocked by mountain ranges, and can propagate asground wavesfollowing the curvature of the Earth and so are not limited by the horizon. Ground waves are absorbed by the resistance of the Earth and are less important beyond several hundred to a thousand kilometres/miles, and the main mode of long-distance propagation is anEarth-ionosphere waveguidemechanism.[2]The Earth is surrounded by a conductive layer ofelectronsandionsin the upper atmosphere at the bottom of theionospherecalled theD layerat 60–90 km (37–56 miles) altitude,[3]which reflects VLF radio waves. The conductive ionosphere and the conductive Earth form a horizontal "duct" a few VLF wavelengths high, which acts as awaveguideconfining the waves so they don't escape into space. The waves travel in a zig-zag path around the Earth, reflected alternately by the Earth and the ionosphere, intransverse magnetic(TM) mode.
VLF waves have very low path attenuation, 2–3 dB per 1,000 km,[2]with little of the "fading"experienced at higher frequencies.[3]This is because VLF waves are reflected from the bottom of the ionosphere, while higher frequency shortwave signals are returned to Earth from higher layers in the ionosphere, theF1andF2layers, by a refraction process, and spend most of their journey in the ionosphere, so they are much more affected by ionization gradients and turbulence. Therefore, VLF transmissions are very stable and reliable, and are used for long-distance communication. Propagation distances of 5,000–20,000 km have been realized.[2]However, atmospheric noise ( "sferics") is high in the band,[3]including such phenomena as "whistlers",caused bylightning.
- VLF waves can penetrateseawaterto a depth of at least 10–40 meters (30–130 feet), depending on the frequency employed and the salinity of the water, so they are used to communicate with submarines.
- VLF waves at certain frequencies have been found to causeelectron precipitation.
- VLF waves used to communicate with submarines have created an artificial bubble around the Earth that can protect it fromsolar flaresandcoronal mass ejections;this occurred through interaction with high-energy radiation particles.[4]
Antennas
editA major practical drawback to the VLF band is that because of the length of the waves, full size resonant antennas (half wave dipoleorquarter wave monopoleantennas) cannot be built because of their physical height.[5]: 14 Vertical antennas must be used because VLF waves propagate in vertical polarization, but a quarter-wave vertical antenna at 30 kHz (10 km wavelength) would be 2.5 kilometres (8,200 feet) high. So practical transmitting antennas areelectrically short,a small fraction of the length at which they would be self-resonant.[6][7]: 24.5–24.6 Due to their lowradiation resistance(often less than one ohm) they are inefficient, radiating only 10% to 50% of the transmitter power at most,[2][5]: 14 with the rest of the power dissipated in the antenna/ground system resistances. Very high power transmitters (~1 megawatt) are required for long-distance communication, so the efficiency of the antenna is an important factor.
VLF transmitting antennas
editHigh power VLF transmitting stations use capacitively-toploadedmonopole antennas.These are very large wire antennas, up to several kilometers long.[8]: 3.9–3.21 [7]: 24.8–24.12 They consist of a series of steelradio masts,linked at the top with a network of cables, often shaped like an umbrella or clotheslines.[5]: p.14 Either the towers themselves or vertical wires serve asmonopoleradiators, and the horizontal cables form acapacitive top-loadto increase the current in the vertical wires, increasing the radiated power and efficiency of the antenna. High-power stations use variations on theumbrella antennasuch as the "delta" and "trideco"antennas, or multiwireflattop(triatic) antennas.[5]: p.129-162 For low-power transmitters, inverted-L andT antennasare used.
Due to the low radiation resistance, to minimize power dissipated in the ground these antennas require extremely low resistanceground(Earthing) systems, consisting of radial networks of buried copper wires under the antenna. To minimizedielectric lossesin the soil, the ground conductors are buried shallowly, only a few inches in the ground, and the ground surface near the antenna is sometimes protected by copper ground screens.Counterpoisesystems have also been used, consisting of radial networks of copper cables supported several feet above the ground under the antenna.
A largeloading coilis required at the antenna feed point to cancel thecapacitive reactanceof the antenna to make itresonant.At VLF the design of this coil is challenging; it must have low resistance at the operating RF frequency,highQ,must handle very high currents, and must withstand the extremely high voltage on the antenna. These are usually huge air core coils 2-4 meters high wound on a nonconductive frame, with RF resistance reduced by using thicklitz wireseveral centimeters in diameter, consisting of thousands of insulated strands of fine wire braided together.[5]: p.95
The high capacitance and inductance and low resistance of the antenna-loading coil combination makes it act electrically like ahighQtuned circuit.VLF antennas have very narrowbandwidthand to change the transmitting frequency requires a variable inductor (variometer) to tune the antenna. The large VLF antennas used for high-power transmitters usually have bandwidths of only 50–100 hertz. The highQresults in very high voltages (up to 250 kV)[5]: p.58 on the antenna and very good insulation is required.[5]: p.14,19 Large VLF antennas usually operate in 'voltage limited' mode: the maximum power of the transmitter is limited by the voltage the antenna can accept withoutair breakdown,corona,and arcing from the antenna.
Dynamic antenna tuning
editThe bandwidth of large capacitively loaded VLF antennas is so narrow (50–100 Hz) that even the small frequency shifts of FSK and MSK modulation may exceed it, throwing the antenna out ofresonance,causing the antenna to reflect some power back down the feedline. The traditional solution is to use a "bandwidth resistor" in the antenna which reduces theQ,increasing the bandwidth; however this also reduces the power output. A recent alternative used in some military VLF transmitters is a circuit which dynamically shifts the antenna'sresonant frequencybetween the two output frequencies with the modulation.[7]: 24.7 [8]: 3.36 This is accomplished with asaturable reactorin series with the antennaloading coil.This is aferromagnetic coreinductorwith a second control winding through which a DC current flows, which controls the inductance by magnetizing the core, changing itspermeability.The keying datastream is applied to the control winding. So when the frequency of the transmitter is shifted between the '1' and '0' frequencies, the saturable reactor changes the inductance in the antenna resonant circuit to shift the antenna resonant frequency to follow the transmitter's frequency.
VLF receiving antennas
editThe requirements for receiving antennas are less stringent, because of the high level of naturalatmospheric noisein the band. At VLF frequencies atmosphericradio noiseis far above thereceiver noiseintroduced by the receiver circuit and determines the receiversignal-to-noise ratio.So small inefficient receiving antennas can be used, and the low voltage signal from the antenna can simply be amplified by the receiver without introducing significant noise. Ferriteloop antennasare usually used for reception.
Modulation
editBecause of the smallbandwidthof the band, and the extremely narrow bandwidth of the antennas used, it is impractical to transmitaudio signals(AMorFMradiotelephony).[9]A typical AM radio signal with a bandwidth of 10 kHz would occupy one third of the VLF band. More significantly, it would be difficult to transmit any distance because it would require an antenna with 100 times the bandwidth of current VLF antennas, which due to theChu-Harrington limitwould be enormous in size. Therefore, only text data can be transmitted, at lowbit rates.In military networksfrequency-shift keying(FSK)modulationis used to transmitradioteletypedata using 5 bitITA2or 8 bitASCIIcharacter codes. A small frequency shift of 30–50 hertz is used due to the small bandwidth of the antenna.
In high power VLF transmitters, to increase the allowable data rate, a special form of FSK calledminimum-shift keying(MSK) is used. This is required due to the highQof the antenna.[8]: 3.2–3.4, §3.1.1 The huge capacitively-loaded antenna andloading coilform a highQtuned circuit,which stores oscillating electrical energy. TheQof large VLF antennas is typically over 200; this means the antenna stores far more energy (200 times as much) than is supplied or radiated in any single cycle of the transmitter current. The energy is stored alternately aselectrostatic energyin the topload and ground system, and magnetic energy in the vertical wires and loading coil. VLF antennas typically operate "voltage-limited", with the voltage on the antenna close to the limit that the insulation will stand, so they will not tolerate any abrupt change in the voltage or current from the transmitter without arcing or other insulation problems. As described below, MSK is able to modulate the transmitted wave at higher data rates without causing voltage spikes on the antenna.
The three types ofmodulationthat have been used in VLF transmitters are:
- Continuous Wave(CW), Interrupted Continuous Wave (ICW), or On-Off Keying
- Morse coderadiotelegraphytransmission with unmodulated carrier. The carrier is turned on and off, with carrier on representing the Morse code "dots" and "dashes" and carrier off representing spaces. The simplest and earliest form of radio data transmission, this was used from the beginning of the 20th century to the 1960s in commercial and military VLF stations. Because of the highantennaQthe carrier cannot be switched abruptly on and off but requires a long time constant, many cycles, to build up the oscillating energy in the antenna when the carrier turns on, and many cycles to dissipate the stored energy when the carrier turns off. This limits the data rate that can be transmitted to 15–20 words/minute. CW is now only used in small hand-keyed transmitters, and for testing large transmitters.
- Frequency-shift keying(FSK)
- FSK is the second oldest and second simplest form of digital radio data modulation, after CW. For FSK, the carrier shifted between two frequencies, one representing the binary digit '1' and the other representing binary '0'. For example, a frequency of 9070 Hz might be used to indicate a '1' and the frequency 9020 Hz, 50 Hz lower, to indicate a '0'. The two frequencies are generated by a continuously-runningfrequency synthesizer.The transmitter is periodically switched between these frequencies to represent 8 bitASCIIcodes for the characters of the message. A problem at VLF is that when the frequency is switched the twosine wavesusually have differentphases,which creates a sudden phase-shift transient which can cause arcing on the antenna. To avoid arcing, FSK can only be used at slow rates of 50–75 bit/s.
- Minimum-shift keying(MSK)
- Acontinuous phaseversion of FSK designed specifically for small bandwidths, this was adopted by naval VLF stations in the 1970s to increase the data rate and is now the standard mode used in military VLF transmitters. If the two frequencies representing '1' and '0' are 50 Hz apart, the standard frequency shift used in military VLF stations, their phases coincide every 20 ms. In MSK the frequency of the transmitter is switched only when the two sine waves have the same phase, at the point both sine waves cross zero in the same direction. This creates a smooth continuous transition between the waves, avoiding transients which can cause stress and arcing on the antenna. MSK can be used at data rates up to 300 bit/s, or about 35ASCIIcharacters (8 bits each) per second, approximately 450 words per minute.
Applications
editEarly wireless telegraphy
editHistorically, this band was used for long distance transoceanic radio communication during thewireless telegraphyera between about 1905 and 1925. Nations built networks of high-power LF and VLFradiotelegraphystations that transmitted text information byMorse code,to communicate with other countries, their colonies, and naval fleets. Early attempts were made to use radiotelephone usingamplitude modulationandsingle-sideband modulationwithin the band starting from 20 kHz, but the result was unsatisfactory because the available bandwidth was insufficient to contain thesidebands.
In the 1920s the discovery of theskywave(skip) radio propagation method allowed lower power transmitters operating athigh frequencyto communicate at similar distances by reflecting their radio waves off a layer ofionizedatoms in theionosphere,and long-distance radio communication stations switched to theshortwavefrequencies. TheGrimeton VLF transmitterat Grimeton near Varberg inSweden,one of the few remaining transmitters from that era that has been preserved as a historical monument, can be visited by the public at certain times, such as onAlexanderson Day.
Navigation beacons and time signals
editDue to its long propagation distances and stable phase characteristics, during the 20th century the VLF band was used for long rangehyperbolicradio navigationsystems which allowed ships and aircraft to determine their geographical position by comparing the phase of radio waves received from fixed VLFnavigation beacontransmitters.
The worldwideOmegasystem used frequencies from 10 to 14 kHz, as did Russia'sAlpha.
VLF was also used forstandard time and frequencybroadcasts. In the US, thetime signalstationWWVLbegan transmitting a 500 W signal on 20 kHz in August 1963. It used frequency-shift keying (FSK) to send data, shifting between 20 kHz and 26 kHz. The WWVL service was discontinued in July 1972.
Geophysical and atmospheric measurement
editNaturally occurring signals in the VLF band are used bygeophysicistsfor long range lightning location and for research into atmospheric phenomena such as the aurora. Measurements ofwhistlersare employed to infer the physical properties of themagnetosphere.[10]
Geophysicistsuse VLF-electromagneticreceivers to measure conductivity in the near surface of the Earth.[11]
VLF signals can be measured as ageophysicalelectromagneticsurvey that relies on transmitted currents inducing secondary responses in conductive geologic units. A VLF anomaly represents a change in the attitude of the electromagnetic vector overlying conductive materials in the subsurface.
Mine communication systems
editVLF can also penetrate soil and rock for some distance, so these frequencies are also used forthrough-the-earth mine communicationssystems.
Military communications
editPowerful VLF transmitters are used by the military to communicate with their forces worldwide. The advantage of VLF frequencies is their long range, high reliability, and the prediction that in anuclear warVLF communications will be less disrupted by nuclear explosions than higher frequencies. Since it can penetrate seawater VLF is used by the military tocommunicate with submarinesnear the surface, whileELFfrequencies are used for deeply submerged subs.
Examples of naval VLF transmitters are
- Britain'sSkelton Transmitting Stationin Skelton, Cumbria
- Germany'sDHO38inRhauderfehn,which transmits on 23.4 kHz with a power of 800 kW
- U.S.Jim Creek Naval Radio StationinOso, Washingtonstate, which transmits on 24.8 kHz with a power of 1.2 MW
- U.S.Cutler Naval Radio StationatCutler, Mainewhich transmits on 24 kHz with 1.8 MW.
Since 2004 theUS Navyhas stopped using ELF transmissions, with the statement that improvements in VLF communication has made them unnecessary, so it may have developed technology to allow submarines to receive VLF transmissions while at operating depth.
High power land-based and aircraft transmitters in countries that operate submarines send signals that can be received thousands of miles away. Transmitter sites typically cover great areas (manyacresor square kilometers), with transmitted power anywhere from 20 kW to 2,000 kW. Submarines receive signals from land based and aircraft transmitters using some form of towed antenna that floats just under the surface of the water – for example aBuoyant Cable Array Antenna(BCAA).
Modern receivers use sophisticateddigital signal processingtechniques to remove the effects of atmospheric noise (largely caused by lightning strikes around the world) and adjacent channel signals, extending the useful reception range. Strategic nuclear bombers of the United States Air Force receive VLF signals as part of hardened nuclear resilient operations.
Two alternative character sets may be used: 5 bitITA2or 8 bitASCII.Because these are military transmissions they are almost alwaysencryptedfor security reasons. Although it is relatively easy to receive the transmissions and convert them into a string of characters, enemies cannot decode the encrypted messages; military communications usually use unbreakableone-time padcipherssince the amount of text is so small.
Amateur use
editThe frequency range below 8.3 kHz is not allocated by theInternational Telecommunication Unionand in some nations may be used license-free. Radio amateurs in some countries have been granted permission (or have assumed permission) to operate at frequencies below 8.3 kHz.[12]
Operations tend to congregate around the frequencies 8.27 kHz, 6.47 kHz, 5.17 kHz, and 2.97 kHz.[13]Transmissions typically last from one hour up to several days and both receiver and transmitter must have their frequency locked to a stable reference such as aGPS disciplined oscillatoror arubidium standardin order to support such long duration coherent detection and decoding.
Amateur equipment
editRadiated power from amateur stations is very small, ranging from 1 μW to 100 μW for fixed base station antennas, and up to 10 mW from kite or balloon antennas. Despite the low power, stable propagation with low attenuation in theearth-ionosphere cavityenable very narrow bandwidths to be used to reach distances up to several thousand kilometers. The modes used areQRSS,MFSK,and coherentBPSK.
The transmitter generally consists of an audio amplifier of a few hundred watts, an impedance matching transformer, aloading coiland a large wire antenna. Receivers employ an electric field probe or magnetic loop antenna, a sensitive audio preamplifier, isolating transformers, and a PCsound cardto digitise the signal. Extensivedigital signal processingis required to retrieve the weak signals from beneathinterferencefrompower line harmonicsandVLF radio atmospherics.Useful received signal strengths are as low as3×10−8volts/meter (electric field) and1×10−16tesla (magnetic field), withsignaling ratestypically between 1 and 100 bits per hour.
PC based reception
editVLF signals are often monitored byradio amateursusing simple homemade VLFradio receiversbased on personal computers (PCs).[14][15]An aerial in the form of a coil of insulated wire is connected to the input of the soundcard of the PC (via a jack plug) and placed a few meters away from it.Fast Fourier transform(FFT) software in combination with a sound card allows reception of all frequencies below theNyquist frequencysimultaneously in the form ofspectrogrammes.
Because CRT monitors are strong sources of noise in the VLF range, it is recommended to record the spectrograms with any PC CRT monitors turned off. These spectrograms show many signals, which may include VLF transmitters and the horizontal electron beam deflection of TV sets. The strength of the signal received can vary with asudden ionospheric disturbance.These cause the ionization level to increase in the ionosphere producing a rapid change to the amplitude and phase of the received VLF signal.
List of VLF transmissions
editFor a more detailed list, seeList of VLF-transmitters
Callsign | Frequency | Location of transmitter | Remarks |
---|---|---|---|
— | 11.905 kHz | various locations (Russia) | Alpha-Navigation |
— | 12.649 kHz | various locations (Russia) | Alpha-Navigation |
— | 14.881 kHz | various locations (Russia) | Alpha-Navigation |
HWU | 15.1 kHz | Rosnay (France) | 400 kW[16] |
— | 15.625 kHz | — | Frequency for horizontal deflection of electron beam inCRT televisions(576i) |
— | 15.734 kHz | — | Frequency for horizontal deflection of electron beam inCRT televisions(480i) |
JXN | 16.4 kHz | Gildeskål Municipality(Norway) | |
SAQ | 17.2 kHz | Grimeton(Sweden) | Only active at special occasions(Alexanderson Day) |
NAA | 17.8 kHz | VLF station (NAA) atCutler,Maine (US)[17] | |
RDL UPD UFQE UPP UPD8 | 18.1 kHz | various locations, includingMatochkin Shar(Russia)[16] | |
HWU | 18.3 kHz | Le Blanc(France) | Frequently inactive for long periods |
RKS | 18.9 kHz | various locations (Russia) | Rarely active |
GQD | 19.6 kHz | Anthorn(UK) | Many operation modes. |
NWC | 19.8 kHz | Exmouth,Western Australia (AUS) | Used for submarine communication, 1 megawatt.[18] |
ICV | 20.27 kHz | Tavolara(Italy) | |
RJH63 RJH66RJH69RJH77 RJH99 | 20.5 kHz | various locations (Russia) | Time signal transmitter Beta |
ICV | 20.76 kHz | Tavolara (Italy) | |
HWU | 20.9 kHz | Saint-Assise (France)[16] | |
RDL | 21.1 kHz | various locations (Russia) | rarely active |
NPM | 21.4 kHz | Hawaii (USA) | |
HWU | 21.75 kHz | Rosnay (France)[16] | |
GZQ | 22.1 kHz | Skelton(UK) | |
JJI | 22.2 kHz | Ebino(Japan) | |
RJH63 RJH66RJH69RJH77 RJH99 | 23 kHz | various locations (Russia) | Time signal transmitter Beta |
DHO38 | 23.4 kHz | nearRhauderfehn(Germany) | submarine communication |
NAA | 24 kHz | Cutler, Maine(USA) | Used for submarine communication, at2 megawatts[19] |
NLK | 24.6 kHz | Oso, Washington(USA) | 192 kW[16] |
NLF | 24.8 kHz | Arlington, Washington(USA) | Used for submarine communication.[20] |
NML | 25.2 kHz | LaMoure, North Dakota(USA) | |
PNSH | 14–25.2? kHz | Karachi coast,Sindh(Pakistan) |
See also
editReferences
edit- ^"Nomenclature of the frequency and wavelength bands used in telemmunications"(PDF).ITU.Rec. ITU-R V.431-7. Archived fromthe original(PDF)on 31 October 2013.Retrieved20 February2013.
- ^abcdHunsucker, R.D.; Hargreaves, John Keith (2002).The high-latitude ionosphere and its effects on radio propagation.Cambridge University Press. p. 419.ISBN978-0-521-33083-1.
- ^abcGhosh, S.N. (2002).Electromagnetic theory and wave propagation.CRC Press. p. 89.ISBN978-0-8493-2430-7.
- ^Susannah Darling (17 May 2017)."NASA's Van Allen Probes Spot Man-Made Barrier Shrouding Earth".NASA.Retrieved11 June2024.
- ^abcdefgWatt, Arthur D. (1967).VLF Radio Engineering.Pergamon Press.
- ^Seybold, John S. (2005).Introduction to RF Propagation.John Wiley and Sons. pp. 55–58.ISBN978-0471743682.
- ^abcJohnson, Richard C., ed. (1993).Antenna Engineering Handbook(PDF)(3rd ed.). McGraw-Hill.ISBN007032381X.
- ^abcNaval Shore Electronics Criteria - VLF, LF, and MF communications systems(PDF).Naval Electronics Systems Command. Washington, DC: U.S. Navy. August 1972. Manual NAVELEX 0101-113.
- ^Holtet, J.A., ed. (17–27 April 1974).ELF-VLF Radio Wave Propagation.NATO Advanced Study Institute. Spåtind, Norway: Springer Science and Business Media. pp. 372–373.ISBN9789401022651.
- ^"AWDANet".plasmon.elte.hu.
- ^"Geonics Limited - VLF Receivers".Retrieved13 June2014.
- ^"Sub 9 kHz spectrum in the Amateur Service".Retrieved13 May2017.
- ^"Some recent milestones with amateur radio experiments at VLF".Retrieved13 May2017.
- ^Renato Romero, IK1QFK (2008).Radio Nature.Radio Society of Great Britain.p. 77.ISBN9781-9050-8637-5.
{{cite book}}
:CS1 maint: numeric names: authors list (link) - ^Mardina Abdullah; et al. (2013) [2012].Development of UKM-SID teaching module for space science education.6th International Forum on Engineering Education (IFEE 2012).Procedia - Social and Behavioral Sciences.Vol. 102. pp. 80–85.doi:10.1016/j.sbspro.2013.10.716.
- ^abcdeFidani, Cristiano (8 December 2011)."The Central Italy Electromagnetic Network and the 2009 L'Aquila earthquake: Observed electric activity".Geosciences.1(1) (published 2012): 3–25.Bibcode:2011Geosc...1....3F.doi:10.3390/geosciences1010003.ISSN2076-3263.Retrieved14 January2021.
- ^"Shortwave HF VHF UHF utilities monitoring".Random Abstract.
- ^"Naval base link to jet plunge".The Sydney Morning Herald.Sydney, AU. 14 November 2008.Retrieved14 November2008.
- ^"Cutler".GlobalSecurity.Military Facilities.
- ^"20–25kHz".vlf.it.[full citation needed]
"WA3248".ludb.clui.org.Archived fromthe originalon 2011-09-27.Retrieved2009-07-13.[full citation needed]
Further reading
edit- Romero, R. (2006).Radio Natura(in Italian). Albino, Italy: SANDIT S.r.l.
- Klawitter, G.; Oexner, M.; Herold, K. (2000).Langwelle und Längstwelle(in German). Meckenheim, DE: Siebel Verlag GmbH.ISBN978-3-89632-043-8.
- Friese (January 2006)."Very low wave reception with ferrite antennas 5-50 kHz"(PDF).
External links
edit- Longwave club of America
- Radio waves below 22 kHz
- VLF Discussion Group
- Tomislav Stimac, "Definition of frequency bands (VLF, ELF... etc.)".
- PC-based VLF-reception
- Gallery of VLF-signals
- NASA live streaming ELF -> VLF ReceiverNOTE: As of 05/03/2014, the "Listen live" links are down, but the site has some previously recorded examples to listen to.
- World Wide Lightning Location Network
- Stanford University VLF group
- University of Louisville VLF Monitor
- Larry's Very Low Frequency site
- Mark's Live Online VLF Receiver, UKArchived2009-02-28 at theWayback Machine
- IW0BZD VLF TUBE receiver
- Internet based VLF listening guide with server list
- List of VLF-transmitters