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%About_Yourself%
{{About|waveform manipulation}}
[[Image:IdealMixer.svg|thumb|350px|Frequency Mixer Symbol.]]
 
'''Heterodyning''' is a [[radio]] [[signal processing]] technique invented in 1901 by Canadian inventor-engineer [[Reginald Fessenden]], in which new [[frequency|frequencies]] are created by combining or mixing two frequencies.<ref name="Cooper2001">{{cite book|author=Christopher E. Cooper|title=Physics|url=http://books.google.com/books?id=lEHsmDZigYMC&pg=PA25|accessdate=27 July 2013|date=January 2001|publisher=Fitzroy Dearborn Publishers|isbn=978-1-57958-358-3|pages=25–}}</ref><ref name="Naval">{{cite book | last = United States Bureau of Naval Personnel | first = | authorlink = | coauthors = | title = Basic Electronics | publisher = Courier Dover | date = 1973 | location = USA | pages = 338 | url = http://books.google.com/books?id=o6pn1Pdas1UC&pg=PA338&dq=heterodyne+mixer+modulation&hl=en&ei=GKoTTeqpF4aasAPHrrioAg&sa=X&oi=book_result&ct=result&resnum=5&ved=0CDcQ6AEwBA#v=onepage&q=heterodyne%20mixer%20modulation&f=false | doi = | id = | isbn = 0-486-21076-6}}</ref><ref name="Graf">{{cite book | last = Graf | first = Rudolf F. | authorlink = | coauthors = | title = Modern dictionary of electronics, 7th Ed. | publisher = Newnes | date = 1999 | location = USA | pages = 344 | url = http://books.google.com/books?id=uah1PkxWeKYC&pg=PA344&dq=heterodyning+frequencies&hl=en&sa=X&ei=6ZRgT4iMOeORiQLp6OC4BA&ved=0CE0Q6AEwBQ#v=onepage&q=heterodyning%20frequencies&f=false | doi = | id = | isbn = 0-7506-9866-7}}</ref> Heterodyning is useful for frequency shifting signals into a new [[frequency range]], and is also involved in the processes of [[modulation]] and [[demodulation]].<ref name="Naval" /><ref name="Horowitz">{{cite book | last = Horowitz | first = Paul | authorlink = | coauthors = Winfield Hill | title = The Art of Electronics, 2nd Ed. | publisher = Cambridge University Press | date = 1989 | location = London | pages = 885,897 | url = http://books.google.com/books?id=bkOMDgwFA28C&printsec=frontcover&dq=paul+horowitz&hl=en&ei=iKMTTffEK4SasAPJ4_ymDw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC4Q6AEwAA#v=snippet&q=heterodyning&f=false | doi = | id = | isbn = 0-521-37095-7}}</ref>  The two frequencies are combined in a [[linear circuit|nonlinear]] signal-processing device such as a  [[vacuum tube]], [[transistor]], or [[diode]], usually called a ''[[frequency mixer|mixer]]''.<ref name="Naval" />    In the most common application, two signals at frequencies ''f<sub>1</sub>'' and  ''f<sub>2</sub>'' are mixed, creating two new signals, one at the sum ''f<sub>1</sub>'' + ''f<sub>2</sub>'' of the two frequencies, and the other at the difference  ''f<sub>1</sub>'' − ''f<sub>2</sub>''.<ref name="Graf" />    These new frequencies are called '''heterodynes'''. Typically only one of the new frequencies is desired, and the other signal is [[filter (signal processing)|filtered]] out of the output of the mixer.  Heterodynes are related to the phenomenon of "[[beat (acoustics)|beat]]s" in acoustics.
 
==History==
In 1901, [[Reginald Fessenden]] demonstrated a [[direct-conversion receiver|direct-conversion heterodyne receiver]] or [[beat receptor|beat receiver]] as a method of making [[continuous wave]] [[radiotelegraphy]] signals audible.  Fessenden's receiver did not see much application because of its local oscillator's stability problem.  While complex [[isochronous]] electromechanical oscillators existed, a stable yet inexpensive local oscillator would not be available until [[Lee de Forest|Lee de Forest's]] invention of the [[triode|triode vacuum tube]] oscillator.<ref name=nahin1>{{Harvnb|Nahin|2001|p=91}}, stating "Fessenden's circuit was ahead of its time, however, as there simply was no technology available then with which to build the required local oscillator with the necessary frequency stability." Figure 7.10 shows a simplified 1907 heterodyne detector.</ref>  In a 1905 patent, Fessenden stated the frequency stability of his local oscillator was one part per thousand.<ref>{{Harvnb|Fessenden|1905|p=4}}</ref>
 
Early spark gap [[Transmitter|radio transmitters]] sent information exclusively by means of [[radio telegraphy]].  In radio telegraphy, the characters of text messages are translated into the short duration dots and long duration dashes of [[Morse code]] that are broadcast as bursts of radio waves.  The heterodyne detector was not needed to hear the signals produced by these spark gap transmitters.  The transmitted damped wave signals were amplitude modulated at an audio frequency by the spark.  A simple detector produced an audible buzzing sound in the radiotelegraph operator's headphones that could be transcribed back into alpha-numeric characters.
 
With the advent of the [[arc converter]], [[continuous wave]] (CW) transmitters were adopted. CW Morse code signals are not amplitude modulated, so a different detector was needed.  The direct-conversion detector was invented to make continuous wave radio-frequency signals audible.<ref>{{cite book |last=Ashley |first=Charles Grinnell |authorlink= |last2=Heyward |first2=Charles Brian |title=Wireless Telegraphy and Wireless Telephony |publisher=American School of Correspondence |year=1912 |location=Chicago |pages=103/15–104/16 |url=http://books.google.com/books?id=pK-EAAAAIAAJ&pg=PA103 |isbn= |doi= }}</ref>
 
The "heterodyne" or "beat" receiver has a local [[local oscillator|beat frequency oscillator]] (BFO) that produces a radio signal adjusted to be close in frequency to the incoming signal being received.  When the two signals are mixed, a "beat" frequency equal to the difference between the two frequencies is created.  By adjusting the local oscillator frequency correctly, the beat frequency is in the [[audio signal|audio]] range, and can be heard as a tone in the receiver's [[earphone]]s whenever the transmitter signal is present.  Thus the Morse code "dots" and "dashes" are audible as beeping sounds. This technique is still used in radio telegraphy, the local oscillator now being called the [[beat frequency oscillator]] or BFO. Fessenden coined the word ''heterodyne'' from the Greek roots ''hetero-'' "different", and ''dyn-'' "power" (cf. [[Wiktionary:δύναμις|δύναμις or dunamis]]).<ref>[http://books.google.com/books?id=49jgQvbrvCUC&pg=PA370&dq=heterodyne+Fessenden+coined&hl=en&ei=T4XrTcX8C4f4gAeHxN3XCQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCoQ6AEwAA#v=onepage&q=heterodyne%20Fessenden%20coined&f=false Tapan K. Sarkar, History of wireless, page 372]</ref>
 
===Superheterodyne receiver===
The most important and widely used application of the heterodyne technique is in the [[superheterodyne receiver]] (superhet), invented by U.S. engineer [[Edwin Howard Armstrong]] in 1918.  In this circuit, the incoming [[radio frequency]] signal from the antenna is mixed with a signal from a local oscillator and converted by the heterodyne technique to a somewhat lower fixed frequency signal called the [[intermediate frequency]] (IF).  This IF signal is amplified and filtered, before being applied to a [[detector (radio)|detector]] which extracts the audio signal, which is sent to the loudspeaker.
 
The advantage of this technique is that the different frequencies of the different stations received are all converted to the ''same'' IF frequency before amplification and filtering.  The complicated amplifier and bandpass filter stages, which in previous receivers had to be made tunable to work at the different station frequencies, in the superheterodyne can be built to work at one fixed frequency, the IF, simplifying their design.  Another advantage is that the IF is at a considerably lower frequency than the RF frequency of the incoming radio signal.
 
The superior superheterodyne system replaced the earlier [[Tuned radio frequency receiver|TRF]] and [[regenerative radio receiver|regenerative]] receiver designs, and since the 1930s almost all commercial radio receivers have been superheterodynes.
 
==Applications==
Heterodyning is used very widely in [[communications engineering]] to generate new frequencies and move information from one frequency channel to another. Besides its use in the superheterodyne circuit which is found in almost all radio and television receivers, it is used in [[radio transmitter]]s, [[modem]]s, [[satellite]] communications and set-top boxes, [[radar]], [[radio telescope]]s, [[telemetry]] systems, [[cell phone]]s, [[cable television]] converter boxes and [[Cable television headend|headends]], [[microwave relay]]s, [[metal detector]]s, [[atomic clock]]s, and military [[electronic countermeasures]] (jamming) systems.
 
===Up and down converters===
In large scale [[telecommunication network]]s such as [[telephone network]] trunks, [[microwave relay]] networks,  [[cable television]] systems, and [[communication satellite]] links, large [[bandwidth (signal processing)|bandwidth]] capacity links are shared by many individual communication channels by using heterodyning to move the frequency of the individual signals up to different frequencies, which share the channel.  This is called [[frequency division multiplexing]] (FDM). 
 
For example, a [[coaxial cable]] used by a [[cable television]] system can carry 500 television channels at the same time because each one is given a different frequency, so they don't interfere with one another.  At the cable source or [[Cable television headend|headend]], electronic upconverters convert each incoming television channel to a new, higher frequency.  They do this by mixing the television signal frequency, ''f<sub>CH</sub>'' with a [[local oscillator]] at a much higher frequency ''f<sub>LO</sub>'', creating a heterodyne at the sum  ''f<sub>CH</sub>''+''f<sub>LO</sub>'', which is added to the cable.  At the consumer's home, the cable [[set top box]] has a downconverter that mixes the incoming signal at frequency ''f<sub>CH</sub>''+''f<sub>LO</sub>'' with the same local oscillator frequency ''f<sub>LO</sub>'' creating the difference heterodyne, converting the television channel back to its original frequency: (''f<sub>CH</sub>''+''f<sub>LO</sub>'') − ''f<sub>LO</sub>'' = ''f<sub>CH</sub>''.  Each channel is moved to a different higher frequency.  The original lower basic frequency of the signal is called the [[baseband]], while the higher channel it is moved to is called the [[passband]].
 
===Analog videotape recording===
Many analog [[videotape]] systems rely on a downconverted color subcarrier in order to record color information in their limited bandwidth. These systems are referred to as "heterodyne systems" or "color-under systems". For instance, for [[NTSC]] video systems, the [[VHS]] (and [[S-VHS]]) recording system converts the color subcarrier from the NTSC standard 3.58&nbsp;MHz to ~629&nbsp;kHz.<ref name = lionlamb>[http://www.lionlmb.org/quad/format.html#12incomposite Videotape formats using {{convert|1/2|in|mm|adj=mid|-wide}} tape] ; Retrieved 2007-01-01</ref> [[PAL]] VHS color subcarrier is similarly downconverted (but from 4.43&nbsp;MHz). The now-obsolete 3/4" [[U-matic]] systems use a heterodyned ~688&nbsp;kHz subcarrier for NTSC recordings (as does [[Sony]]'s [[Betamax]], which is at its basis a 1/2″ consumer version of U-matic), while PAL U-matic decks came in two mutually incompatible varieties, with different subcarrier frequencies, known as Hi-Band and Low-Band. Other videotape formats with heterodyne color systems include [[Video-8]] and [[Hi8]].<ref name = poynton>Poynton, Charles. ''Digital Video and HDTV: Algorithms and Interfaces'' San Francisco: Morgan Kaufmann Publishers, 2003 PP 582, 583 ISBN 1-55860-792-7</ref>
 
The heterodyne system in these cases is used to convert quadrature phase-encoded and amplitude modulated sine waves from the broadcast frequencies to frequencies recordable in less than 1&nbsp;MHz bandwidth. On playback, the recorded color information is heterodyned back to the standard subcarrier frequencies for display on televisions and for interchange with other standard video equipment.
 
Some U-matic (3/4″) decks feature 7-pin mini-[[DIN connector]]s to allow dubbing of tapes without a heterodyne up-conversion and down-conversion, as do some industrial VHS, S-VHS, and Hi8 recorders.
 
===Music synthesis===
The [[theremin]], an [[electronic musical instrument]], traditionally uses the heterodyne principle to produce a variable [[audio frequency]] in response to the movement of the [[musician]]'s hands in the vicinity of one or more antennas, which act both as capacitor plates. The output of a fixed radio frequency oscillator is mixed with that of an oscillator whose frequency is affected by the [[variable capacitance]] between the antenna and the thereminist as that person moves her or his hand near the pitch control antenna. The difference between the two oscillator frequencies produces a tone in the audio range.
 
The [[Ring modulator]] is a type of heterodyne incorporated into some [[synthesizers]] or used as a stand-alone audio effect.
 
===Optical heterodyning===
[[Optical heterodyne detection]] (an area of active research) is an extension of the heterodyning technique to higher (visible) frequencies. This technique could greatly improve [[optical modulator]]s, increasing the density of information carried by [[optical fiber]]s. It is also being applied in the creation of more accurate [[atomic clock]]s based on directly measuring the frequency of a laser beam. See NIST subtopic 9.07.9-4.R for a description of research on one system to do this.<ref>[http://tsapps.nist.gov/ts_sbir/sbirrss/index.cfm?action=contractdetails&id=78 Contract Details: Robust Nanopopous Ceramic Microsensor Platform<!-- Bot generated title -->]</ref><ref>[http://tsapps.nist.gov/ts_sbir/sbirrss/index.cfm?action=contractdetails&id=147 Contract Details: High Pulsed Power Varactor Multipliers for Imaging<!-- Bot generated title -->]</ref>
 
Since optical frequencies are far beyond the manipulation capacity of any feasible electronic circuit, all photon detectors are inherently energy detectors not oscillating electric field detectors. However, since energy detection is inherently "square-law" detection, it intrinsically mixes any optical frequencies present on the detector. Thus, sensitive detection of specific optical frequencies necessitates [[optical heterodyne detection]], in which two different (close-by) wavelengths of light illuminate the detector so that the oscillating electrical output corresponds to the difference between their frequencies. This allows extremely narrow band detection (much narrower than any possible color filter can achieve) as well as precision measurements of phase and frequency of a light signal relative to a reference light source, as in a [[laser Doppler vibrometer]].
 
This phase sensitive detection has been applied for Doppler measurements of wind speed, and imaging through dense media. The high sensitivity against background light is especially useful for [[LIDAR]].
 
In [[optical Kerr effect]] (OKE) spectroscopy, optical heterodyning of the OKE signal and a small part of the probe signal produces a mixed signal consisting of probe, heterodyne OKE-probe and homodyne OKE signal. The probe and homodyne OKE signals can be filtered out, leaving the heterodyne signal for detection.
 
==Mathematical principle==
Heterodyning is based on the [[trigonometric identity]]:
 
:<math>\sin \theta \sin \varphi = \frac{1}{2}\cos(\theta - \varphi) - \frac{1}{2}\cos(\theta + \varphi)</math>
 
The product on the left hand side represents the multiplication ("mixing") of a [[sine wave]] with another [[sine wave]]. The right hand side shows that the resulting signal is the difference of two [[sinusoidal]] terms, one at the sum of the two original frequencies, and one at the difference, which can be considered to be separate signals.
 
Using this trigonometric identity, the result of multiplying two sine wave signals, <math>\sin (2 \pi f_1 t)\,</math> and <math>\sin (2 \pi f_2 t)\,</math> can be calculated:
 
:<math>\sin (2 \pi f_1 t)\sin (2 \pi f_2 t) = \frac{1}{2}\cos [2 \pi (f_1 - f_2) t] - \frac{1}{2}\cos [2 \pi (f_1 + f_2) t] \,</math>
 
The result is the sum of two sinusoidal signals, one at the sum ''f<sub>1</sub>'' + ''f<sub>2</sub>'' and one at the difference ''f<sub>1</sub>'' - ''f<sub>2</sub>'' of the original frequencies
 
===Mixer===
The two signals are combined in a device called a ''[[Frequency mixer|mixer]]''.  It can be seen from the previous section that an ideal mixer would be a device that multiplies the two signals.  Some widely used mixer circuits, such as the [[Gilbert cell]], operate in this way, but they are limited to lower frequencies.  However, any ''[[linear circuit|nonlinear]]'' electronic component will also multiply signals applied to it, producing heterodyne frequencies in its output, so a variety of nonlinear components are used as mixers.  A nonlinear component is one in which the output current or voltage is a [[Linear function|nonlinear function]] of its input. Most circuit elements in communications circuits are designed to be [[Linear circuit|linear]]. This means they obey the [[superposition principle]]; if ''F(v)'' is the output of a linear element with an input of ''v'':
 
:<math>F(v_1 + v_2) = F(v_1) + F(v_2) \,</math>
 
So if two sine wave signals at frequencies ''f''<sub>1</sub> and ''f''<sub>2</sub> are applied to a linear device, the output is simply the sum of the outputs when the two signals are applied separately with no product terms. So the function ''F'' must be nonlinear to create heterodynes (mixer products).  A perfect multiplier only produces mixer products at the sum and difference frequencies (''f''<sub>1</sub>±''f''<sub>2</sub>), but more general nonlinear functions produce higher order mixer products: ''n''&sdot;''f''<sub>1</sub>+''m''&sdot;''f''<sub>2</sub> for integers ''n'' and ''m''.  Some mixer designs, such as double-balanced mixers, suppress some high order undesired products, while other designs, such as [[harmonic mixer]]s exploit high order differences.
 
Examples of nonlinear components that are used as mixers are [[vacuum tube]]s and [[transistor]]s biased near cutoff ([[class C amplifier|class C]]), and [[diode]]s.  [[Magnetic core|Ferromagnetic core]] [[inductor]]s driven into [[saturation (magnetic)|saturation]] can also be used at lower frequencies.  In [[nonlinear optics]], crystals that have nonlinear characteristics are used to mix [[laser]] light beams to create [[Optical heterodyne detection|heterodynes at optical frequencies]].
 
===Output of a mixer===
To demonstrate mathematically how a nonlinear component can multiply signals and generate heterodyne frequencies, the nonlinear function ''F'' can be expanded in a [[power series]] ([[MacLaurin series]]):
 
:<math>F(v) = \alpha_1 v + \alpha_2 v^2 + \alpha_3 v^3 + \ldots \,</math>
 
To simplify the math, the higher order terms above ''α<sub>2</sub>'' will be indicated by an ellipsis (". . .") and only the first terms will be shown. Applying the two sine waves at frequencies ''ω<sub>1</sub>'' = 2π''f<sub>1</sub>'' and ''ω<sub>2</sub>'' = 2π''f<sub>2</sub>'' to this device:
 
:<math>v_\text{out} = F(A_1 \sin \omega_1 t + A_2 \sin \omega_2 t)\,</math>
 
:<math>v_\text{out} = \alpha_1 (A_1 \sin \omega_1 t + A_2 \sin \omega_2 t) + \alpha_2(A_1 \sin \omega_1 t + A_2 \sin \omega_2 t)^2 + \ldots \,</math>
 
:<math>v_\text{out} = \alpha_1 (A_1 \sin \omega_1 t + A_2 \sin \omega_2 t) + \alpha_2(A_1^2 \sin^2 \omega_1 t + 2 A_1 A_2 \sin \omega_1 t \sin \omega_2 t + A_2^2 \sin^2 \omega_2 t) + \ldots \,</math>
 
It can be seen that the second term above contains a product of the two sine waves. Simplifying with [[trigonometric identity|trigonometric identities]]:
 
:<math>v_\text{out} = \alpha_1 (A_1 \sin \omega_1 t + A_2 \sin \omega_2 t) + \alpha_2\left( \frac{A_1^2}{2} [1 - \cos 2 \omega_1 t] + A_1 A_2 [\cos (\omega_1 t - \omega_2 t) - \cos (\omega_1 t + \omega_2 t) ] + \frac{A_2^2}{2} [1 - \cos 2 \omega_2 t] \right) + \ldots \,</math>
 
:<math>v_\text{out} = \alpha_2 A_1 A_2 \cos (\omega_1 - \omega_2 )t - \alpha_2 A_1 A_2 \cos (\omega_1 + \omega_2 ) t + \ldots \,</math>
 
So the output contains sinusoidal terms with frequencies at the sum ''ω<sub>1</sub>'' + ''ω<sub>2</sub>'' and difference ''ω<sub>1</sub>'' - ''ω<sub>2</sub>'' of the two original frequencies. It also contains terms at the original frequencies and at multiples of the original frequencies 2''ω<sub>1</sub>'', 2''ω<sub>2</sub>'', 3''ω<sub>1</sub>'', 3''ω<sub>2</sub>'', etc.; the latter are called [[harmonics]], as well as more complicated terms at frequencies of M''ω<sub>1</sub>'' + N''ω<sub>2</sub>'', called [[intermodulation product]]s.    These unwanted frequencies, along with the unwanted heterodyne frequency, must be filtered out of the mixer output by an [[electronic filter]] to leave the desired heterodyne.
 
==See also==
* [[Beat receptor]]
* [[Direct-conversion receiver]] - heterodyne conversion of a signal directly to baseband instead of to an intermediate frequency
* [[Heterodyne detection]]
* [[Optical heterodyne detection]]
* [[Beat (acoustics)]]
* [[Edwin Howard Armstrong]]
* [[Electroencephalography]]
* [[Homodyne]]
* [[Superheterodyne receiver]]
* [[Transverter]]
* [[Intermodulation]] - a problem with strong higher-order terms produced in some non-linear mixers
 
==Notes==
{{Reflist|30em}}
 
==References==
*{{Citation |inventor-last=Fessenden |inventor-first=Reginald A. |inventorlink=Reginald Fessenden |title=Electric Signaling Apparatus |country-code=US |patent-number=1050441 |issue-date=January 14, 1913 |publication-date=July 27, 1905 |ref=CITEREFFessenden1905 }}
* {{Citation |last=Glinsky |first=Albert |title=Theremin: Ether Music and Espionage |location=Urbana, IL |publisher=University of Illinois Press |year=2000 |isbn=0-252-02582-2 |doi= }}
* {{Citation |last=Nahin |first=Paul J. |title=The Science of Radio with Matlab and Electronics Workbench Demonstrations |edition=second |location=New York |publisher=Springer-Verlag, AIP Press |year=2001 |isbn=0-387-95150-4 |url=http://books.google.com/books?id=V1GBW6UD4CcC&printsec=frontcover#v=onepage&q&f=false |doi= }}
 
==External links==
*{{Citation |first=John V. L. |last=Hogan |journal=Electric Journal |title=The Heterodyne Receiver |date=April 1921 |volume=18 |issue= |page=116 |url=http://archive.org/details/electricjournal18elecuoft }}
*{{Citation |inventor-last=Fessenden |inventor-first=Reginald A. |inventorlink=Reginald Fessenden |title=Wireless Signaling |country-code=US |patent-number= 706740 |issue-date=August 12, 1902 |publication-date= September 28, 1901 }}
*{{Citation |inventor-last=Fessenden |inventor-first=Reginald A. |inventorlink=Reginald Fessenden |title=Method of Signaling |country-code=US |patent-number=1050728 |issue-date=January 14, 1913 |publication-date=August 21, 1906 }}
 
[[Category:Frequency mixers]]
[[Category:Signal processing]]

Revision as of 23:21, 29 January 2014

29 yr old Orthopaedic Surgeon Grippo from Saint-Paul, spends time with interests including model railways, top property developers in singapore developers in singapore and dolls. Finished a cruise ship experience that included passing by Runic Stones and Church.

Frequency Mixer Symbol.

Heterodyning is a radio signal processing technique invented in 1901 by Canadian inventor-engineer Reginald Fessenden, in which new frequencies are created by combining or mixing two frequencies.[1][2][3] Heterodyning is useful for frequency shifting signals into a new frequency range, and is also involved in the processes of modulation and demodulation.[2][4] The two frequencies are combined in a nonlinear signal-processing device such as a vacuum tube, transistor, or diode, usually called a mixer.[2] In the most common application, two signals at frequencies f1 and f2 are mixed, creating two new signals, one at the sum f1 + f2 of the two frequencies, and the other at the difference f1f2.[3] These new frequencies are called heterodynes. Typically only one of the new frequencies is desired, and the other signal is filtered out of the output of the mixer. Heterodynes are related to the phenomenon of "beats" in acoustics.

History

In 1901, Reginald Fessenden demonstrated a direct-conversion heterodyne receiver or beat receiver as a method of making continuous wave radiotelegraphy signals audible. Fessenden's receiver did not see much application because of its local oscillator's stability problem. While complex isochronous electromechanical oscillators existed, a stable yet inexpensive local oscillator would not be available until Lee de Forest's invention of the triode vacuum tube oscillator.[5] In a 1905 patent, Fessenden stated the frequency stability of his local oscillator was one part per thousand.[6]

Early spark gap radio transmitters sent information exclusively by means of radio telegraphy. In radio telegraphy, the characters of text messages are translated into the short duration dots and long duration dashes of Morse code that are broadcast as bursts of radio waves. The heterodyne detector was not needed to hear the signals produced by these spark gap transmitters. The transmitted damped wave signals were amplitude modulated at an audio frequency by the spark. A simple detector produced an audible buzzing sound in the radiotelegraph operator's headphones that could be transcribed back into alpha-numeric characters.

With the advent of the arc converter, continuous wave (CW) transmitters were adopted. CW Morse code signals are not amplitude modulated, so a different detector was needed. The direct-conversion detector was invented to make continuous wave radio-frequency signals audible.[7]

The "heterodyne" or "beat" receiver has a local beat frequency oscillator (BFO) that produces a radio signal adjusted to be close in frequency to the incoming signal being received. When the two signals are mixed, a "beat" frequency equal to the difference between the two frequencies is created. By adjusting the local oscillator frequency correctly, the beat frequency is in the audio range, and can be heard as a tone in the receiver's earphones whenever the transmitter signal is present. Thus the Morse code "dots" and "dashes" are audible as beeping sounds. This technique is still used in radio telegraphy, the local oscillator now being called the beat frequency oscillator or BFO. Fessenden coined the word heterodyne from the Greek roots hetero- "different", and dyn- "power" (cf. δύναμις or dunamis).[8]

Superheterodyne receiver

The most important and widely used application of the heterodyne technique is in the superheterodyne receiver (superhet), invented by U.S. engineer Edwin Howard Armstrong in 1918. In this circuit, the incoming radio frequency signal from the antenna is mixed with a signal from a local oscillator and converted by the heterodyne technique to a somewhat lower fixed frequency signal called the intermediate frequency (IF). This IF signal is amplified and filtered, before being applied to a detector which extracts the audio signal, which is sent to the loudspeaker.

The advantage of this technique is that the different frequencies of the different stations received are all converted to the same IF frequency before amplification and filtering. The complicated amplifier and bandpass filter stages, which in previous receivers had to be made tunable to work at the different station frequencies, in the superheterodyne can be built to work at one fixed frequency, the IF, simplifying their design. Another advantage is that the IF is at a considerably lower frequency than the RF frequency of the incoming radio signal.

The superior superheterodyne system replaced the earlier TRF and regenerative receiver designs, and since the 1930s almost all commercial radio receivers have been superheterodynes.

Applications

Heterodyning is used very widely in communications engineering to generate new frequencies and move information from one frequency channel to another. Besides its use in the superheterodyne circuit which is found in almost all radio and television receivers, it is used in radio transmitters, modems, satellite communications and set-top boxes, radar, radio telescopes, telemetry systems, cell phones, cable television converter boxes and headends, microwave relays, metal detectors, atomic clocks, and military electronic countermeasures (jamming) systems.

Up and down converters

In large scale telecommunication networks such as telephone network trunks, microwave relay networks, cable television systems, and communication satellite links, large bandwidth capacity links are shared by many individual communication channels by using heterodyning to move the frequency of the individual signals up to different frequencies, which share the channel. This is called frequency division multiplexing (FDM).

For example, a coaxial cable used by a cable television system can carry 500 television channels at the same time because each one is given a different frequency, so they don't interfere with one another. At the cable source or headend, electronic upconverters convert each incoming television channel to a new, higher frequency. They do this by mixing the television signal frequency, fCH with a local oscillator at a much higher frequency fLO, creating a heterodyne at the sum fCH+fLO, which is added to the cable. At the consumer's home, the cable set top box has a downconverter that mixes the incoming signal at frequency fCH+fLO with the same local oscillator frequency fLO creating the difference heterodyne, converting the television channel back to its original frequency: (fCH+fLO) − fLO = fCH. Each channel is moved to a different higher frequency. The original lower basic frequency of the signal is called the baseband, while the higher channel it is moved to is called the passband.

Analog videotape recording

Many analog videotape systems rely on a downconverted color subcarrier in order to record color information in their limited bandwidth. These systems are referred to as "heterodyne systems" or "color-under systems". For instance, for NTSC video systems, the VHS (and S-VHS) recording system converts the color subcarrier from the NTSC standard 3.58 MHz to ~629 kHz.[9] PAL VHS color subcarrier is similarly downconverted (but from 4.43 MHz). The now-obsolete 3/4" U-matic systems use a heterodyned ~688 kHz subcarrier for NTSC recordings (as does Sony's Betamax, which is at its basis a 1/2″ consumer version of U-matic), while PAL U-matic decks came in two mutually incompatible varieties, with different subcarrier frequencies, known as Hi-Band and Low-Band. Other videotape formats with heterodyne color systems include Video-8 and Hi8.[10]

The heterodyne system in these cases is used to convert quadrature phase-encoded and amplitude modulated sine waves from the broadcast frequencies to frequencies recordable in less than 1 MHz bandwidth. On playback, the recorded color information is heterodyned back to the standard subcarrier frequencies for display on televisions and for interchange with other standard video equipment.

Some U-matic (3/4″) decks feature 7-pin mini-DIN connectors to allow dubbing of tapes without a heterodyne up-conversion and down-conversion, as do some industrial VHS, S-VHS, and Hi8 recorders.

Music synthesis

The theremin, an electronic musical instrument, traditionally uses the heterodyne principle to produce a variable audio frequency in response to the movement of the musician's hands in the vicinity of one or more antennas, which act both as capacitor plates. The output of a fixed radio frequency oscillator is mixed with that of an oscillator whose frequency is affected by the variable capacitance between the antenna and the thereminist as that person moves her or his hand near the pitch control antenna. The difference between the two oscillator frequencies produces a tone in the audio range.

The Ring modulator is a type of heterodyne incorporated into some synthesizers or used as a stand-alone audio effect.

Optical heterodyning

Optical heterodyne detection (an area of active research) is an extension of the heterodyning technique to higher (visible) frequencies. This technique could greatly improve optical modulators, increasing the density of information carried by optical fibers. It is also being applied in the creation of more accurate atomic clocks based on directly measuring the frequency of a laser beam. See NIST subtopic 9.07.9-4.R for a description of research on one system to do this.[11][12]

Since optical frequencies are far beyond the manipulation capacity of any feasible electronic circuit, all photon detectors are inherently energy detectors not oscillating electric field detectors. However, since energy detection is inherently "square-law" detection, it intrinsically mixes any optical frequencies present on the detector. Thus, sensitive detection of specific optical frequencies necessitates optical heterodyne detection, in which two different (close-by) wavelengths of light illuminate the detector so that the oscillating electrical output corresponds to the difference between their frequencies. This allows extremely narrow band detection (much narrower than any possible color filter can achieve) as well as precision measurements of phase and frequency of a light signal relative to a reference light source, as in a laser Doppler vibrometer.

This phase sensitive detection has been applied for Doppler measurements of wind speed, and imaging through dense media. The high sensitivity against background light is especially useful for LIDAR.

In optical Kerr effect (OKE) spectroscopy, optical heterodyning of the OKE signal and a small part of the probe signal produces a mixed signal consisting of probe, heterodyne OKE-probe and homodyne OKE signal. The probe and homodyne OKE signals can be filtered out, leaving the heterodyne signal for detection.

Mathematical principle

Heterodyning is based on the trigonometric identity:

The product on the left hand side represents the multiplication ("mixing") of a sine wave with another sine wave. The right hand side shows that the resulting signal is the difference of two sinusoidal terms, one at the sum of the two original frequencies, and one at the difference, which can be considered to be separate signals.

Using this trigonometric identity, the result of multiplying two sine wave signals, and can be calculated:

The result is the sum of two sinusoidal signals, one at the sum f1 + f2 and one at the difference f1 - f2 of the original frequencies

Mixer

The two signals are combined in a device called a mixer. It can be seen from the previous section that an ideal mixer would be a device that multiplies the two signals. Some widely used mixer circuits, such as the Gilbert cell, operate in this way, but they are limited to lower frequencies. However, any nonlinear electronic component will also multiply signals applied to it, producing heterodyne frequencies in its output, so a variety of nonlinear components are used as mixers. A nonlinear component is one in which the output current or voltage is a nonlinear function of its input. Most circuit elements in communications circuits are designed to be linear. This means they obey the superposition principle; if F(v) is the output of a linear element with an input of v:

So if two sine wave signals at frequencies f1 and f2 are applied to a linear device, the output is simply the sum of the outputs when the two signals are applied separately with no product terms. So the function F must be nonlinear to create heterodynes (mixer products). A perfect multiplier only produces mixer products at the sum and difference frequencies (f1±f2), but more general nonlinear functions produce higher order mixer products: nf1+mf2 for integers n and m. Some mixer designs, such as double-balanced mixers, suppress some high order undesired products, while other designs, such as harmonic mixers exploit high order differences.

Examples of nonlinear components that are used as mixers are vacuum tubes and transistors biased near cutoff (class C), and diodes. Ferromagnetic core inductors driven into saturation can also be used at lower frequencies. In nonlinear optics, crystals that have nonlinear characteristics are used to mix laser light beams to create heterodynes at optical frequencies.

Output of a mixer

To demonstrate mathematically how a nonlinear component can multiply signals and generate heterodyne frequencies, the nonlinear function F can be expanded in a power series (MacLaurin series):

To simplify the math, the higher order terms above α2 will be indicated by an ellipsis (". . .") and only the first terms will be shown. Applying the two sine waves at frequencies ω1 = 2πf1 and ω2 = 2πf2 to this device:

It can be seen that the second term above contains a product of the two sine waves. Simplifying with trigonometric identities:

So the output contains sinusoidal terms with frequencies at the sum ω1 + ω2 and difference ω1 - ω2 of the two original frequencies. It also contains terms at the original frequencies and at multiples of the original frequencies 2ω1, 2ω2, 3ω1, 3ω2, etc.; the latter are called harmonics, as well as more complicated terms at frequencies of Mω1 + Nω2, called intermodulation products. These unwanted frequencies, along with the unwanted heterodyne frequency, must be filtered out of the mixer output by an electronic filter to leave the desired heterodyne.

See also

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

External links

  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
  1. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  2. 2.0 2.1 2.2 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  3. 3.0 3.1 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  4. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  5. Template:Harvnb, stating "Fessenden's circuit was ahead of its time, however, as there simply was no technology available then with which to build the required local oscillator with the necessary frequency stability." Figure 7.10 shows a simplified 1907 heterodyne detector.
  6. Template:Harvnb
  7. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  8. Tapan K. Sarkar, History of wireless, page 372
  9. Videotape formats using Template:Convert tape ; Retrieved 2007-01-01
  10. Poynton, Charles. Digital Video and HDTV: Algorithms and Interfaces San Francisco: Morgan Kaufmann Publishers, 2003 PP 582, 583 ISBN 1-55860-792-7
  11. Contract Details: Robust Nanopopous Ceramic Microsensor Platform
  12. Contract Details: High Pulsed Power Varactor Multipliers for Imaging