Heterodyne
Encyclopedia
Heterodyning is a radio
signal processing
technique invented in 1901 by Canadian inventor-engineer Reginald Fessenden
where high frequency signals are converted to lower frequencies by combining two frequencies. Heterodyning is useful for frequency shifting information of interest into a useful frequency range following modulation
or prior to demodulation
. The two frequencies are combined in a vacuum tube
, transistor
, diode
, or other non-linear signal processing device. Heterodyning creates two new frequencies, according to the properties of the sine function; one is the sum of the two frequencies mixed, the other is their difference. These new frequencies are called heterodynes. Typically only one of the new frequencies is desired—the higher one after modulation, and the lower one after demodulation. The other signal is filtered
out of the output of the mixer.
in 1901, but was not pursued very far because the local oscillators being used at the time were unstable. The technique was invented as a means to make Morse code
radiotelegraph (Continuous wave
) signals used during the wireless telegraphy
era audible. A "heterodyne" or "beat" receiver has a local oscillator
(LO), that produces a radio signal adjusted to be close in frequency to the incoming signal being received. When the two signals are mixed the difference or a "beat" frequency exists in the audible range. This conjoint action of two radio-frequency oscillations produces a musical tone in a telephonic receiver or loud speaker. 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. dynamis).
An improvement on the heterodyne receiver is the superheterodyne receiver
(superhet), invented by Edwin Howard Armstrong in 1918. It converts the incoming Radio Frequency
(RF) signal to a fixed Intermediate Frequency
(IF), using the heterodyne technique. The difference between the superhet and Fessenden's heterodyne is the use of a tunable RF filter on the front end, a mixer
circuit, a stable local oscillator, and a fixed frequency high-gain band-pass amplifier
. The original heterodyne technique tried to accomplish all of this in one stage thus producing an unstable amplifier.
s, satellite
communications and set-top boxes, radar
, radio telescope
s, telemetry
systems, cell phones, cable television
converter boxes and headends
, microwave relays, metal detector
s, atomic clock
s, and military electronic countermeasures
(jamming) systems.
or passband
. Typically, a down-converter is used on the receiving end to transform the signal from the passband
back to the baseband
for further processing.
The local oscillator frequency is
, with 
being the carrier frequency. This results in a scaling of the received signal by 
and a phase shifting by 
to the left, so that the resulting signal is located in the baseband.
A radio frequency upconverter is a device that takes an input of radio frequency
energy of a specific frequency
range and outputs it on a higher frequency. Likewise, downconverters take an input frequency and reduce it to a lower output frequency. Both converters are commonly used in transverter
s and satellite communications. Upconverters achieve this frequency conversion via heterodyning, the same principle as modern receivers and transmitters to offset the frequency.
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. 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.
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 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.
, an electronic musical instrument
, uses the heterodyne principle to produce a variable audio frequency
in response to the movement of the musician
's hands in the vicinity of some antennas
. 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.
(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.
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 Laser Doppler Vibrometry.
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.
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
The two signals are multiplied in the mixer
. In order to multiply the signals, the mixer must be a nonlinear component, that is, its output current or voltage must be 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 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. Examples of nonlinear components that are used as mixers are vacuum tube
s and transistor
s biased near cutoff (class C), and diode
s. For lower frequencies, IC analog multiplier
s can be used which multiply signals precisely. Ferromagnetic core
inductor
s driven into saturation
can also be used. In nonlinear optics
, crystals that have nonlinear characteristics are used to mix laser
light beams to create heterodynes at optical frequencies.
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. These unwanted frequencies, along with the unwanted heterodyne frequency, must be filtered out of the mixer output to leave the desired heterodyne.
Radio
Radio is the transmission of signals through free space by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...
signal processing
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
technique invented in 1901 by Canadian inventor-engineer Reginald Fessenden
Reginald Fessenden
Reginald Aubrey Fessenden , a naturalized American citizen born in Canada, was an inventor who performed pioneering experiments in radio, including early—and possibly the first—radio transmissions of voice and music...
where high frequency signals are converted to lower frequencies by combining two frequencies. Heterodyning is useful for frequency shifting information of interest into a useful frequency range following modulation
Modulation
In electronics and telecommunications, modulation is the process of varying one or more properties of a high-frequency periodic waveform, called the carrier signal, with a modulating signal which typically contains information to be transmitted...
or prior to demodulation
Demodulation
Demodulation is the act of extracting the original information-bearing signal from a modulated carrier wave.A demodulator is an electronic circuit that is used to recover the information content from the modulated carrier wave.These terms are traditionally used in connection with radio receivers,...
. The two frequencies are combined in a vacuum tube
Vacuum tube
In electronics, a vacuum tube, electron tube , or thermionic valve , reduced to simply "tube" or "valve" in everyday parlance, is a device that relies on the flow of electric current through a vacuum...
, transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...
, diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...
, or other non-linear signal processing device. Heterodyning creates two new frequencies, according to the properties of the sine function; one is the sum of the two frequencies mixed, the other is their difference. These new frequencies are called heterodynes. Typically only one of the new frequencies is desired—the higher one after modulation, and the lower one after demodulation. The other signal is filtered
Filter (signal processing)
In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal...
out of the output of the mixer.
History
The heterodyne technique was pioneered by Canadian inventor-engineer Reginald FessendenReginald Fessenden
Reginald Aubrey Fessenden , a naturalized American citizen born in Canada, was an inventor who performed pioneering experiments in radio, including early—and possibly the first—radio transmissions of voice and music...
in 1901, but was not pursued very far because the local oscillators being used at the time were unstable. The technique was invented as a means to make Morse code
Morse code
Morse code is a method of transmitting textual information as a series of on-off tones, lights, or clicks that can be directly understood by a skilled listener or observer without special equipment...
radiotelegraph (Continuous wave
Continuous wave
A continuous wave or continuous waveform is an electromagnetic wave of constant amplitude and frequency; and in mathematical analysis, of infinite duration. Continuous wave is also the name given to an early method of radio transmission, in which a carrier wave is switched on and off...
) signals used during the wireless telegraphy
Wireless telegraphy
Wireless telegraphy is a historical term used today to apply to early radio telegraph communications techniques and practices, particularly those used during the first three decades of radio before the term radio came into use....
era audible. A "heterodyne" or "beat" receiver has a local oscillator
Local oscillator
A local oscillator is an electronic device used to generate a signal normally for the purpose of converting a signal of interest to a different frequency using a mixer. This process of frequency conversion, also referred to as heterodyning, produces the sum and difference frequencies of the...
(LO), that produces a radio signal adjusted to be close in frequency to the incoming signal being received. When the two signals are mixed the difference or a "beat" frequency exists in the audible range. This conjoint action of two radio-frequency oscillations produces a musical tone in a telephonic receiver or loud speaker. 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. dynamis).
An improvement on the heterodyne receiver is the superheterodyne receiver
Superheterodyne receiver
In electronics, a superheterodyne receiver uses frequency mixing or heterodyning to convert a received signal to a fixed intermediate frequency, which can be more conveniently processed than the original radio carrier frequency...
(superhet), invented by Edwin Howard Armstrong in 1918. It converts the incoming Radio Frequency
Radio frequency
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...
(RF) signal to a fixed Intermediate Frequency
Intermediate frequency
In communications and electronic engineering, an intermediate frequency is a frequency to which a carrier frequency is shifted as an intermediate step in transmission or reception. The intermediate frequency is created by mixing the carrier signal with a local oscillator signal in a process called...
(IF), using the heterodyne technique. The difference between the superhet and Fessenden's heterodyne is the use of a tunable RF filter on the front end, a mixer
Frequency mixer
In electronics a mixer or frequency mixer is a nonlinear electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals at frequencies f1 and f2 are applied to a mixer, and it produces new signals at the sum f1 + f2 and difference f1 -...
circuit, a stable local oscillator, and a fixed frequency high-gain band-pass amplifier
Amplifier
Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...
. The original heterodyne technique tried to accomplish all of this in one stage thus producing an unstable amplifier.
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, modemModem
A modem is a device that modulates an analog carrier signal to encode digital information, and also demodulates such a carrier signal to decode the transmitted information. The goal is to produce a signal that can be transmitted easily and decoded to reproduce the original digital data...
s, satellite
Satellite
In the context of spaceflight, a satellite is an object which has been placed into orbit by human endeavour. Such objects are sometimes called artificial satellites to distinguish them from natural satellites such as the Moon....
communications and set-top boxes, radar
Radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...
, radio telescope
Radio telescope
A radio telescope is a form of directional radio antenna used in radio astronomy. The same types of antennas are also used in tracking and collecting data from satellites and space probes...
s, telemetry
Telemetry
Telemetry is a technology that allows measurements to be made at a distance, usually via radio wave transmission and reception of the information. The word is derived from Greek roots: tele = remote, and metron = measure...
systems, cell phones, cable television
Cable television
Cable television is a system of providing television programs to consumers via radio frequency signals transmitted to televisions through coaxial cables or digital light pulses through fixed optical fibers located on the subscriber's property, much like the over-the-air method used in traditional...
converter boxes and headends
Cable television headend
A cable television headend is a master facility for receiving television signals for processing and distribution over a cable television system. The headend facility is normally unstaffed and surrounded by some type of security fencing and is typically a building or large shed housing electronic...
, microwave relays, metal detector
Metal detector
A metal detector is a device which responds to metal that may not be readily apparent.The simplest form of a metal detector consists of an oscillator producing an alternating current that passes through a coil producing an alternating magnetic field...
s, atomic clock
Atomic clock
An atomic clock is a clock that uses an electronic transition frequency in the microwave, optical, or ultraviolet region of the electromagnetic spectrum of atoms as a frequency standard for its timekeeping element...
s, and military electronic countermeasures
Electronic countermeasures
An electronic countermeasure is an electrical or electronic device designed to trick or deceive radar, sonar or other detection systems, like infrared or lasers. It may be used both offensively and defensively to deny targeting information to an enemy...
(jamming) systems.
Up and down converters
In digital communications signals can be transmitted in basebandBaseband
In telecommunications and signal processing, baseband is an adjective that describes signals and systems whose range of frequencies is measured from close to 0 hertz to a cut-off frequency, a maximum bandwidth or highest signal frequency; it is sometimes used as a noun for a band of frequencies...
or passband
Passband
A passband is the range of frequencies or wavelengths that can pass through a filter without being attenuated.A bandpass filtered signal , is known as a bandpass signal, as opposed to a baseband signal....
. Typically, a down-converter is used on the receiving end to transform the signal from the passband
Passband
A passband is the range of frequencies or wavelengths that can pass through a filter without being attenuated.A bandpass filtered signal , is known as a bandpass signal, as opposed to a baseband signal....
back to the baseband
Baseband
In telecommunications and signal processing, baseband is an adjective that describes signals and systems whose range of frequencies is measured from close to 0 hertz to a cut-off frequency, a maximum bandwidth or highest signal frequency; it is sometimes used as a noun for a band of frequencies...
for further processing.
The local oscillator frequency is
, with being the carrier frequency. This results in a scaling of the received signal by and a phase shifting by to the left, so that the resulting signal is located in the baseband.A radio frequency upconverter is a device that takes an input of radio frequency
Radio frequency
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...
energy of a specific frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
range and outputs it on a higher frequency. Likewise, downconverters take an input frequency and reduce it to a lower output frequency. Both converters are commonly used in transverter
Transverter
A transverter is a radio frequency device that consists of an upconverter and a downconverter in one unit. Transverters are used in conjunction with transceivers to change the range of frequencies over which the transceiver can communicate....
s and satellite communications. Upconverters achieve this frequency conversion via heterodyning, the same principle as modern receivers and transmitters to offset the frequency.
Analog videotape recording
Many analog videotapeVideotape
A videotape is a recording of images and sounds on to magnetic tape as opposed to film stock or random access digital media. Videotapes are also used for storing scientific or medical data, such as the data produced by an electrocardiogram...
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
NTSC
NTSC, named for the National Television System Committee, is the analog television system that is used in most of North America, most of South America , Burma, South Korea, Taiwan, Japan, the Philippines, and some Pacific island nations and territories .Most countries using the NTSC standard, as...
video systems, the VHS
VHS
The Video Home System is a consumer-level analog recording videocassette standard developed by Victor Company of Japan ....
(and S-VHS
S-VHS
S-VHS is an improved version of the VHS standard for consumer-level analog recording videocassettes. It was introduced by JVC in Japan in April 1987 with the HR-S7000 VCR and certain overseas markets soon afterwards...
) recording system converts the color subcarrier from the NTSC standard 3.58 MHz to ~629 kHz. PAL
PAL
PAL, short for Phase Alternating Line, is an analogue television colour encoding system used in broadcast television systems in many countries. Other common analogue television systems are NTSC and SECAM. This page primarily discusses the PAL colour encoding system...
VHS color subcarrier is similarly downconverted (but from 4.43 MHz). The now-obsolete 3/4" U-matic
U-matic
U-matic is an analog recording videocassette format first shown by Sony in prototype in October 1969, and introduced to the market in September 1971. It was among the first video formats to contain the videotape inside a cassette, as opposed to the various Reel-to-Reel or open-reel formats of the...
systems use a heterodyned ~688 kHz subcarrier for NTSC recordings (as does Sony
Sony
, commonly referred to as Sony, is a Japanese multinational conglomerate corporation headquartered in Minato, Tokyo, Japan and the world's fifth largest media conglomerate measured by revenues....
's Betamax
Betamax
Betamax was a consumer-level analog videocassette magnetic tape recording format developed by Sony, released on May 10, 1975. The cassettes contain -wide videotape in a design similar to the earlier, professional wide, U-matic format...
, 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.
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 connector
DIN connector
A DIN connector is a connector that was originally standardized by the , the German national standards organization. There are DIN standards for a large number of different connectors, therefore the term "DIN connector" alone does not unambiguously identify any particular type of connector unless...
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 thereminTheremin
The theremin , originally known as the aetherphone/etherophone, thereminophone or termenvox/thereminvox is an early electronic musical instrument controlled without discernible physical contact from the player. It is named after its Russian inventor, Professor Léon Theremin, who patented the device...
, an electronic musical instrument
Electronic musical instrument
An electronic musical instrument is a musical instrument that produces its sounds using electronics. Such an instrument sounds by outputting an electrical audio signal that ultimately drives a loudspeaker....
, uses the heterodyne principle to produce a variable audio frequency
Audio frequency
An audio frequency or audible frequency is characterized as a periodic vibration whose frequency is audible to the average human...
in response to the movement of the musician
Musician
A musician is an artist who plays a musical instrument. It may or may not be the person's profession. Musicians can be classified by their roles in performing music and writing music.Also....* A person who makes music a profession....
's hands in the vicinity of some antennas
Antenna (radio)
An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
. 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 detectionOptical heterodyne detection
Optical heterodyne detection is an important special case of heterodyne detection. In heterodyne detection, a signal of interest at some frequency is non-linearly mixed with a reference "local oscillator" that is set at a close-by frequency...
(an area of active research) is an extension of the heterodyning technique to higher (visible) frequencies. This technique could greatly improve optical modulator
Optical modulator
An optical modulator is a device which is used to modulate a beam of light. The beam may be carried over free space, or propagated through an optical waveguide. Depending on the parameter of a light beam which is manipulated, modulators may be categorized into amplitude modulators, phase...
s, increasing the density of information carried by optical fiber
Optical fiber
An optical fiber is a flexible, transparent fiber made of a pure glass not much wider than a human hair. It functions as a waveguide, or "light pipe", to transmit light between the two ends of the fiber. The field of applied science and engineering concerned with the design and application of...
s. It is also being applied in the creation of more accurate atomic clock
Atomic clock
An atomic clock is a clock that uses an electronic transition frequency in the microwave, optical, or ultraviolet region of the electromagnetic spectrum of atoms as a frequency standard for its timekeeping element...
s based on directly measuring the frequency of a laser beam.
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
Optical heterodyne detection
Optical heterodyne detection is an important special case of heterodyne detection. In heterodyne detection, a signal of interest at some frequency is non-linearly mixed with a reference "local oscillator" that is set at a close-by frequency...
, 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 Laser Doppler Vibrometry.
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
LIDAR
LIDAR is an optical remote sensing technology that can measure the distance to, or other properties of a target by illuminating the target with light, often using pulses from a laser...
.
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
Sine wave
The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...
with another sine wave
Sine wave
The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...
. 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
The two signals are multiplied in the mixer
Frequency mixer
In electronics a mixer or frequency mixer is a nonlinear electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals at frequencies f1 and f2 are applied to a mixer, and it produces new signals at the sum f1 + f2 and difference f1 -...
. In order to multiply the signals, the mixer must be a nonlinear component, that is, its output current or voltage must be a nonlinear function of its input. Most circuit elements in communications circuits are designed to be linear
Linear circuit
A linear circuit is an electronic circuit in which, for a sinusoidal input voltage of frequency f, any output of the circuit is also sinusoidal with frequency f...
. This means they obey the superposition principle
Superposition principle
In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...
; if F(v) is the output of a linear element with an input of v:
So if two sine wave signals 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. Examples of nonlinear components that are used as mixers are vacuum tube
Vacuum tube
In electronics, a vacuum tube, electron tube , or thermionic valve , reduced to simply "tube" or "valve" in everyday parlance, is a device that relies on the flow of electric current through a vacuum...
s and transistor
Transistor
A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...
s biased near cutoff (class C), and diode
Diode
In electronics, a diode is a type of two-terminal electronic component with a nonlinear current–voltage characteristic. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material connected to two electrical terminals...
s. For lower frequencies, IC analog multiplier
Analog multiplier
In electronics, an analog multiplier is a device which takes two analog signals and produces an output which is their product. Such circuits can be used to implement related functions such as squares , and square roots....
s can be used which multiply signals precisely. Ferromagnetic core
Magnetic core
A magnetic core is a piece of magnetic material with a high permeability used to confine and guide magnetic fields in electrical, electromechanical and magnetic devices such as electromagnets, transformers, electric motors, inductors and magnetic assemblies. It is made of ferromagnetic metal such...
inductor
Inductor
An inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...
s driven into saturation
Saturation (magnetic)
Seen in some magnetic materials, saturation is the state reached when an increase in applied external magnetizing field H cannot increase the magnetization of the material further, so the total magnetic field B levels off...
can also be used. In nonlinear optics
Nonlinear optics
Nonlinear optics is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light...
, crystals that have nonlinear characteristics are used to mix laser
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
light beams to create heterodynes at optical frequencies.
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. These unwanted frequencies, along with the unwanted heterodyne frequency, must be filtered out of the mixer output to leave the desired heterodyne.
See also
- Optical heterodyne detectionOptical heterodyne detectionOptical heterodyne detection is an important special case of heterodyne detection. In heterodyne detection, a signal of interest at some frequency is non-linearly mixed with a reference "local oscillator" that is set at a close-by frequency...
- Beat (acoustics)Beat (acoustics)In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies....
- Edwin Howard Armstrong
- ElectroencephalographyElectroencephalographyElectroencephalography is the recording of electrical activity along the scalp. EEG measures voltage fluctuations resulting from ionic current flows within the neurons of the brain...
- Heterodyne detectionHeterodyne detectionHeterodyne detection is a method of detecting radiation by non-linear mixing with radiation of a reference frequency. It is commonly used in telecommunications and astronomy for detecting and analysing signals....
- Homodyne
- Superheterodyne receiverSuperheterodyne receiverIn electronics, a superheterodyne receiver uses frequency mixing or heterodyning to convert a received signal to a fixed intermediate frequency, which can be more conveniently processed than the original radio carrier frequency...
- TransverterTransverterA transverter is a radio frequency device that consists of an upconverter and a downconverter in one unit. Transverters are used in conjunction with transceivers to change the range of frequencies over which the transceiver can communicate....
- IntermodulationIntermodulationIntermodulation or intermodulation distortion is the amplitude modulation of signals containing two or more different frequencies in a system with nonlinearities...
- a problem with strong higher-order terms produced in some non-linear mixers