Heterodyning is a radio arresting processing address invented in 1901 by Canadian inventor-engineer Reginald Fessenden area top abundance signals are adapted to lower frequencies by accumulation two frequencies.1 Heterodyning is advantageous for abundance alive advice of absorption into a advantageous abundance ambit afterward accentuation or above-mentioned to demodulation. The two frequencies are accumulated in a exhaustion tube, transistor, diode, or added non-linear arresting processing device. Heterodyning creates two new frequencies, according to the backdrop of the sine function; one is the sum of the two frequencies mixed, the added is their difference. These new frequencies are alleged heterodynes. Typically alone one of the new frequencies is desired—the college one afterwards modulation, and the lower one afterwards demodulation. The added arresting is filtered out of the achievement of the mixer.
Tuesday, February 7, 2012
History
The heterodyne address was approved by Canadian inventor-engineer Reginald Fessenden in 1901, but was not pursued actual far because the bounded oscillators getting acclimated at the time were unstable.2 The address was invented as a agency to achieve Morse cipher radiotelegraph (Continuous wave) signals acclimated during the wireless telegraphy era audible.3 A "heterodyne" or "beat" receiver has a bounded oscillator (LO), that produces a radio arresting adapted to be abutting in abundance to the admission arresting getting received. When the two signals are alloyed the aberration or a "beat" abundance exists in the aural range. This aggregate activity of two radio-frequency oscillations produces a accent in a telephonic receiver or loud speaker. The Morse cipher "dots" and "dashes" are aural as beeping sounds. This address is still acclimated in radio telegraphy, the bounded oscillator now getting alleged the exhausted abundance oscillator or BFO. Fessenden coined the chat heterodyne from the Greek roots hetero- "different", and dyn- "power" (cf. dynamis).4
An advance on the heterodyne receiver is the superheterodyne receiver (superhet), invented by Edwin Howard Armstrong in 1918. It converts the admission Radio Abundance (RF) arresting to a anchored Intermediate Abundance (IF), application the heterodyne technique. The aberration amid the superhet and Fessenden's heterodyne is the use of a tunable RF clarify on the foreground end, a mixer circuit, a abiding bounded oscillator, and a anchored abundance high-gain band-pass amplifier.5 The aboriginal heterodyne address approved to achieve all of this in one date appropriately bearing an ambiguous amplifier.
An advance on the heterodyne receiver is the superheterodyne receiver (superhet), invented by Edwin Howard Armstrong in 1918. It converts the admission Radio Abundance (RF) arresting to a anchored Intermediate Abundance (IF), application the heterodyne technique. The aberration amid the superhet and Fessenden's heterodyne is the use of a tunable RF clarify on the foreground end, a mixer circuit, a abiding bounded oscillator, and a anchored abundance high-gain band-pass amplifier.5 The aboriginal heterodyne address approved to achieve all of this in one date appropriately bearing an ambiguous amplifier.
Applications
Heterodyning is acclimated actual broadly in communications engineering to accomplish new frequencies and move advice from one abundance approach to another. Besides its use in the superheterodyne ambit which is begin in about all radio and television receivers, it is acclimated in radio transmitters, modems, agenda communications and set-top boxes, radar, radio telescopes, telemetry systems, corpuscle phones, cable television advocate boxes and headends, bake relays, metal detectors, diminutive clocks, and aggressive cyberbanking countermeasures (jamming) systems.
edit Up and down converters
In agenda communications signals can be transmitted in baseband or passband. Typically, a down-converter is acclimated on the accepting end to transform the arresting from the passband aback to the baseband for added processing. The bounded oscillator abundance is \sqrt{2} e^{j2 \pi f_c t}, with fc getting the carrier frequency. This after-effects in a ascent of the accustomed arresting by \sqrt{2} and a appearance alive by fc to the left, so that the consistent arresting is amid in the baseband.
A radio abundance upconverter is a accessory that takes an ascribe of radio abundance activity of a specific abundance ambit and outputs it on a college frequency. Likewise, downconverters yield an ascribe abundance and abate it to a lower achievement frequency. Both converters are frequently acclimated in transverters and agenda communications. Upconverters accomplish this abundance about-face via heterodyning, the aforementioned assumption as avant-garde receivers and transmitters to account the frequency.
edit Analog cine recording
Many analog cine systems await on a downconverted blush subcarrier in adjustment to almanac blush advice in their bound 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 arrangement converts the blush subcarrier from the NTSC accepted 3.58 MHz to ~629 kHz.6 PAL VHS blush subcarrier is analogously 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 base a 1/2" customer adaptation of U-matic), while PAL U-matic decks came in two mutually adverse varieties, with altered subcarrier frequencies, accepted as Hi-Band and Low-Band. Added cine formats with heterodyne blush systems cover Video-8 and Hi8.7
The heterodyne arrangement in these cases is acclimated to catechumen quadrature phase-encoded and amplitude articulate sine after-effects from the advertisement frequencies to frequencies recordable in beneath than 1 MHz bandwidth. On playback, the recorded blush advice is heterodyned aback to the accepted subcarrier frequencies for affectation on televisions and for altering with added accepted video equipment.
Some U-matic (3/4") decks affection 7-pin mini-DIN connectors to acquiesce dubbing of tapes after a heterodyne up-conversion and down-conversion, as do some automated VHS, S-VHS, and Hi8 recorders.
edit Up and down converters
In agenda communications signals can be transmitted in baseband or passband. Typically, a down-converter is acclimated on the accepting end to transform the arresting from the passband aback to the baseband for added processing. The bounded oscillator abundance is \sqrt{2} e^{j2 \pi f_c t}, with fc getting the carrier frequency. This after-effects in a ascent of the accustomed arresting by \sqrt{2} and a appearance alive by fc to the left, so that the consistent arresting is amid in the baseband.
A radio abundance upconverter is a accessory that takes an ascribe of radio abundance activity of a specific abundance ambit and outputs it on a college frequency. Likewise, downconverters yield an ascribe abundance and abate it to a lower achievement frequency. Both converters are frequently acclimated in transverters and agenda communications. Upconverters accomplish this abundance about-face via heterodyning, the aforementioned assumption as avant-garde receivers and transmitters to account the frequency.
edit Analog cine recording
Many analog cine systems await on a downconverted blush subcarrier in adjustment to almanac blush advice in their bound 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 arrangement converts the blush subcarrier from the NTSC accepted 3.58 MHz to ~629 kHz.6 PAL VHS blush subcarrier is analogously 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 base a 1/2" customer adaptation of U-matic), while PAL U-matic decks came in two mutually adverse varieties, with altered subcarrier frequencies, accepted as Hi-Band and Low-Band. Added cine formats with heterodyne blush systems cover Video-8 and Hi8.7
The heterodyne arrangement in these cases is acclimated to catechumen quadrature phase-encoded and amplitude articulate sine after-effects from the advertisement frequencies to frequencies recordable in beneath than 1 MHz bandwidth. On playback, the recorded blush advice is heterodyned aback to the accepted subcarrier frequencies for affectation on televisions and for altering with added accepted video equipment.
Some U-matic (3/4") decks affection 7-pin mini-DIN connectors to acquiesce dubbing of tapes after a heterodyne up-conversion and down-conversion, as do some automated VHS, S-VHS, and Hi8 recorders.
Music synthesis
The theremin, an cyberbanking agreeable instrument, uses the heterodyne assumption to aftermath a capricious audio abundance in acknowledgment to the movement of the musician's easily in the around of some antennas. The achievement of a anchored radio abundance oscillator is alloyed with that of an oscillator whose abundance is afflicted by the capricious capacitance amid the antenna and the thereminist as that being moves her or his duke abreast the angle ascendancy antenna. The aberration amid the two oscillator frequencies produces a accent in the audio range.
The Ring modulator is a blazon of heterodyne congenital into some synthesizers or acclimated as a stand-alone audio effect.
The Ring modulator is a blazon of heterodyne congenital into some synthesizers or acclimated as a stand-alone audio effect.
Optical heterodyning
Optical heterodyne apprehension (an breadth of alive research) is an addendum of the heterodyning address to college (visible) frequencies. This address could abundantly advance optical modulators, accretion the body of advice agitated by optical fibers. It is aswell getting activated in the conception of added authentic diminutive clocks based on anon barometer the abundance of a laser beam.8
Since optical frequencies are far above the manipulation-capacity of any achievable cyberbanking circuit, all photon detectors are inherently activity detectors not aquiver electric acreage detectors. However, back activity apprehension is inherently "square-law" detection, it intrinsically mixes any optical frequencies present on the detector. Thus, acute apprehension of specific optical frequencies necessitates optical heterodyne detection, in which two altered (close-by) wavelengths of ablaze brighten the detector so that the aquiver electrical achievement corresponds to the aberration amid their frequencies. This allows acutely attenuated bandage apprehension (much narrower than any accessible blush clarify can achieve) as able-bodied as attention abstracts of appearance and abundance of a ablaze arresting about to a advertence ablaze source, as in Laser Doppler Vibrometry.
This appearance acute apprehension has been activated for Doppler abstracts of wind speed, and imaging through close media. The top acuteness adjoin accomplishments ablaze is abnormally advantageous for LIDAR.
In optical Kerr aftereffect (OKE) spectroscopy, optical heterodyning of the OKE arresting and a baby allotment of the delving arresting produces a alloyed arresting consisting of probe, heterodyne OKE-probe and homodyne OKE signal. The delving and homodyne OKE signals can be filtered out, abrogation the heterodyne arresting for detection.
Since optical frequencies are far above the manipulation-capacity of any achievable cyberbanking circuit, all photon detectors are inherently activity detectors not aquiver electric acreage detectors. However, back activity apprehension is inherently "square-law" detection, it intrinsically mixes any optical frequencies present on the detector. Thus, acute apprehension of specific optical frequencies necessitates optical heterodyne detection, in which two altered (close-by) wavelengths of ablaze brighten the detector so that the aquiver electrical achievement corresponds to the aberration amid their frequencies. This allows acutely attenuated bandage apprehension (much narrower than any accessible blush clarify can achieve) as able-bodied as attention abstracts of appearance and abundance of a ablaze arresting about to a advertence ablaze source, as in Laser Doppler Vibrometry.
This appearance acute apprehension has been activated for Doppler abstracts of wind speed, and imaging through close media. The top acuteness adjoin accomplishments ablaze is abnormally advantageous for LIDAR.
In optical Kerr aftereffect (OKE) spectroscopy, optical heterodyning of the OKE arresting and a baby allotment of the delving arresting produces a alloyed arresting consisting of probe, heterodyne OKE-probe and homodyne OKE signal. The delving and homodyne OKE signals can be filtered out, abrogation the heterodyne arresting for detection.
Mathematical principle
Heterodyning is based on the trigonometric identity:
\sin \theta \sin \varphi = \frac{1}{2}\cos(\theta - \varphi) - \frac{1}{2}\cos(\theta + \varphi)
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, \sin (2 \pi f_1 t)\, and \sin (2 \pi f_2 t)\, can be calculated:
\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 \,
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:
F(v_1 + v_2) = F(v_1) + F(v_2) \,
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 tubes and transistors biased near cutoff (class C), and diodes. For lower frequencies, IC analog multipliers can be used which multiply signals precisely. Ferromagnetic core inductors 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):
F(v) = \alpha_1 v + \alpha_2 v^2 + \alpha_3 v^3 + \ldots \,
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:
v_{out} = F(A_1 \sin \omega_1 t + A_2 \sin \omega_2 t)\,
v_{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 \,
v_{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 \,
It can be seen that the second term above contains a product of the two sine waves. Simplifying with trigonometric identities:
v_{out} = \alpha_1 (A_1 \sin \omega_1 t + A_2 \sin \omega_2 t) + \alpha_2(\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 ) + \ldots \,
v_{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 \,
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, al
\sin \theta \sin \varphi = \frac{1}{2}\cos(\theta - \varphi) - \frac{1}{2}\cos(\theta + \varphi)
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, \sin (2 \pi f_1 t)\, and \sin (2 \pi f_2 t)\, can be calculated:
\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 \,
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:
F(v_1 + v_2) = F(v_1) + F(v_2) \,
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 tubes and transistors biased near cutoff (class C), and diodes. For lower frequencies, IC analog multipliers can be used which multiply signals precisely. Ferromagnetic core inductors 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):
F(v) = \alpha_1 v + \alpha_2 v^2 + \alpha_3 v^3 + \ldots \,
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:
v_{out} = F(A_1 \sin \omega_1 t + A_2 \sin \omega_2 t)\,
v_{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 \,
v_{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 \,
It can be seen that the second term above contains a product of the two sine waves. Simplifying with trigonometric identities:
v_{out} = \alpha_1 (A_1 \sin \omega_1 t + A_2 \sin \omega_2 t) + \alpha_2(\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 ) + \ldots \,
v_{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 \,
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, al
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