Heterodyne
A heterodyne is a
In the most common application, two signals at frequencies f1 and f2 are mixed, creating two new signals, one at the sum of the two frequencies f1 + f2, and the other at the difference between the two frequencies f1 − f2.[3] The new signal frequencies are called heterodynes. Typically, only one of the heterodynes is required and the other signal is filtered out of the output of the mixer. Heterodyne frequencies are related to the phenomenon of "beats" in acoustics.[2][5][6]
A major application of the heterodyne process is in the superheterodyne radio receiver circuit, which is used in virtually all modern radio receivers.
History
In 1901,
In radio telegraphy, the characters of text messages are translated into the short duration dots and long duration dashes of
With the development of the arc converter radio transmitter in 1904, continuous wave (CW) modulation began to be used for radiotelegraphy. CW Morse code signals are not amplitude modulated, but rather consist of bursts of sinusoidal carrier frequency. When CW signals are received by an AM receiver, the operator does not hear a sound. The direct-conversion (heterodyne) detector was invented to make continuous wave radio-frequency signals audible.[10]
The "heterodyne" or "beat" receiver has a
Superheterodyne receiver
An important and widely used application of the heterodyne technique is in the superheterodyne receiver (superhet). In the typical superhet, the incoming radio frequency signal from the antenna is mixed (heterodyned) with a signal from a local oscillator (LO) to produce a lower fixed frequency signal called the intermediate frequency (IF) signal. The IF signal is amplified and filtered and then applied to a detector that extracts the audio signal; the audio is ultimately sent to the receiver's loudspeaker.
The superheterodyne receiver has several advantages over previous receiver designs. One advantage is easier tuning; only the RF filter and the LO are tuned by the operator; the fixed-frequency IF is tuned ("aligned") at the factory and is not adjusted. In older designs such as the
The superior superheterodyne system replaced the earlier TRF and regenerative receiver designs, and since the 1930s most commercial radio receivers have been superheterodynes.
Applications
Heterodyning, also called frequency conversion, is used very widely in
(jamming) systems.Up and down converters
In large scale
For example, a
Analog videotape recording
Many analog
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 conversion, as do some industrial VHS, S-VHS, and Hi8 recorders.
Music synthesis
The
The
Optical heterodyning
Optical heterodyne detection (an area of active research) is an extension of the heterodyning technique to higher (visible) frequencies. Guerra[14] (1995) first published the results of what he called a "form of optical heterodyning" in which light patterned by a 50 nm pitch grating illuminated a second grating of pitch 50 nm, with the gratings rotated with respect to each other by the angular amount needed to achieve magnification. Although the illuminating wavelength was 650 nm, the 50 nm grating was easily resolved. This showed a nearly 5-fold improvement over the Abbe resolution limit of 232 nm that should have been the smallest obtained for the numerical aperture and wavelength used. This super-resolution microscopic imaging through optical heterodyning later came to be know by many as "structured illumination microscopy".
In addition to super-resolution optical microscopy, optical heterodyning 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.[15][16]
Since optical frequencies are far beyond the manipulation capacity of any feasible electronic circuit, all visible frequency 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
Heterodyne detection is often used in interferometry but usually confined to single point detection rather than widefield interferometry, however, widefield heterodyne interferometry is possible using a special camera.[17] Using this technique which a reference signal extracted from a single pixel it is possible to build a highly stable widefield heterodyne interferometer by removing the piston phase component caused by microphonics or vibrations of the optical components or object.[18]
Mathematical principle
Heterodyning is based on the
The product on the left hand side represents the multiplication ("mixing") of a
Using this trigonometric identity, the result of multiplying two cosine wave signals and at different frequencies 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. As seen in the previous section, 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 also multiplies signals applied to it, producing heterodyne frequencies in its output—so a variety of nonlinear components serve 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 is the output of a linear element with an input of :
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. Thus, the function must be nonlinear to create 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: n⋅f1 + m⋅f2 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
Output of a mixer
To demonstrate mathematically how a nonlinear component can multiply signals and generate heterodyne frequencies, the nonlinear function can be expanded in a
To simplify the math, the higher order terms above α2 are indicated by an ellipsis () and only the first terms are 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
Which leaves the two heterodyne frequencies as two among the many terms:
along with many other terms not shown.
Among many other frequencies, 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 terms at multiples of the original frequencies 2 ω1 , 2 ω2 , 3 ω1 , 3 ω2 , etc., called
See also
- Electroencephalography
- Homodyne
- Intermodulation – a problem with strong higher-order terms produced in some non-linear mixers
- Transverter
References
Citations
- ISBN 978-1-57958-358-3.
- ^ ISBN 978-0-7506-9866-5.
- ISBN 978-0-521-37095-0.
- ISBN 978-0-520-22409-4.
- ISBN 978-1-934015-08-7.
- ^ Discussion of A History of Some Foundations of Modern Radio-Electronic Technology, Comments by Lloyd Espenschied, Proceedings of the IRE, July, 1959 (Vol. 47, No. 7), pp. 1254, 1256. Critique. ". . . the roots of our modern technology trace back generally to sources other than the Hammond Laboratory." Comment. Many of the roots that nourished the work of the Hammond group and its contemporaries were recorded in our paper: the pioneering work of Wilson and Evans, Tesla, Shoemaker, in basic radiodynamics; . . . of Tesla and Fessenden leading to the development of basic intermediate frequency circuitry.
- ^ 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.
- ^ Fessenden 1905, p. 4
- ^ Ashley, Charles Grinnell; Heyward, Charles Brian (1912). Wireless Telegraphy and Wireless Telephony. Chicago: American School of Correspondence. pp. 103/15–104/16.
- ^ Tapan K. Sarkar, History of wireless, page 372
- ^ Videotape formats using 1⁄2-inch-wide (13 mm) tape Archived June 16, 2006, at the Wayback Machine ; Retrieved 2007-01-01
- ISBN 978-1-55860-792-7.
- ISSN 0003-6951.
- ^ Contract Details: Robust Nanopopous Ceramic Microsensor Platform
- ^ Contract Details: High Pulsed Power Varactor Multipliers for Imaging
- PMID 22109482.
- PMID 23038324.
General and cited references
- US 1050441, Fessenden, Reginald A., "Electric Signaling Apparatus", published July 27, 1905, issued January 14, 1913
- ISBN 978-0-252-02582-2.
- ISBN 978-0-387-95150-8.
Further reading
- Hogan, John V. L. (April 1921). "The Heterodyne Receiver". Electric Journal. Vol. 18. p. 116.
- US 706740, Fessenden, Reginald A., "Wireless Signaling", published September 28, 1901, issued August 12, 1902
- US 1050728, Fessenden, Reginald A., "Method of Signaling", published August 21, 1906, issued January 14, 1913