Heterodyning

In radio and signal processing, heterodyning is the generation of new frequencies by mixing, or multiplying, two oscillating waveforms. It is useful for modulation and demodulation of signals, or placing information of interest into a useful frequency range. This operation may be accomplished by a vacuum tube, transistor, or other signal processing device. Mixing two frequencies creates two new frequencies, according to the properties of the sine function: one at the sum of the two frequencies mixed, and the other at their difference. Typically only one of these frequencies is desired—the higher one after modulation and the lower one after demodulation. The other signal is either not passed by the tuned circuitry that follows, or may be filtered out.

Origin and use of term

The word "heterodyne" is derived from the Greek roots "hetero-" "different", and "-dyne" "power". This technique was pioneered by Canadian inventor-engineer Reginald Fessenden.

A superheterodyne receiver converts an incoming frequency to an intermediate frequency, using heterodyne action. The incoming signal is mixed with a generated signal, producing sum and difference frequencies. The signal of interest is selected by using a bandpass filter. The filter is usually fixed, common choices being 455 kHz and 10.7 MHz. The receiver's operating frequency is tuned simply by changing the frequency of the generated signal.

Optical heterodyne detection receivers are a special case in part because unlike antennas, which detect electric fields, a photon receiver directly measures energy and thus the non-linear mixing element arises directly from the physics of the photo-electric effect and is not imposed at later stage in the electronic receiver. Additionally, in optical heterodyne detection the optical carrier bandwidth of the LO [? requires definition] and Signal beams are non-negligible in the analysis: these bandwidths are generally much wider (generally orders of magnitude) than the bandwidth of the mixed signal.

The term "heterodyne" is sometimes applied also to one of the new frequencies produced by heterodyne signal mixing.

Mathematical principle

Heterodyning is based on the simple trigonometric identity:

$sin\; heta\; sin\; varphi\; =\; \{cos(\; heta\; -\; varphi)\; -\; cos(\; heta\; +\; varphi)\; over\; 2\}.$

The product on the left hand side represents the multiplication of a sinusoidal signal waveform by another sine wave (the "mixing frequency"). This wave must have greater frequency than the bandwidth of the signal. The right hand side is the sum of two co-sinusoids, which can be considered to be separate signals in different frequency bands.

None of the sinusoids in the above equation is equivalent to a complete signal waveform [? ambiguous; reword] . Any waveform may be converted to a combination of sinusoids by Fourier analysis, however. The equation then applies to the constituent frequencies. For example, if frequency "φ" is weak in the Fourier spectrum of the input signal, the output signal will also have low amplitudes at "θ" ± "φ".

Applications

Analog videotape recording

Many analog videotape systems relied 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 systems, the VHS (and S-VHS) system converts the color subcarrier from the NTSC standard 3.58 MHz to ~629 kHz. [http://www.lionlmb.org/quad/format.html#12incomposite Videotape formats using 1/2 inch wide tape] ; Retrieved 2007-01-01 ] PAL VHS color subcarrier is similarly downconverted (but from 4.43 MHz). The now-obsolete 3/4" U-matic systems used a heterodyned ~688 kHz subcarrier for NTSC recordings (as did Sony's Betamax), 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. Poynton, Charles. "Digital Video and HDTV: Algorithms and Interfaces" San Francisco: Morgan Kaufmann Publishers, 2003 PP 582, 583 ISBN 1-55860-792-7 ]

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 on formats with less than 1 MHz bandwidth. On playback, the recorded color information was heterodyned back to the standard subcarrier frequencies for playback on televisions and for interchange with other standard video equipment.

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

ee also

*Beat (acoustics)
*Edwin Howard Armstrong
*Electroencephalography
*Ring modulation
*Heterodyne detection
*Optical heterodyne detection

References

Notations

*Glinsky, Albert. "Theremin: Ether Music and Espionage." Urbana: University of Illinois Press, 2000. ISBN 0-252-02582-2.

Footnotes