Heterodyne

This article is about waveform manipulation. For the use of the term in poetry, see Heterodyne (poetry). For the webcomic characters, see Girl Genius.

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. The two frequencies are mixed in a vacuum tube, transistor, diode, 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. 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.

Origin and use of term

The word heterodyne is derived from the Greek roots hetero- "different", and dyn- "power" (cf. dynamis). The original heterodyne technique was pioneered by Canadian inventor-engineer Reginald Fessenden in 1901, but was not pursued very far because local oscillators were not very stable at the time. Heterodyning was invented by Fessenden as a technique to make the Morse code radiotelegraph (CW) signals used during the wireless era audible. A "heterodyne" receiver had a local oscillator that was adjusted to be close in frequency to the signal being received, so that when the two signals were mixed the difference or "beat" frequency was in the audible range. This produced a musical tone in the speaker, so the "dots" and "dashes" of Morse code were audible as beeping sounds.

The superheterodyne receiver (superhet) was invented by Edwin Howard Armstrong in 1918. It converts the incoming Radio Frequency (RF) to a predetermined fixed Intermediate Frequency (IF) using the heterodyne technique. The incoming RF signal is combined with the output of a stable local oscillator (LO) in a mixer circuit to produce a signal at the intermediate frequency (often but not invariably lower in frequency than the original signal). This is then amplified by a fixed-frequency high-gain bandpass amplifier. Tuning is achieved by varying the resonant frequency of a fairly-simple RF input filter in conjunction with the LO frequency, the latter selecting which RF signal heterodynes to the accepted IF. The main advance this provided was that amplifier stages no longer needed to be capable of handling signals of widely-different frequencies, so could now be much less complex yet provide uniform high-performance operation regardless of the original signal frequency.

How it works

In a superheterodyne receiver, the incoming radio signal of interest at frequency f_IN is mixed (that is, multiplied) with a second signal f_LO produced by an oscillator circuit in the receiver, called the local oscillator (LO). This mixing produces two new frequencies, at the sum (f_IN + f_LO) and difference (f_IN - f_LO) of the original frequencies. One of these two new frequencies is discarded, usually the higher one (f_IN + f_LO), by filtering it out of the mixer output. The remaining difference frequency is called the intermediate frequency (IF), and it is passed to a high gain amplifier, and signal processing that eventually extracts the desired modulation carried by the signal. Common choices for the IF frequency are 455 kHz in some AM radios and 10.7 MHz in FM radios. This process of shifting the RF signal down to a lower IF frequency is called "down conversion".

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

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, telemetry systems, cell phones, cable television converter boxes and headends, microwave relays, metal detectors, atomic clocks, and military electronic countermeasures (jamming) systems.

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. 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 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, 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.

Amplitude Modulation

Amplitude Modulation uses the heterodyne principle to move a signal from baseband, centered at 0 Hz, to passband, centered at the carrier frequency, at the transmitter. The process is reversed at the receiver, moving the signal from passband to baseband. There may be indirect frequencies used in the conversion process, known as intermediate frequencies.

Optical heterodyning

A current active area of research is extension of the heterodyning technique to higher frequencies, particularly to light frequencies, which are above radio frequencies in the electromagnetic spectrum. 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.

Since optical frequencies are far beyond 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 is possible by optical heterodyne detection when two different (close-by) wavelengths of light illuminate the detector so that the oscillating electrical output corresponds to their difference frequency. This allows extremely narrow band detection (much narrower band than any possible color filter can achieve) as well as precision measurements of phase and frequency of a signal light 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.

See also

• Optical heterodyne detection
• Beat (acoustics)
• Edwin Howard Armstrong
• Electroencephalography
• Ring modulation
• Heterodyne detection
• Homodyne
• Superheterodyne receiver

References

Notations

• Glinsky, Albert. Theremin: Ether Music and Espionage. Urbana: University of Illinois Press, 2000. ISBN 0-252-02582-2.
• Nahin, Paul J. The Science of Radio. New York: Springer-Verlag, AIP Press, 2001. ISBN 0-387-95150-4.