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Dynamic Range

February 6, 2017

As experimental physicists will verify, we live in a noisy world. There's a photo of Ernest Rutherford, puffing a cigar at the Cavendish Laboratory in conversation with John Ratcliffe under a sign reading, "Talk softly, please."[1-2] The sign was there to remind the normally loud Rutherford to refrain from adding the noise of his usual loud voice to the experimental data. You don't get a Nobel Prize in Physics by being timid.

Even the temperature-induced movement of atoms in a solid will spoil some experiments, so many experiments are conducted cryogenically at temperatures near absolute zero. The first detection of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory (LIGO) is a recent example of physicists overcoming environmental noise to make a significant discovery.[3] Detection of such waves required measurement of a displacement a thousand times smaller than the proton radius.

To accomplish this, LIGO needed systems to dampen seismic noise. These were both "passive," involving elaborate mechanical mounting, and "active," using sensors and actuator circuitry. Since air molecules pinging the detection mirrors will also spoil sensitivity, LIGO operates in a vacuum. Creating this vacuum was no small feat, since the chamber volume is 10,000 cubic meters.[4]

Joseph WeberElectrical engineer, Joseph Weber, in his 1940 class photo at the US Naval Academy.

Weber attempted to detect gravitational waves using resonant detection in huge aluminum cylinders that would "ring" at 1660 hertz.

Weber's cylinders were covered with piezoelectric sensors that could detect a displacement of about 10-16 meters, or a tenth of a proton radius.

(Wikimedia Commons image, modified for artistic effect.)

The range between a largest and smallest value is known as the dynamic range, with the "noise floor" representing the smallest value that can be sensed by an electronic system. It's hard for most electronics to match the dynamic range of human hearing and vision; or, the scent detection by many animals. Human vision functions from darkest night to brightest day, for a range of about 90 decibels (dB), and hearing operates over a 100 dB range.

The dynamic range of human hearing was taken into account when designing the compact disc (CD) digital audio system. The 16-bit encoding of compact discs gives a dynamic range of 96 dB (20log10(216)). This is quite an improvement over 1960s era magnetic tape recorders that were limited by noise to about 55 dB.[5] This places a limit on the dynamic range of phonograph records of that era, since the music was recorded first on tape, although a vinyl phonograph record can have fundamentally about the same dynamic range as a compact disc.

When CDs were first introduced, some record producers tried to utilize their full dynamic range to disastrous result. My copy of Mike Oldfield's 1974 "The Orchestral Tubular Bells" is impossible to enjoy because of the large excursions in volume level. I could listen to this CD and some other music only when the dynamic range was compressed through some electronics of my own design (see photograph).

Figure caption
Old school audio engineering. This was my 1970s version of a platform gain controller based on the CBS Laboratories Audimax.[6-8] I wrote an article on a simplified version of this for a hobby electronics magazine in 2012.[9] (Photo by author. Click for larger image.)

Dynamic range can be a problem in scientific measurement, and that's why our voltmeters and other instruments have range switches to match the instrument to the quantities being measured. While 16-bits are enough for music, the 16-bit Analog-to-digital converters for magnetic field measurement on the Van Allen Probes, launched in 2012 to study the Van Allen radiation belt, had automatic range switching to allow seven orders of magnitude of measurement (140 dB) within the 96 dB dynamic range.[10]

Energy in our universe has a wide dynamic range. Photons of the cosmic microwave background radiation have a frequency of about 160 GHz, so their energy (E = hν = (6.63 x 10-34 joule-s)(1.6 x 1011 s-1)) is about 1 x 10-22 J. Ultra-high-energy cosmic rays have been detected with an energy of nearly 10 joules. The dynamic range of particle energy in the universe is thus 1023, or 460 dB!

Image of George Washington rendered in 1-, 4-, 8-, and 16-bit dynamic range.
Image of George Washington rendered in 1-, 4-, 8-, and 16-bit dynamic range. (Monochrome detail from a 1797 painting by Gilbert Stuart (1755-1828), presently located at the Crystal Bridges Museum of American Art, Via Wikimedia Commons.)

While the dynamic range of magnetic tape recording was limited to about 55 dB, there was a method of extending the dynamic range of audio recording by a technique known as companding. A compander is a combination of a compressor and a complementary expander, with the dBx noise reduction system as a notable example. The dBx compressed audio onto magnetic tape in a 2:1 ratio; that is, it put 120 dB of signal into a 60 dB range. On playback, the 1:2 expansion recovered a 120 dB signal. The Dolby Type A noise reduction system had a similar action with additional circuitry that reduced processing artifacts.


  1. Z. Capri Anton, "Quips, Quotes and Quanta : An Anecdotal History of Physics," World Scientific Publishing Company, May 31, 2011, 252 pp., ISBN: 978-9814343473.
  2. Rutherford image at the Emilio Segre Visual Archives, American Physical Society, via Flickr.
  3. B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), "Observation of Gravitational Waves from a Binary Black Hole Merger," Phys. Rev. Lett., vol. 116, Document No. 061102, February 11, 2016, DOI:https://doi.org/10.1103/PhysRevLett.116.061102. Also available at arXiv.
  4. LIGO Technology, LIGO Laboratory, California Institute of Technology.
  5. NAB Magnetic Tape Recording and Reproducing Standards, Reel-To-Reel, Document E-416 (1965), Engineering Department, National Association of Broadcasters, PDF File via richardhess.com.
  6. B.B. Bauer and Arthur Kaiser, Gain Control Apparatus Providing Constant Gain Interval, US Patent No. 3,187,268, June 1, 1965.
  7. Arthur Kaiser and Emil Torick, "Compensated Platform Gain Control Apparatus, US Patent No. 3,260,957, July 12, 1966.
  8. Emil Torick and Arthur Kaiser, Control Circuit for Restricting Instantaneous Peak Levels in Audio Signals, US Patent No. 3,398,381, August 20, 1968.
  9. D.M. Gualtieri, "Build A Stereo Gain Controller," Nuts and Volts, January, 2012, pp. 28-33.
  10. Nicola Fox and James L. Burch, The Van Allen Probes Mission, Springer Science & Business Media, Jan 10, 2014, 647 pp.

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