# Electronic oscillator

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An electronic oscillator is an electronic circuit that produces a periodic, oscillating electronic signal, often a sine wave or a square wave. [1] [2] [3] Oscillators convert direct current (DC) from a power supply to an alternating current (AC) signal. They are widely used in many electronic devices ranging from simplest clock generator s to digital instruments (like calculators) and complex computers and peripherals etc. [3] Common examples of signals generated by oscillators include signals broadcast by radio and television transmitters, clock signal s that regulate computers and quartz clocks, and the sounds produced by electronic beepers and video games. [1]

An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow. To be referred to as electronic, rather than electrical, generally at least one active component must be present. The combination of components and wires allows various simple and complex operations to be performed: signals can be amplified, computations can be performed, and data can be moved from one place to another.

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.

A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation. A sine wave is a continuous wave. It is named after the function sine, of which it is the graph. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time (t) is:

## Contents

Oscillators are often characterized by the frequency of their output signal:

Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light.

• A low-frequency oscillator (LFO) is an electronic oscillator that generates a frequency below approximately 20 Hz. This term is typically used in the field of audio synthesizers, to distinguish it from an audio frequency oscillator.
• An audio oscillator produces frequencies in the audio range, about 16 Hz to 20 kHz. [2]
• An RF oscillator produces signals in the radio frequency (RF) range of about 100 kHz to 100 GHz. [2]

Low-frequency oscillation (LFO) is an electronic frequency which is usually below 20 Hz and creates a rhythmic pulse or sweep. This pulse or sweep is often used to modulate synthesizers, delay lines and other audio equipment in order to create effects used in the production of electronic music. Audio effects such as vibrato, tremolo and phasing are examples. The abbreviation LFO is also very often used to refer to low-frequency oscillators themselves.

A synthesizer or synthesiser is an electronic musical instrument that generates audio signals that may be converted to sound. Synthesizers may imitate traditional musical instruments such as piano, flute, vocals, or natural sounds such as ocean waves; or generate novel electronic timbres. They are often played with a musical keyboard, but they can be controlled via a variety of other devices, including music sequencers, instrument controllers, fingerboards, guitar synthesizers, wind controllers, and electronic drums. Synthesizers without built-in controllers are often called sound modules, and are controlled via USB, MIDI or CV/gate using a controller device, often a MIDI keyboard or other controller.

An audio frequency or audible frequency is a periodic vibration whose frequency is in the band audible to the average human. The SI unit of audio frequency is the hertz (Hz). It is the property of sound that most determines pitch.

Oscillators designed to produce a high-power AC output from a DC supply are usually called inverters.

A power inverter, or inverter, is a power electronic device or circuitry that changes direct current (DC) to alternating current (AC).

There are two main types of electronic oscillator – the linear or harmonic oscillator and the nonlinear or relaxation oscillator. [2] [4]

In electronics a relaxation oscillator is a nonlinear electronic oscillator circuit that produces a nonsinusoidal repetitive output signal, such as a triangle wave or square wave. The circuit consists of a feedback loop containing a switching device such as a transistor, comparator, relay, op amp, or a negative resistance device like a tunnel diode, that repetitively charges a capacitor or inductor through a resistance until it reaches a threshold level, then discharges it again. The period of the oscillator depends on the time constant of the capacitor or inductor circuit. The active device switches abruptly between charging and discharging modes, and thus produces a discontinuously changing repetitive waveform. This contrasts with the other type of electronic oscillator, the harmonic or linear oscillator, which uses an amplifier with feedback to excite resonant oscillations in a resonator, producing a sine wave. Relaxation oscillators are used to produce low frequency signals for applications such as blinking lights and electronic beepers and in voltage controlled oscillators (VCOs), inverters and switching power supplies, dual-slope analog to digital converters, and function generators.

## Harmonic oscillator

The harmonic, or linear , oscillator produces a sinusoidal output. [2] [4] There are two types:

A linear circuit is an electronic circuit which obeys the superposition principle. This means that the output of the circuit F(x) when a linear combination of signals ax1(t) + bx2(t) is applied to it is equal to the linear combination of the outputs due to the signals x1(t) and x2(t) applied separately:

### Feedback oscillator

The most common form of linear oscillator is an electronic amplifier such as a transistor or operational amplifier connected in a feedback loop with its output fed back into its input through a frequency selective electronic filter to provide positive feedback. When the power supply to the amplifier is first switched on, electronic noise in the circuit provides a non-zero signal to get oscillations started. The noise travels around the loop and is amplified and filtered until very quickly it converges on a sine wave at a single frequency.

Feedback oscillator circuits can be classified according to the type of frequency selective filter they use in the feedback loop: [2] [4]

• In a crystal oscillator circuit the filter is a piezoelectric crystal (commonly a quartz crystal). [2] [4] The crystal mechanically vibrates as a resonator, and its frequency of vibration determines the oscillation frequency. Crystals have a very high Q-factor and also better temperature stability than tuned circuits, so crystal oscillators have much better frequency stability than LC or RC oscillators. Crystal oscillators are the most common type of linear oscillator, used to stabilize the frequency of most radio transmitters, and to generate the clock signal in computers and quartz clocks. Crystal oscillators often use the same circuits as LC oscillators, with the crystal replacing the tuned circuit; [2] the Pierce oscillator circuit is also commonly used. Quartz crystals are generally limited to frequencies of 30 MHz or below. [2] Other types of resonators, dielectric resonators and surface acoustic wave (SAW) devices, are used to control higher frequency oscillators, up into the microwave range. For example, SAW oscillators are used to generate the radio signal in cell phones.

### Negative-resistance oscillator

(left) Typical block diagram of a negative resistance oscillator. In some types the negative resistance device is connected in parallel with the resonant circuit. (right) A negative-resistance microwave oscillator consisting of a Gunn diode in a cavity resonator. The negative resistance of the diode excites microwave oscillations in the cavity, which radiate out the aperture into a waveguide.

In addition to the feedback oscillators described above, which use two-port amplifying active elements such as transistors and operational amplifiers, linear oscillators can also be built using one-port (two terminal) devices with negative resistance, [2] [4] such as magnetron tubes, tunnel diodes, IMPATT diodes and Gunn diodes. Negative-resistance oscillators are usually used at high frequencies in the microwave range and above, since at these frequencies feedback oscillators perform poorly due to excessive phase shift in the feedback path.

In negative-resistance oscillators, a resonant circuit, such as an LC circuit, crystal, or cavity resonator, is connected across a device with negative differential resistance, and a DC bias voltage is applied to supply energy. A resonant circuit by itself is "almost" an oscillator; it can store energy in the form of electronic oscillations if excited, but because it has electrical resistance and other losses the oscillations are damped and decay to zero. The negative resistance of the active device cancels the (positive) internal loss resistance in the resonator, in effect creating a resonator with no damping, which generates spontaneous continuous oscillations at its resonant frequency.

The negative-resistance oscillator model is not limited to one-port devices like diodes; feedback oscillator circuits with two-port amplifying devices such as transistors and tubes also have negative resistance. [5] [6] [7] At high frequencies, transistors and FETs do not need a feedback loop, but with certain loads applied to one port can become unstable at the other port and show negative resistance due to internal feedback, causing them to oscillate. [5] [6] [8] High-frequency oscillators in general are designed using negative-resistance techniques. [5] [6] [7]

Some of the many harmonic oscillator circuits are listed below:

Active devices used in oscillators and approximate maximum frequencies [6]
DeviceFrequency
Triode vacuum tube~1 GHz
Bipolar transistor (BJT)~20 GHz
Heterojunction bipolar transistor (HBT)~50 GHz
Metal–semiconductor field-effect transistor (MESFET)~100 GHz
Gunn diode, fundamental mode~100 GHz
Magnetron tube~100 GHz
High electron mobility transistor (HEMT)~200 GHz
Klystron tube~200 GHz
Gunn diode, harmonic mode~200 GHz
IMPATT diode~300 GHz
Gyrotron tube~600 GHz

## Relaxation oscillator

A nonlinear or relaxation oscillator produces a non-sinusoidal output, such as a square, sawtooth or triangle wave. [4] It consists of an energy-storing element (a capacitor or, more rarely, an inductor) and a nonlinear switching device (a latch, Schmitt trigger, or negative-resistance element) connected in a feedback loop. The switching device periodically charges and discharges the energy stored in the storage element thus causing abrupt changes in the output waveform.

Square-wave relaxation oscillators are used to provide the clock signal for sequential logic circuits such as timers and counters, although crystal oscillators are often preferred for their greater stability. Triangle-wave or sawtooth oscillators are used in the timebase circuits that generate the horizontal deflection signals for cathode ray tubes in analogue oscilloscopes and television sets. They are also used in voltage-controlled oscillators (VCOs), inverters and switching power supplies, dual-slope analog to digital converters (ADCs), and in function generators to generate square and triangle waves for testing equipment. In general, relaxation oscillators are used at lower frequencies and have poorer frequency stability than linear oscillators.

Ring oscillators are built of a ring of active delay stages. Generally the ring has an odd number of inverting stages, so that there is no single stable state for the internal ring voltages. Instead, a single transition propagates endlessly around the ring.

Some of the more common relaxation oscillator circuits are listed below:

## Voltage-controlled oscillator (VCO)

An oscillator can be designed so that the oscillation frequency can be varied over some range by an input voltage or current. These voltage controlled oscillators are widely used in phase-locked loops, in which the oscillator's frequency can be locked to the frequency of another oscillator. These are ubiquitous in modern communications circuits, used in filters, modulators, demodulators, and forming the basis of frequency synthesizer circuits which are used to tune radios and televisions.

Radio frequency VCOs are usually made by adding a varactor diode to the tuned circuit or resonator in an oscillator circuit. Changing the DC voltage across the varactor changes its capacitance, which changes the resonant frequency of the tuned circuit. Voltage controlled relaxation oscillators can be constructed by charging and discharging the energy storage capacitor with a voltage controlled current source. Increasing the input voltage increases the rate of charging the capacitor, decreasing the time between switching events.

## History

The first practical oscillators were based on electric arcs, which were used for lighting in the 19th century. The current through an arc light is unstable due to its negative resistance, and often breaks into spontaneous oscillations, causing the arc to make hissing, humming or howling sounds [9] which had been noticed by Humphry Davy in 1821, Benjamin Silliman in 1822, [10] Auguste Arthur de la Rive in 1846, [11] and David Edward Hughes in 1878. [12] Ernst Lecher in 1888 showed that the current through an electric arc could be oscillatory. [13] [14] [15] An oscillator was built by Elihu Thomson in 1892 [16] [17] by placing an LC tuned circuit in parallel with an electric arc and included a magnetic blowout. Independently, in the same year, George Francis FitzGerald realized that if the damping resistance in a resonant circuit could be made zero or negative, the circuit would produce oscillations, and, unsuccessfully, tried to build a negative resistance oscillator with a dynamo, what would now be called a parametric oscillator. [18] [9] The arc oscillator was rediscovered and popularized by William Duddell in 1900. [19] [20] Duddell, a student at London Technical College, was investigating the hissing arc effect. He attached an LC circuit (tuned circuit) to the electrodes of an arc lamp, and the negative resistance of the arc excited oscillation in the tuned circuit. [9] Some of the energy was radiated as sound waves by the arc, producing a musical tone. Duddell demonstrated his oscillator before the London Institute of Electrical Engineers by sequentially connecting different tuned circuits across the arc to play the national anthem "God Save the Queen". [9] Duddell's "singing arc" did not generate frequencies above the audio range. In 1902 Danish physicists Valdemar Poulsen and P. O. Pederson were able to increase the frequency produced into the radio range by operating the arc in a hydrogen atmosphere with a magnetic field, inventing the Poulsen arc radio transmitter, the first continuous wave radio transmitter, which was used through the 1920s. [21] [22] [23]

The vacuum-tube feedback oscillator was invented around 1912, when it was discovered that feedback ("regeneration") in the recently invented audion vacuum tube could produce oscillations. At least six researchers independently made this discovery, although not all of them can be said to have a role in the invention of the oscillator. [24] [25] In the summer of 1912, Edwin Armstrong observed oscillations in audion radio receiver circuits [26] and went on to use positive feedback in his invention of the regenerative receiver. [27] [28] Austrian Alexander Meissner independently discovered positive feedback and invented oscillators in March 1913. [26] [29] Irving Langmuir at General Electric observed feedback in 1913. [29] Fritz Lowenstein may have preceded the others with a crude oscillator in late 1911. [30] In Britain, H. J. Round patented amplifying and oscillating circuits in 1913. [26] In August 1912, Lee De Forest, the inventor of the audion, had also observed oscillations in his amplifiers, but he didn't understand the significance and tried to eliminate it [31] [32] until he read Armstrong's patents in 1914, [33] which he promptly challenged. [34] Armstrong and De Forest fought a protracted legal battle over the rights to the "regenerative" oscillator circuit [34] [35] which has been called "the most complicated patent litigation in the history of radio". [36] De Forest ultimately won before the Supreme Court in 1934 on technical grounds, but most sources regard Armstrong's claim as the stronger one. [32] [34]

The first and most widely used relaxation oscillator circuit, the astable multivibrator, was invented in 1917 by French engineers Henri Abraham and Eugene Bloch. [37] [38] [39] They called their cross-coupled, dual-vacuum-tube circuit a multivibrateur, because the square-wave signal it produced was rich in harmonics, [38] [39] compared to the sinusoidal signal of other vacuum-tube oscillators.

Vacuum-tube feedback oscillators became the basis of radio transmission by 1920. However, the triode vacuum tube oscillator performed poorly above 300 MHz because of interelectrode capacitance.[ citation needed ] To reach higher frequencies, new "transit time" (velocity modulation) vacuum tubes were developed, in which electrons traveled in "bunches" through the tube. The first of these was the Barkhausen–Kurz oscillator (1920), the first tube to produce power in the UHF range. The most important and widely used were the klystron (R. and S. Varian, 1937) and the cavity magnetron (J. Randall and H. Boot, 1940).

Mathematical conditions for feedback oscillations, now called the Barkhausen criterion, were derived by Heinrich Georg Barkhausen in 1921. The first analysis of a nonlinear electronic oscillator model, the Van der Pol oscillator, was done by Balthasar van der Pol in 1927. [40] He showed that the stability of the oscillations (limit cycles) in actual oscillators was due to the nonlinearity of the amplifying device. He originated the term "relaxation oscillation" and was first to distinguish between linear and relaxation oscillators. Further advances in mathematical analysis of oscillation were made by Hendrik Wade Bode and Harry Nyquist [41] in the 1930s. In 1969 K. Kurokawa derived necessary and sufficient conditions for oscillation in negative-resistance circuits, [42] which form the basis of modern microwave oscillator design. [8]

## Related Research Articles

An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the power of a signal. It is a two-port electronic circuit that uses electric power from a power supply to increase the amplitude of a signal applied to its input terminals, producing a proportionally greater amplitude signal at its output. The amount of amplification provided by an amplifier is measured by its gain: the ratio of output voltage, current, or power to input. An amplifier is a circuit that has a power gain greater than one.

A crystal oscillator is an electronic oscillator circuit that uses the mechanical resonance of a vibrating crystal of piezoelectric material to create an electrical signal with a precise frequency. This frequency is often used to keep track of time, as in quartz wristwatches, to provide a stable clock signal for digital integrated circuits, and to stabilize frequencies for radio transmitters and receivers. The most common type of piezoelectric resonator used is the quartz crystal, so oscillator circuits incorporating them became known as crystal oscillators, but other piezoelectric materials including polycrystalline ceramics are used in similar circuits.

In electronics and telecommunications a transmitter or radio transmitter is an electronic device which produces radio waves with an antenna. The transmitter itself generates a radio frequency alternating current, which is applied to the antenna. When excited by this alternating current, the antenna radiates radio waves.

In electronics, negative resistance (NR) is a property of some electrical circuits and devices in which an increase in voltage across the device's terminals results in a decrease in electric current through it.

The Hartley oscillator is an electronic oscillator circuit in which the oscillation frequency is determined by a tuned circuit consisting of capacitors and inductors, that is, an LC oscillator. The circuit was invented in 1915 by American engineer Ralph Hartley. The distinguishing feature of the Hartley oscillator is that the tuned circuit consists of a single capacitor in parallel with two inductors in series, and the feedback signal needed for oscillation is taken from the center connection of the two inductors.

A regenerative circuit is an amplifier circuit that employs positive feedback. Some of the output of the amplifying device is applied back to its input so as to add to the input signal, increasing the amplification. One example is the Schmitt trigger, but the most common use of the term is in RF amplifiers, and especially regenerative receivers, to greatly increase the gain of a single amplifier stage.

A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator can be either electromagnetic or mechanical. Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators that produce sound waves of specific tones. Another example is quartz crystals used in electronic devices such as radio transmitters and quartz watches to produce oscillations of very precise frequency.

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A voltage-controlled oscillator (VCO) is an electronic oscillator whose oscillation frequency is controlled by a voltage input. The applied input voltage determines the instantaneous oscillation frequency. Consequently, a VCO can be used for frequency modulation (FM) or phase modulation (PM) by applying a modulating signal to the control input. A VCO is also an integral part of a phase-locked loop.

The Armstrong oscillator is an electronic oscillator circuit which uses an inductor and capacitor to generate an oscillation. It is the earliest oscillator circuit, invented by US engineer Edwin Armstrong in 1912 and independently by Austrian engineer Alexander Meissner in 1913, and was used in the first vacuum tube radio transmitters. It is sometimes called a tickler oscillator because its distinguishing feature is that the feedback signal needed to produce oscillations is magnetically coupled into the tank inductor in the input circuit by a "tickler coil" (L2, right) in the output circuit. Assuming the coupling is weak, but sufficient to sustain oscillation, the oscillation frequency f is determined primarily by the tank circuit (L1 and C in the figure on the right) and is approximately given by

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Linear electronic oscillator circuits, which generate a sinusoidal output signal, are composed of an amplifier and a frequency selective element, a filter. A linear oscillator circuit which uses an RC network, a combination of resistors and capacitors, for its frequency selective part is called an RC oscillator.

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In electronics, motorboating is a type of low frequency parasitic oscillation that sometimes occurs in audio and radio equipment and often manifests itself as a sound similar to an idling motorboat engine, a "put-put-put", in audio output from speakers or earphones. It is a problem encountered particularly in radio transceivers and older vacuum tube audio systems, guitar amplifiers, PA systems and is caused by some type of unwanted feedback in the circuit. The amplifying devices in audio and radio equipment are vulnerable to a variety of feedback problems, which can cause distinctive noise in the output. The term motorboating is applied to oscillations whose frequency is below the range of hearing, from 1 to 10 hertz, so the individual oscillations are heard as pulses. Sometimes the oscillations can even be seen visually as the woofer cones in speakers slowly moving in and out.

The arc converter, sometimes called the arc transmitter, or Poulsen arc after Danish engineer Valdemar Poulsen who invented it in 1903, was a variety of spark transmitter used in early wireless telegraphy. The arc converter used an electric arc to convert direct current electricity into radio frequency alternating current. It was used as a radio transmitter from 1903 until the 1920s when it was replaced by vacuum tube transmitters. One of the first transmitters that could generate continuous sinusoidal waves, it was one of the first technologies used to transmit sound by radio. It is on the list of IEEE Milestones as a historic achievement in electrical engineering.

William Du Bois Duddell was an English physicist and electrical engineer. His inventions include the moving coil oscillograph, as well as the thermo-ammeter and thermo-galvanometer.

## References

1. Snelgrove, Martin (2011). "Oscillator". McGraw-Hill Encyclopedia of Science and Technology, 10th Ed., Science Access online service. McGraw-Hill. Archived from the original on July 19, 2013. Retrieved March 1, 2012.
2. Chattopadhyay, D. (2006). Electronics (fundamentals And Applications). New Age International. pp. 224–225. ISBN   978-81-224-1780-7.
3. Horowitz, Paul; Hill, Winfield (2015). The Art of Electronics. USA. p. 425. ISBN   978-0-521-80926-9.
4. Garg, Rakesh Kumar; Ashish Dixit; Pavan Yadav (2008). Basic Electronics. Firewall Media. p. 280. ISBN   978-8131803028.
5. Kung, Fabian Wai Lee (2009). "Lesson 9: Oscillator Design". RF/Microwave Circuit Design. Prof. Kung's website, Multimedia University. Archived from the original (PDF) on July 16, 2015. Retrieved October 17, 2012., Sec. 3 Negative Resistance Oscillators, pp. 9–10, 14
6. Räisänen, Antti V.; Arto Lehto (2003). Radio Engineering for Wireless Communication and Sensor Applications. USA: Artech House. pp. 180–182. ISBN   978-1580535427.
7. Ellinger, Frank (2008). Radio Frequency Integrated Circuits and Technologies, 2nd Ed. USA: Springer. pp. 391–394. ISBN   978-3540693246.
8. Maas, Stephen A. (2003). Nonlinear Microwave and RF Circuits, 2nd Ed. Artech House. pp. 542–544. ISBN   978-1580534840.
9. Hong, Sungook (2001). Wireless: From Marconi's Black-Box to the Audion. MIT Press. ISBN   978-0262082983., pp. 161165
10. Silliman, Benjamin (1859). "First Principles of Physics: Or Natural Philosophy, Designed for the Use of Schools and Colleges".
11. Casperson, L. W (1991). "The humming telephone as an acoustic maser". Optical and Quantum Electronics. 23 (8): 995–1010. doi:10.1007/BF00611436.
12. Anders, André (2009). Cathodic Arcs: From Fractal Spots to Energetic Condensation. Springer Science and Business Media. pp. 31–32. ISBN   978-0387791081.
13. Cady, W. G.; Arnold, H. D. (1907). "On the electric arc between metallic electrodes". American Journal of Science. 24 (143): 406. Retrieved April 12, 2017.
14. "Notes". The Electrical Review. 62 (1578): 812. February 21, 1908. Retrieved April 12, 2017.
15. Morse 1925 , p. 23
16. US 500630,Thomson, Elihu,"Method of and Means for Producing Alternating Currents",published 18 July 1892,issued 4 July 1893
17. G. Fitzgerald, On the Driving of Electromagnetic Vibrations by Electromagnetic and Electrostatic Engines, read at the January 22, 1892 meeting of the Physical Society of London, in Larmor, Joseph, ed. (1902). The Scientific Writings of the late George Francis Fitzgerald. London: Longmans, Green and Co. pp. 277–281.
18. Morse 1925 , pp. 8081
19. GB 190021629, Duddell, William du Bois,"Improvements in and connected with Means for the Conversion of Electrical Energy, Derived from a Source of Direct Current, into Varying or Alternating Currents",published 29 Nov 1900,issued 23 Nov 1901
20. Morse 1925 , p. 31
21. GB 190315599, Poulsen, Valdemar,"Improvements relating to the Production of Alternating Electric Currents",issued 14 July 1904
22. US 789449, Poulsen, Valdemar,"Method of Producing Alternating Currents with a High Number of Vibrations",issued 9 May 1905
23. Hempstead, Colin; William E. Worthington (2005). Encyclopedia of 20th-Century Technology. 2. Taylor & Francis. p. 648. ISBN   978-1579584641.
24. Hong 2001 , p. 156
25. Fleming, John Ambrose (1919). The Thermionic Valve and its Developments in Radiotelegraphy and Telephony. London: The Wireless Press. pp. 148–155.
26. Hong, Sungook (2003). "A history of the regeneration circuit: From invention to patent litigation" (PDF). IEEE. Retrieved August 29, 2012.Cite journal requires `|journal=` (help), pp. 910
27. Armstrong, Edwin H. (September 1915). "Some recent developments in the Audion receiver" (PDF). Proc. IRE. 3 (9): 215–247. doi:10.1109/jrproc.1915.216677 . Retrieved August 29, 2012.
28. Hong 2003 , p. 13
29. Hong 2003 , p. 5
30. Hong 2003 , pp. 67
31. Hijiya, James A. (1992). Lee De Forest and the Fatherhood of Radio. Lehigh University Press. pp. 89–90. ISBN   978-0934223232.
32. Hong 2003 , p. 14
33. Nahin, Paul J. (2001). The Science of Radio: With Matlab and Electronics Workbench Demonstration, 2nd Ed. Springer. p. 280. ISBN   978-0387951508.
34. Hong 2001 , pp. 181189
35. Hong 2003 , p. 2
36. Abraham, H.; E. Bloch (1919). "Measurement of period of high frequency oscillations". Comptes Rendus. 168: 1105.
37. Glazebrook, Richard (1922). A Dictionary of Applied Physics, Vol. 2: Electricity. London: Macmillan and Co. Ltd. pp. 633–634.
38. Calvert, James B. (2002). "The Eccles-Jordan Circuit and Multivibrators". Dr. J. B. Calvert website, Univ. of Denver. Retrieved May 15, 2013.
39. Van der Pol, Balthazar (1927). "On relaxation-oscillations". The London, Edinburgh and Dublin Philosophical Magazine. 2 (7): 978–992. doi:10.1080/14786442608564127.
40. Nyquist, H. (January 1932). "Regeneration Theory" (PDF). Bell System Tech. J. 11 (1): 126–147. doi:10.1002/j.1538-7305.1932.tb02344.x . Retrieved December 5, 2012.
41. Kurokawa, K. (July 1969). "Some Basic Characteristics of Broadband Negative Resistance Oscillator Circuits" (PDF). Bell System Tech. J. 48 (6): 1937–1955. doi:10.1002/j.1538-7305.1969.tb01158.x . Retrieved December 8, 2012. Eq. 10 is a necessary condition for oscillation; eq. 12 is a sufficient condition,
• Morse, A. H. (1925), Radio: Beam and Broadcast: Its story and patents, London: Ernest Benn. History of radio in 1925. Oscillator claims 1912; De Forest and Armstrong court case cf p. 45. Telephone hummer/oscillator by A. S. Hibbard in 1890 (carbon microphone has power gain); Larsen "used the same principle in the production of alternating current from a direct current source"; accidental development of vacuum tube oscillator; all at p. 86. Von Arco and Meissner first to recognize application to transmitter; Round for first transmitter; nobody patented triode transmitter at p. 87.