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==Harmonic oscillators== [[File:Oscillator diagram1.svg|thumb|Block diagram of a feedback linear oscillator; an amplifier ''A'' with its output ''v<sub>o</sub>'' fed back into its input ''v<sub>f</sub>'' through a [[electronic filter|filter]], ''β(jω)''.]] {{anchor|linear oscillator}} [[Linear circuit|'''Linear''']] or '''harmonic oscillators''' generate a [[sinusoidal]] (or nearly-sinusoidal) signal. There are two types: ===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 switched on initially, [[electronic noise]] in the circuit provides a non-zero signal to get oscillations started.{{sfn|Gottlieb|1997|p=113–114}} The noise travels around the loop and is amplified and [[Filter (signal processing)|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:<ref name="Chattopadhyay" /><ref name="Garg" /> *In an ''[[RC oscillator]]'' circuit, the filter is a network of [[resistor]]s and [[capacitor]]s.<ref name="Chattopadhyay" /><ref name="Garg" /> RC oscillators are mostly used to generate lower frequencies, for example in the audio range. Common types of RC oscillator circuits are the [[phase shift oscillator]] and the [[Wien bridge oscillator]]. LR oscillators, using [[inductor]] and resistor filters also exist, however they are much less common due to the required size of an inductor to achieve a value appropriate for use at lower frequencies. {{anchor|LC oscillator}} [[File:Oscillator comparison.svg|thumb|right|400px|Two common LC oscillator circuits, the Hartley and Colpitts oscillators]] *In an ''[[LC circuit| LC oscillator]]'' circuit, the filter is a [[tuned circuit]] (often called a ''tank circuit'') consisting of an [[inductor]] (L) and [[capacitor]] (C) connected together, which acts as a [[resonator]].<ref name="Chattopadhyay" /><ref name="Garg" /> Charge flows back and forth between the capacitor's plates through the inductor, so the tuned circuit can store electrical energy oscillating at its [[resonant frequency]]. The amplifier adds power to compensate for resistive energy losses in the circuit and supplies the power for the output signal. LC oscillators are often used at [[radio frequency|radio frequencies]],<ref name="Chattopadhyay" /> when a tunable frequency source is necessary, such as in [[signal generator]]s, tunable radio [[transmitter]]s and the [[local oscillator]]s in [[radio receiver]]s. Typical LC oscillator circuits are the [[Hartley oscillator|Hartley]], [[Colpitts oscillator|Colpitts]]<ref name="Chattopadhyay" /> and [[Clapp oscillator|Clapp]] circuits. *In a [[Crystal oscillator#Crystal oscillator circuits|''crystal oscillator'' circuit]] the filter is a [[piezoelectric]] crystal (commonly a [[quartz crystal]]).<ref name="Chattopadhyay" /><ref name="Garg" /> The crystal mechanically vibrates as a [[resonator]], and its frequency of vibration determines the oscillation frequency. Since the [[resonant frequency]] of the crystal is determined by its dimensions, crystal oscillators are fixed frequency oscillators, their frequency can only be adjusted over a tiny range of less than one percent.<ref name="Terman" /><ref name="Misra" /><ref name="Scroggie" />{{sfn|Gottlieb|1997|p=39-40}} 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 transmitter]]s, and to generate the [[clock signal]] in computers and [[quartz clock]]s. Crystal oscillators often use the same circuits as LC oscillators, with the crystal replacing the [[tuned circuit]];<ref name="Chattopadhyay" /> the [[Pierce oscillator]] circuit is also commonly used. Quartz crystals are generally limited to frequencies of 30 MHz or below.<ref name="Chattopadhyay" /> Other types of resonators, [[dielectric resonator]]s 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 phone]]s.<ref>{{Cite web|last=APITech|title=SAW Technology|url=https://info.apitech.com/saw-technology-va|access-date=2021-05-12|website=info.apitech.com|language=en}}</ref> {{clear}} ===Negative-resistance oscillator=== {{multiple image | align = right | direction = horizontal | header = | image1 = Negative resistance oscillator.svg | width1 = 190 | image2 = Ganna gjenerators M31102-1.jpg | width2 = 162 | footer = ''(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 network|two-port]] amplifying active elements such as transistors and operational amplifiers, linear oscillators can also be built using [[port (circuit theory)|one-port]] (two terminal) devices with [[negative resistance]],<ref name="Chattopadhyay" /><ref name="Garg" /> such as [[magnetron]] tubes, [[tunnel diode]]s, [[IMPATT diode]]s and [[Gunn diode]]s.<ref name=" Raisanen" /><ref name="Solymar" />{{rp|p.197–198}}{{sfn|Gottlieb|1997|p=103}} 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 oscillator|crystal]], or [[Resonator#Cavity resonators|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 [[Harmonic oscillator#Damped harmonic oscillator|damped]] and decay to zero.<ref name="Edson">{{cite book | last = Edson | first = William A. | title = Vacuum Tube Oscillators | publisher = John Wiley and Sons | date = 1953 | location = | pages = 7–8 | language = | url = https://archive.org/details/dli.ernet.504339/page/7/mode/2up | archive-url= | archive-date= | doi = | id = | isbn = | mr = | zbl = | jfm =}}</ref><ref name="Solymar">{{cite book | last1 = Solymar | first1 = Laszlo | last2 = Walsh | first2 = Donald | title = Electrical Properties of Materials | publisher = Oxford University Press | date = 2009 | location = | pages = 181–182 | language = | url = https://books.google.com/books?id=AiWyp0NQW6UC&q=%22negative+resistance%22 | archive-url= | archive-date= | doi = | id = | isbn = 9780191574351 | mr = | zbl = | jfm =}}</ref> The negative resistance of the active device cancels the (positive) internal loss resistance in the resonator, in effect creating a resonator circuit 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 network|two-port]] amplifying devices such as transistors and [[vacuum tube|tubes]] also have negative resistance.{{sfn|Gottlieb|1997|p=104}}<ref name="Kung">{{cite web | last = Kung | first = Fabian Wai Lee | title = Lesson 9: Oscillator Design | website = RF/Microwave Circuit Design | publisher = Prof. Kung's website, Multimedia University | year = 2009 | url = http://pesona.mmu.edu.my/~wlkung/ADS/rf/lesson9.pdf | access-date = October 17, 2012 | archive-url = https://web.archive.org/web/20150722165131/http://pesona.mmu.edu.my/~wlkung/ADS/rf/lesson9.pdf | archive-date = July 22, 2015 | url-status = dead }}, Sec. 3 Negative Resistance Oscillators, pp. 9–10, 14</ref><ref name=" Raisanen" /><ref name="Ellinger">{{cite book | last = Ellinger | first = Frank | title = Radio Frequency Integrated Circuits and Technologies, 2nd Ed | publisher = Springer | year = 2008 | location = USA | pages = 391–394 | url = https://books.google.com/books?id=0pl9xYD0QNMC&pg=PA391 | isbn = 978-3540693246}}</ref> At high frequencies, three terminal devices such as transistors and FETs are also used in negative resistance oscillators. At high frequencies these devices 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. The negative resistance port is connected to a tuned circuit or resonant cavity, causing them to oscillate.<ref name="Kung" /><ref name=" Raisanen">{{cite book | last = Räisänen | first = Antti V. | author2=Arto Lehto | title = Radio Engineering for Wireless Communication and Sensor Applications | publisher = Artech House | year = 2003 | location = USA | pages = 180–182 | url = https://books.google.com/books?id=m8Dgkvf84xoC&pg=PA181 | isbn = 978-1580535427}}</ref><ref name="Maas" /> High-frequency oscillators in general are designed using negative-resistance techniques.<ref name="Kung" /><ref name=" Raisanen" /><ref name="Ellinger" /> === List of harmonic oscillator circuits === Some of the many harmonic oscillator circuits are listed below: {| class="wikitable" style="float:right;margin:0 0 1em 1em;" |+ style="font-size: 80%"|Amplifying devices used in oscillators and approximate maximum frequencies<ref name=" Raisanen" /> |- ! Amplifying device ! Frequency |- | [[Triode]] vacuum tube | ~1 GHz |- | [[Bipolar junction transistor|Bipolar transistor]] (BJT) | ~20 GHz |- | [[Heterojunction bipolar transistor]] (HBT) | ~50 GHz |- | [[MESFET|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 |- |} * [[Armstrong oscillator]], a.k.a. Meissner oscillator * [[Hartley oscillator]] * [[Colpitts oscillator]] * [[Clapp oscillator]] * [[Seiler oscillator]] * [[Vackář oscillator]] * [[Pierce oscillator]] * [[Tri-tet oscillator]] * [[Cathode follower oscillator]] * [[Wien bridge oscillator]] * [[Phase-shift oscillator]] * Cross-coupled oscillator * [[Dynatron oscillator]] * [[Opto-electronic oscillator]] * [[Robinson oscillator]] {{clear}}
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