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The '''Hartley oscillator''' is an [[electronic oscillator]] [[electronic circuit|circuit]] that uses an [[inductor]] and a [[capacitor]] in parallel to determine the frequency.  Invented in 1915 by American engineer [[Ralph Hartley]], the distinguishing feature of the Hartley circuit is that the [[feedback]] needed for oscillation is taken from a tap on the coil, or the junction of two coils in series.
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


==Operation==
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[[Image:Hartley osc.svg|framed|Schematic diagram]]
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A Hartley oscillator is essentially any configuration that uses positive feedback into two series-connected coils and a single capacitor forming a resonant LC [[tank circuit]] (see [[Colpitts oscillator]] for the equivalent oscillator using ''two'' capacitors and ''one'' coil).  Although there is no requirement for there to be mutual coupling between the two coil segments, the circuit is usually implemented using a tapped coil, as shown here. The optimal tapping point (or ratio of coil inductances) depends on the amplifying device used, which may be a [[bipolar junction transistor]], [[FET]], triode, or amplifier of almost any type (non-inverting in this case, although variations of the circuit with an earthed centre-point and feedback from an [[inverting amplifier]] or the collector/drain of a transistor are also common), but a [[Junction FET]] (shown) or triode is often employed as a good degree of amplitude stability (and thus [[distortion]] reduction) can be achieved with a simple [[grid leak]] <!-- is grid-leak confusing here? Hope not --> resistor-capacitor combination in series with the gate or grid (see the Scott circuit below) thanks to [[diode]] conduction on signal peaks building up enough [[reverse bias|negative bias]] to limit amplification.
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It is made up of the following:
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* Two [[inductor]]s in series, which need not be mutual
'''MathML'''
* One tuning capacitor
:<math forcemathmode="mathml">E=mc^2</math>


Advantages of the Hartley oscillator include:
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


* The frequency may be adjusted using a single variable capacitor, one side of which can be earthed
'''source'''
* The output amplitude remains constant over the frequency range
:<math forcemathmode="source">E=mc^2</math> -->
* Either a tapped coil or two fixed inductors are needed, and very few other components
* Easy to create an accurate fixed-frequency [[Crystal oscillator]] variation by replacing the capacitor with a (parallel-resonant) [[quartz crystal]] or replacing the top half of the [[tank circuit]] with a crystal and grid-leak resistor (as in the [[Tri-tet oscillator]]).


Disadvantages include:
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


* Harmonic-rich output if taken from the amplifier and not directly from the LC circuit (unless amplitude-stabilisation circuitry is employed).
==Demos==


Note that, if the inductance of the two partial coils <math>L_1</math> and <math>L_2</math> is given (e.g. in a simulator), the total effective inductance that determines the frequency of the oscillation is (coupling factor <math>k</math>):
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


<math>
L_0 = L_1 + L_2 + k*\sqrt{L_1*L_2}
</math>


(see <ref>Jim McLucas, Hartley oscillator requires no coupled inductors, EDN October 26, 2006 http://www.edn.com/article/CA6343253.html</ref>)
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


== History ==
==Test pages ==
[[Image:Hartley-US-Pat 1,356,763.png|thumb|Original [[Patent Drawing]].]]
The Hartley oscillator was invented by [[Ralph Hartley|Ralph V.L. Hartley]] while he was working for the Research Laboratory of the Western Electric Company.  Hartley invented and patented the design in 1915 while overseeing Bell System's transatlantic radiotelephone tests; it was awarded patent number [http://patimg2.uspto.gov/.piw?Docid=01356763&homeurl=http%3A%2F%2Fpatft.uspto.gov%2Fnetacgi%2Fnph-Parser%3FSect1%3DPTO1%2526Sect2%3DHITOFF%2526d%3DPALL%2526p%3D1%2526u%3D%25252Fnetahtml%25252FPTO%25252Fsrchnum.htm%2526r%3D1%2526f%3DG%2526l%3D50%2526s1%3D1,356,763.PN.%2526OS%3DPN%2F1,356,763%2526RS%3DPN%2F1,356,763&PageNum=&Rtype=&SectionNum=&idkey=NONE&Input=View+first+page 1,356,763] on October 26, 1920. Note that the above basic schematic is essentially the same as in the patent drawing, except that the tube is replaced by a J-FET, and that the battery for a negative grid bias is not needed.
In 1946 Hartley was awarded the IRE medal of honor "For his early work on oscillating circuits employing triode tubes and likewise for his early recognition and clear exposition of the fundamental relationship between the total amount of information which may be transmitted over a transmission system of limited band-width and the time required."<ref>
Ralph V. L. Hartley, Legacies, IEEE History Center, updated January 23, 2003, http://www.ieee.org/organizations/history_center/legacies/hartley.html</ref>(The second half of the citation refers to Hartley's work in information theory which largely paralleled [[Harry Nyquist]].)


== Applications==
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
[[Image:Scott310E hartley.gif|framed|Part of Scott 310E circuit diagram]]
*[[Displaystyle]]
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*[[Styling]]
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*[[Unique Ids]]
*[[Help:Formula]]


The Hartley oscillator was extensively used on all [[broadcast band]]s including the FM 88-108&nbsp;MHz band. An example is given of the Scott 310E RF oscillator for its FM section.
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
{{-}}
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
== See also ==
LC oscillators:
* [[Armstrong oscillator]]
* [[Colpitts oscillator]]
* [[Clapp oscillator]]
* [[Vačkář oscillator]]
Other (non-LC):
* [[Wien bridge oscillator]]
* [[Opto-electronic oscillator]]
 
== References ==
{{Reflist}}
*{{Citation
|inventor-first= Ralph Vinton Lyon
|inventor-last= Hartley
|inventorlink= Ralph Hartley
 
|title= Oscillation Generator
|description=
|country-code= US
|patent-number= 1356763
|issue-date= October 26, 1920
|publication-date= June 1, 1915
|doi=}}
*{{Citation
|first= F.
|last= Langford-Smith
|title= Radiotron Designer's Handbook
|edition= 4th
|year= 1952
|publisher= Amalgamated Wireless Valve Company Pty., Ltd.
|location= Sydney, Australia
|isbn=
|doi=}}
*{{Citation
|first= F. A.
|last= Record
|first2= J. L.
|last2= Stiles
|title= An Analytical Demonstration of Hartley Oscillator Action
|journal= Proceedings of the IRE
|volume= 31
|issue= 6
|date= June 1943
|issn= 0096-8390
|doi= }}
*{{Citation
|first1= Ulrich L.
|last1= Rohde
|first2= Ajay K.
|last2= Poddar
|first3= Georg
|last3= Böck
|title= The Design of Modern Microwave Oscillators for Wireless Applications: Theory and Optimization
|publisher= John Wiley & Sons
|location= New York, NY
|date= May, 2005
|isbn= 0-471-72342-8
|doi= }} 
*{{Citation
|first= George
|last= Vendelin
|first2= Anthony M.
|last2= Pavio
|first3= Ulrich L.
|last3= Rohde
|title= Microwave Circuit Design Using Linear and Nonlinear Techniques
|publisher= John Wiley & Sons
|location= New York, NY
|date= May, 2005
|isbn= 0-471-41479-4
|doi= }}
 
== External links ==
* [http://www.tpub.com/content/neets/14181/css/14181_81.htm Hartley oscillator], Integrated Publishing
 
[[Category:Oscillators]]
 
[[ca:Oscil·lador Hartley]]
[[de:Hartley-Schaltung]]
[[es:Oscilador Hartley]]
[[fr:Oscillateur Hartley]]
[[nl:Hartley-oscillator]]
[[ja:ハートレー発振回路]]
[[pl:Generator Hartleya]]
[[pt:Oscilador Hartley]]
[[ru:Генератор Хартли]]
[[sr:Hartli oscilator]]
[[sv:Hartley-oscillator]]
[[ur:ہارٹلے ارتعاش]]
[[zh:哈特莱振荡器]]

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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