77.7.78.118: /* Separable Extensions for Noncommutative Rings */ formatted title correctly, removed blank line.

2014-04-01T05:30:31Z

Separable Extensions for Noncommutative Rings: formatted title correctly, removed blank line.

134.100.172.24: /* Definition and First Properties */

2014-01-05T18:56:10Z

Definition and First Properties

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	~~Hi there~~, ~~I am Alyson Boon even though it is~~ not the title [http://~~sirudang~~.~~com~~/~~siroo_Notice~~/~~2110 tarot card readings]~~ on ~~my birth certification~~. ~~Since I~~ was ~~eighteen I~~'~~ve been operating~~ as a ~~bookkeeper~~ but ~~soon my spouse~~ and ~~I will begin~~ our ~~own company~~. ~~Ohio~~ is ~~exactly where her home~~ is. As a ~~woman what she truly likes~~ is ~~style~~ and ~~she~~'s ~~been performing it~~ for ~~quite~~ a ~~while.~~<br><br>~~my homepage online~~ [http://www.~~publicpledge~~.com/~~blogs~~/~~post~~/~~7034 free psychic readings~~] ~~chat (~~[http://~~fashionlinked~~.~~com~~/~~index~~.~~php~~?~~do=~~/~~profile~~-~~13453~~/~~info~~/ ~~relevant resource site~~])		[[Image:Vackar-oscillator.svg\|thumb\|282px\|Schematic of what is commonly called the Vackář oscillator. Vackář credited Radioslava with developing this circuit in 1945.<ref>{{harvnb\|Vackář\|1949\|p=5}}</ref>]]

			A '''Vackář oscillator''' is a wide range variable frequency oscillator that strives for a near constant output amplitude over its frequency range. It is similar to a [[Colpitts oscillator]] or a [[Clapp oscillator]], but those designs do not have a constant output amplitude when tuned.

			==Invention==
			In 1949, the [[Czechoslovakia\|Czech]] engineer Jiří Vackář published a paper on the design of stable variable-frequency oscillators (VFO).<ref name="Vackář">{{citation \|first=Jiří \|last=Vackář \|title=LC Oscillators and their Frequency Stability \|series=Tesla Technial Reports \|id=UDC 621.396.615.12 \|date=December 1949 \|publisher=Tesla National Corporation \|location=Prague, Czechoslovakia \|url=http://www.f6evt.fr/f6evt_fr/vackar_wholepaper.pdf \|archiveurl=http://web.archive.org/web/20120219062848/n1ekv.org/Oscillators/Vackar_wholepaper.pdf \|archivedate=2012-02-19 }}</ref> The paper discussed many stability issues such as variations with temperature, atmospheric pressure, component aging, and microphonics. For example, Vackář describes making inductors by first heating the wire and then winding the wire on a stable ceramic coil form. The resulting inductor has a temperature coefficient of 6 to 8 parts per million per degree Celsius.<ref name="Vp2">{{harvnb\|Vackář\|1949\|p=2}}</ref> Vackář points out that common air variable capacitors have a stability of 2 parts per thousand; to build a VFO with a stability of 50 parts per million requires that the variable capacitor is only 1/40 of the tuning capacity (.002/40 = 50ppm). The stability requirement also implies the variable capacitor may only tune a limited range of 1:1.025.<ref name="Vp2"/> Larger tuning ranges require switching stable fixed capacitors or inductors.<ref>Modern low phase noise voltage controlled oscillators use bank switching.</ref>

			Vackář was interested in high stability designs, so he wanted the highest ''Q'' for his circuits. It is possible to make wide range VFOs with stable output amplitude by heavily damping (loading) the tuned circuit. However, that tactic substantially reduces the ''Q''.<ref>There is an [[insertion loss]] issue that Vackář ignores.</ref>

			Vackář was also concerned with the amplitude variations of the variable-frequency oscillator as it is tuned through its range. Vackář assumes the tuned circuit has a constant ''Q'' over the VFO's frequency range. Vackář reviewed several existing circuits for their amplitude stability.<ref>{{harvnb\|Vackář\|1949\|p=5}}</ref> The Clapp oscillator's transconductance requirement is proportional to ''ω''<sup>3</sup>. If the Clapp transconductance is set to just oscillate at the lower frequency range, then the oscillator will be overdriven at its highest frequency. The Seiler and Lampkin oscillators have a transconductance requirement that is proportional to ''ω''<sup>−1,</sup>.

			Vackář then describes an oscillator circuit due to Radioslava in 1945 that maintained "a comparatively constant amplitude over a wide frequency range."<ref>{{harvnb\|Vackář\|1949\|p=6}}</ref> Vackář reports that VFO circuit being used by the Czechoslovak Post Office since 1946. Vackář does not claim the circuit, but he analyzes the circuit and explains how to get an approximately constant amplitude response. This circuit has become known as the Vackář VFO.<ref>{{Citation \|editor-last=
			Schetgen \|editor-first=Robert \|title=The ARRL Handbook for Radio Amateurs \|edition=seventy-third \|isbn=0-87259-173-5 \|year=1996 \|contribution=The G3PDM Vackar VFO \|pages=14.17–14.18}}</ref> Vackář does refer to the circuit as "our circuit" and states that O. Landini independently discovered the circuit and published it (without an analysis) in Radio Rivista in 1948.<ref name="Vp7">{{harvnb\|Vackář\|1949\|p=7}} citing {{Citation \|last=Landini \|first=O. \|journal=Radio Rivista \|date=November 1948 \|volume= \|issue= \|pages= \|doi= }}</ref> Vackář describes a VFO design using this circuit that covers a range of 1:1.17.<ref name="Vp7"/>

			Vackář then describes a variation of the Radioslavia circuit that can cover a range of 1:2.5.<ref>{{harvnb\|Vackář\|1949\|p=7}}</ref> The circuit need not assume the tuned circuit has a constant ''Q''. Vackář patented this new circuit and two variations of it.<ref>{{citation \|inventor-first=Jiří \|inventor-last=Vackář \|title=Stabilization of resonant circuits \|country-code=US \|patent-number=2706249 \|publication-date=10 February 1950 \|issue-date=12 April 1955 }}</ref>

			==Circuit operation==
			The schematic is the equivalent of Fig. 5 in his paper (Radioslavia design), redrawn for the use of a [[JFET\|junction FET]]. L1 with C0 and Ca form the [[resonant circuit]] of a Colpitts oscillator, and Cv/Cg is the grid voltage divider. The circuit can be tuned with C0. Example values are from his paper.

			It is similar to an earlier [[Seiler oscillator]], the difference is that in Seiler's the C0 is connected to the other side of Ca. Vackář based his design on stability analysis of [[Clapp oscillator\|Gouriet-Clapp]] (Vackář claims it is for fixed frequency or a very narrow band, max 1:1.2), Seiler<ref>{{Citation \|last=Seiler \|first=E. O. \|title=Variable Frequency Oscillator \|journal=QST \|volume= \|issue= \|pages= \|date=November 1941}}</ref> and Lampkin<ref>{{citation \|last=Lampkin \|first=G. F. \|title=An Improvement in Constant Frequency Oscillators \|journal=Proceedings of the IRE \|volume= \|issue= \|date=March 1939 \|doi=}}</ref> oscillators (in the Lampkin's, an inductive voltage divider on the [[tuned circuit]] coil is used instead Cv, Cg, and Ca of Seiler's; schematics in the 1st ref).

			The oscillator's stability is due largely to the dependency of the tube's (or transistor's) forward [[transconductance]] on the [[resonant frequency]] (''ω'') of the tuned circuit. Specifically, Vackář found that forward transconductance varied as ''ω''<sup>3</sup> for the Clapp oscillator, as 1/''ω'' for the Seiler oscillator, and as ''ω''/''Q'' for his design, where the [[Q factor\|''Q'' factor]] of the coil (L1) increases with ''ω''.

			The conditions for a forward tranconductance that varies minimally with respect to ''ω'' are met when:

			::<math> C_v \ll C_0 , </math>

			::<math> C_g \gg C_v , </math>

			::<math> C_a \gg C_0 , </math>

			and the Q of the resonator increases in proportion to ''ω'',<ref name="Vackář"/> which is often approximated by real-world [[inductor]]s.

			== References ==
			{{reflist\|30em}}

			==External links==
			*[http://www.w7ekb.com/glowbugs/VFOs/vackar_vfo.html Vacuum tube Vackář]
			*[http://www.qsl.net/va3diw/vackar.html Transistor Vackář]
			*[http://www.qsl.net/va3iul/Very_Low_Phase_Noise_VFO/Very_Low_Phase_Noise_Vackar_VFO.pdf Very Low Phase Noise Vackar VFO for HF Transceivers]. (Little variation from G3PDM's design. Very low phase noise claim is dubious; NF = 20dB?)
			*[http://ece2011.p4o.net/admin/vco.pdf CMOS Implementation of Voltage Controlled Oscillator] Quote: "...[pdf-page 30]...And here is the winner. If you want to build a very stable, low phase noise, and low spurious VCO, definitely Vackar VCO is the choice...It differs in that the output level is more stable over frequency, and has a wider bandwidth when compared to a Colpitts or Clapp design..."
			*[http://epic.mcmaster.ca/~elmer101/v1.htm No-bias L-C High-Frequency Oscillator]

			{{Electronic oscillators}}

			{{DEFAULTSORT:Vackar oscillator}}
			[[Category:Oscillators]]

en>Lkadison: /* Separable Extensions for Noncommutative Rings */

2011-05-27T12:51:44Z

Separable Extensions for Noncommutative Rings

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Hi there, I am Alyson Boon even though it is not the title [http://sirudang.com/siroo_Notice/2110 tarot card readings] on my birth certification. Since I was eighteen I've been operating as a bookkeeper but soon my spouse and I will begin our own company. Ohio is exactly where her home is. As a woman what she truly likes is style and she's been performing it for quite a while.<br><br>my homepage online [http://www.publicpledge.com/blogs/post/7034 free psychic readings] chat ([http://fashionlinked.com/index.php?do=/profile-13453/info/ relevant resource site])

Separable algebra - Revision history

77.7.78.118: /* Separable Extensions for Noncommutative Rings */ formatted title correctly, removed blank line.

134.100.172.24: /* Definition and First Properties */

en>Lkadison: /* Separable Extensions for Noncommutative Rings */