Friedmann–Lemaître–Robertson–Walker metric: Difference between revisions

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The '''Hartley oscillator''' is an [[electronic oscillator]] [[electronic circuit|circuit]] in which the oscillation frequency is determined by a [[tuned circuit]] consisting of [[capacitor]]s and [[inductor]]s, 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 (or a single tapped inductor), and the [[feedback]] signal needed for oscillation is taken from the center connection of the two inductors.
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==Operation==
[[Image:Hartley osc.svg|framed|Common-drain Hartley circuit]]
The Hartley oscillator is distinguished by a [[tank circuit]] consisting of two series-connected [[inductor|coils]] (or, often, a [[coil tap|tapped]] coil) in parallel with a capacitor, with an amplifier between the relatively [[High impedance]] across the entire LC tank and the relatively low voltage/high current point between the coils. The original 1915 version used a [[triode]] as the amplifying device in [[Common plate]] (cathode follower) configuration, with three batteries, and separate adjustable coils. The most simple of implementations shown here uses nothing but a [[Junction FET|JFET]] (in [[Common-drain]] configuration) and the LC tank circuit (here the single winding is tapped), plus a single battery; it will work, but probably with high [[distortion]] and high current drain (that could be improved by adding resistance between the source and the coil tap), and serves as an uncomplicated illustration of the Hartley oscillator operation:
 
* the output from the JFET's ''source'' (''emitter'', if a [[Bipolar Junction Transistor|BJT]] had been used; ''cathode'' for a triode) has the same [[phase]] as the signal at its gate (or base) -  and roughly the same voltage as its input (which is the voltage across the entire tank circuit), but the ''current is amplified'', i.e. it is acting as a [[Buffer amplifier#Current buffer|current buffer]] or [[VCVS|voltage-controlled voltage-source]].
* this low impedance output is then fed into the coil tapping, effectively into an [[autotransformer]] that will step up the voltage, requiring a relatively high current (compared with that available at the top of the coil).
* With the capacitor-coil [[resonance]], all frequencies other than the tuned frequency will tend to be absorbed  (the tank will appear as nearly zero ohms near DC due to the inductor's low [[reactance]] at low frequencies, and low again at very high frequencies due to the capacitor); they will also shift the phase of the feedback from the zero degrees needed for oscillation at all but the tuned frequency.
 
Variations on the simple circuit often include ways to [[Automatic Gain Control|automatically]] reduce the amplifier gain to maintain a constant output voltage at a level below overload; the simple circuit above will limit the outoput voltage due to the gate conducting on positive peaks, effectively damping oscillations - but not before significant distortion ([[Spurious tone|spurious]] [[harmonics]]) may result. Changing the tapped coil to two separate coils, as in the original patent schematic, still results in a working oscillator but now that the two coils are not [[magnetically coupled]] the inductance, and so frequency, calculation has to be modified (see below), and the explanation of the voltage increase mechanism is more complicated than the autotransformer scenario.
 
A quite different implementation using a tapped coil in an LC tank feedback arrangement, still called a Hartley oscillator (or sometimes "the" Hartley Oscillator circuit<ref>http://www.learnabout-electronics.org/Oscillators/osc21.p The Hartley Oscillator</ref>) is to employ a common-grid (or common-gate or common-base) amplifier stage, which is still [[non-inverting]] but provides ''voltage gain'' instead of ''current gain''; the coil tapping is still connected to the cathode (or source or emitter), but this is now the (low impedance) input to the amplifier; the split tank circuit is now dropping the impedance from the relatively high output impedance of the plate (or drain or collector).
 
The Hartley oscillator is the dual of the [[Colpitts oscillator]] which uses a voltage divider made of two capacitors rather than two inductors.  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, with the feedback taken from the tap, 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.
[[Image:Oscillator hartley opamp.svg|thumb|Op-amp version of Hartley oscillator]]
The frequency of oscillation is approximately the [[resonant frequency]] of the tank circuit. If the capacitance of the tank capacitor is ''C'' and the total [[inductance]] of the tapped coil is ''L'' then
:<math>f =  {1 \over 2 \pi \sqrt {LC}} \,</math>
If two ''uncoupled'' coils of inductance ''L''<sub>1</sub> and ''L''<sub>2</sub> are used then
:<math>L = L_1 + L_2 \,</math>
However if the two coils are magnetically coupled the total inductance will be greater because of [[mutual inductance]] ''k''<ref>Jim McLucas, Hartley oscillator requires no coupled inductors, EDN October 26, 2006 http://www.edn.com/article/CA6343253.html</ref>
:<math>L = L_1 + L_2 + k \sqrt{L_1 L_2} \,</math>
The actual oscillation frequency will be slightly lower than given above, because of [[parasitic capacitance]] in the coil and loading by the transistor.
 
Advantages of the Hartley oscillator include:
 
* The frequency may be adjusted using a single variable capacitor, one side of which can be earthed
* The output amplitude remains constant over the frequency range
* 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:
 
* Harmonic-rich output if taken from the amplifier and not directly from the LC circuit (unless amplitude-stabilisation circuitry is employed).
 
== History ==
[[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]].)
 
== See also ==
* [[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
 
{{Electronic oscillators}}
 
[[Category:Oscillators]]
[[Category:1915 introductions]]

Latest revision as of 04:28, 13 January 2015

Epoxy resins have been in use for almost a century. Epoxies are versatile polymers and exhibit distinctive blend of properties. In any high-tech structural use, where light weight, durability, low cure shrinkage, strength and stiffness, adhesion electrical insulation and corrosion resistance properties are entailed, resins are regarded as the minimum standard of performance for the matrix of the composite. This is the reason why in aerospace, airplanes, aircrafts, offshore racing boats applications, resins have been the 'norm' for years.

Nonetheless, 95% of pleasure boats under sixty feet now are still constructed with polyester resin. The key consideration for materials choice for most composite builders is cost, with value and performance usually being a secondary consideration. As a rule, resins are twice as costly as vinyl ester resins and vinyl ester are twice as costly as polyesters. On the other hand, when considered against the cost of the entire structure (the boat), the cost is fairly insignificant and the value of superior quality and long term benefits of better durability (hence better resale value) can be magnanimous.

Contributing Factors to this Better Value:

Adhesive Properties:

Epoxies have far superior adhesive properties as compared to vinyl and polyester resins. The better adhesion of epoxies is due to 2-key reasons. If you have any questions pertaining to exactly where and how to use epoxi resina, you can speak to us at our page. The first is at the physical level- as epoxy cure with low shrinkage, several surface contacts set up between liquid resin and reinforcement is not disturbed during cure. The outcome is a more homogenous bond between resins and fibres and a better transmission of load between the various components of the matrix. The second one is at molecular level, wherein the presence of polar hydroxyl boosts adhesion.

Mechanical Properties:

Two vital mechanical characteristics of any resin systems are its tensile stiffness and strength. The tensile strength of epoxy resins is 20-30% higher than vinyl ester and polyester. It is to be noted that boats constructed with vinyl or polyester are seldom post cured in the workshop while boats made with epoxies quite often are.

Enhanced Resistance to Micro Cracking and Fatigue:

In majority instances, an appropriately designed hull laminate will never be subjected to its ultimate strength therefore, physical properties of resin matrix, though imperative are not the sole criteria on which the choice has to be made. Long before the final load is transferred and failure occurs, the laminate will reach a stress level, wherein the resin will start to split away from the fibre reinforcements not aligned along with the applied load.

Reduced Degradation from Water Penetration:

A vital property of resin, especially in a marine environment is its capability to resist degradation from water ingress. Both vinyl and polyester are prone to water ingress because of the existence of hydrolysable ester groups in their molecular structures. Consequently, a slender polyester laminate can be anticipated to retain only 65% of its inter-laminate strength after immersion over the tenure of one year. Whereas epoxy resins laminate immersed for an identical time will retain around 90%.