Main Page: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older editNewer edit →
No edit summary
No edit summary
Line 1: Line 1:
{{redirect|FRW}}
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.
{{Physical cosmology |expansion}}


The '''Friedmann–Lemaître–Robertson–Walker''' ('''FLRW''') '''[[Riemannian metric|metric]]''' is an [[Exact solutions in general relativity|exact solution]] of [[Einstein field equations|Einstein's field equations]] of [[general relativity]]; it describes a [[homogeneity (physics)#Translation invariance|homogeneous]], [[isotropic]] [[metric expansion of space|expanding]] or contracting [[universe]] that may be [[simply connected space|simply connected]] or [[multiply connected]].<ref>For an early reference, see Robertson (1935); Robertson ''assumes'' multiple connectedness in the positive curvature case and says that "we are still free to restore" simple connectedness.</ref><ref name="LaLu95">{{Citation |author1=M. Lachieze-Rey |author2=J.-P. Luminet |date=1995 |journal=[[Physics Reports]] |title=Cosmic Topology |volume=254 |issue=3 |pages=135–214 |arxiv=gr-qc/9605010 |doi=10.1016/0370-1573(94)00085-H|bibcode = 1995PhR...254..135L }}</ref><ref name="Ellis98">{{cite conference |author1=G. F. R. Ellis |author2=H. van Elst |date=1999 |title=Cosmological models (Cargèse lectures 1998) |editor=Marc Lachièze-Rey |booktitle=Theoretical and Observational Cosmology |series=NATO Science Series C |volume=541 |pages=1–116 |arxiv=gr-qc/9812046 |bibcode=1999toc..conf....1E |isbn=978-0792359463}}</ref> (If multiply connected, then each event in spacetime will be represented by more than one [[tuple]] of coordinates.) The general form of the metric follows from the geometric properties of homogeneity and isotropy; Einstein's field equations are only needed to derive the [[scale factor (cosmology)|scale factor]] of the universe as a function of time. Depending on geographical or historical preferences, a subset of the four scientists — [[Alexander Friedmann]], [[Georges Lemaître]], [[Howard P. Robertson]] and [[Arthur Geoffrey Walker]] — may be named (e.g., '''Friedmann–Robertson–Walker''' ('''FRW''') or '''Robertson–Walker''' ('''RW''') or '''Friedmann–Lemaître''' ('''FL''')). This model is sometimes called the ''Standard Model'' of modern cosmology.<ref name=Goobar>{{citation |author=L. Bergström, A. Goobar |date=2006 |title=Cosmology and Particle Astrophysics |page=61 |url=http://books.google.com/books?id=CQYu_sutWAoC&pg=PA61 |edition=2nd |publisher=[[Springer (publisher)|Sprint]] |isbn=3-540-32924-2}}</ref> It was developed independently by the named authors in the 1920s and 1930s.
==Operation==
[[Image:Hartley osc.svg|framed|Schematic diagram]]
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.


== General metric ==
It is made up of the following:


The FLRW metric starts with the assumption of [[homogeneity (physics)#Translation invariance|homogeneity]] and [[isotropy]] of space. It also assumes that the spatial component of the metric can be time-dependent. The generic metric which meets these conditions is
* Two [[inductor]]s in series, which need not be mutual
:<math>- c^2 \mathrm{d}\tau^2 = - c^2 \mathrm{d}t^2 + {a(t)}^2 \mathrm{d}\mathbf{\Sigma}^2</math>
* One tuning capacitor
where <math>\mathbf{\Sigma}</math> ranges over a 3-dimensional space of uniform curvature, that is, [[elliptical space]], [[Euclidean space]], or [[hyperbolic space]]. It is normally written as a function of three spatial coordinates, but there are several conventions for doing so, detailed below. <math>\mathrm{d}\mathbf{\Sigma}</math> does not depend on ''t'' — all of the time dependence is in the function ''a''(''t''), known as the "[[Scale factor (universe)|scale factor]]".


===Reduced-circumference polar coordinates===
Advantages of the Hartley oscillator include:
In reduced-circumference polar coordinates the spatial metric has the form
:<math>\mathrm{d}\mathbf{\Sigma}^2 = \frac{\mathrm{d}r^2}{1-k r^2} + r^2 \mathrm{d}\mathbf{\Omega}^2, \quad \text{where } \mathrm{d}\mathbf{\Omega}^2 = \mathrm{d}\theta^2 + \sin^2 \theta \, \mathrm{d}\phi^2.</math>


''k'' is a constant representing the curvature of the space. There are two common unit conventions:
* The frequency may be adjusted using a single variable capacitor, one side of which can be earthed
*''k'' may be taken to have units of length<sup>−2</sup>, in which case ''r'' has units of length and ''a''(''t'') is unitless. ''k'' is then the [[Gaussian curvature]] of the space at the time when ''a''(''t'') = 1. ''r'' is sometimes called the reduced [[circumference]] because it is equal to the measured circumference of a circle (at that value of ''r''), centered at the origin, divided by 2{{pi}} (like the ''r'' of [[Schwarzschild coordinates]]). Where appropriate, ''a''(''t'') is often chosen to equal 1 in the present cosmological era, so that <math>\mathrm{d}\mathbf{\Sigma}</math> measures [[comoving distance]].
* The output amplitude remains constant over the frequency range
*Alternatively, ''k'' may be taken to belong to the set {−1,0,+1} (for negative, zero, and positive curvature respectively). Then ''r'' is unitless and ''a''(''t'') has units of length. When ''k'' = ±1, ''a''(''t'') is the [[Radius of curvature (mathematics)|radius of curvature]] of the space, and may also be written ''R''(''t'').
* 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]]).


A disadvantage of reduced circumference coordinates is that they cover only half of the 3-sphere in the case of positive curvature—circumferences beyond that point begin to decrease, leading to degeneracy. (This is not a problem if space is [[elliptical geometry|elliptical]], i.e. a 3-sphere with opposite points identified.)
Disadvantages include:


===Hyperspherical coordinates===
* Harmonic-rich output if taken from the amplifier and not directly from the LC circuit (unless amplitude-stabilisation circuitry is employed).
In ''hyperspherical'' or ''curvature-normalized'' coordinates the coordinate ''r'' is proportional to radial distance; this gives
:<math>\mathrm{d}\mathbf{\Sigma}^2 = \mathrm{d}r^2 + S_k(r)^2 \, \mathrm{d}\mathbf{\Omega}^2</math>
where <math>\mathrm{d}\mathbf{\Omega}</math> is as before and
:<math>S_k(r) =
\begin{cases}
\sqrt{k}^{\,-1} \sin (r \sqrt{k}), &k > 0 \\
r, &k = 0 \\
\sqrt{|k|}^{\,-1} \sinh (r \sqrt{|k|}), &k < 0.
\end{cases}
</math>


As before, there are two common unit conventions:
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>):
*''k'' may be taken to have units of length<sup>−2</sup>, in which case ''r'' has units of length and ''a''(''t'' ) is unitless.  ''k'' is then the [[Gaussian curvature]] of the space at the time when ''a''(''t'' ) = 1.  Where appropriate, ''a''(''t'' ) is often chosen to equal 1 in the present cosmological era, so that <math>\mathrm{d}\mathbf{\Sigma}</math> measures [[comoving distance]].
*Alternatively, as before, ''k'' may be taken to belong to the set {−1,0,+1} (for negative, zero, and positive curvature respectively). Then ''r'' is unitless and ''a''(''t'' ) has units of length. When ''k'' = ±1, ''a''(''t'' ) is the [[Radius of curvature (mathematics)|radius of curvature]] of the space, and may also be written ''R''(''t'' ).  Note that, when ''k'' = +1, ''r'' is essentially a third angle along with ''θ'' and ''φ''. The letter ''χ''  may be used instead of&nbsp;''r''.


Though it is usually defined piecewise as above, ''S'' is an [[analytic function]] of both ''k'' and ''r''. It can also be written as a [[power series]]
<math>
:<math>S_k(r) = \sum_{n=0}^\infty \frac{(-1)^n k^n r^{2n+1}}{(2n+1)!} = r - \frac{k r^3}{6} + \frac{k^2 r^5}{120} - \cdots</math>
L_0 = L_1 + L_2 + k*\sqrt{L_1*L_2}
or as
</math>
:<math>S_k(r) = r \; \mathrm{sinc} \, (r \sqrt{k})</math>
where sinc is the unnormalized [[sinc function]] and <math>\sqrt{k}</math> is one of the imaginary, zero or real square roots of ''k''. These definitions are valid for all ''k''.
 
===Cartesian coordinates===
When ''k'' = 0 one may write simply
:<math>\mathrm{d}\mathbf{\Sigma}^2 = \mathrm{d}x^2 + \mathrm{d}y^2 + \mathrm{d}z^2.</math>
This can be extended to ''k'' ≠ 0 by defining
:<math> x = r \cos \theta \,</math>,
:<math> y = r \sin \theta \cos \phi \,</math>, and
:<math> z = r \sin \theta \sin \phi \,</math>,
where ''r'' is one of the radial coordinates defined above, but this is rare.
 
== Solutions ==
{{General relativity sidebar |solutions}}
{{main|Friedmann equations}}
 
Einstein's field equations are not used in deriving the general form for the metric: it follows from the geometric properties of homogeneity and isotropy. However, determining the time evolution of <math>a(t)</math> does require Einstein's field equations together with a way of calculating the density, <math>\rho (t),</math> such as a [[equation of state (cosmology)|cosmological equation of state]].
 
This metric has an analytic solution to [[Einstein field equations|Einstein's field equations]] <math>G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^{4}} T_{\mu\nu}</math> giving the [[Friedmann equations]] when the [[energy-momentum tensor]] is similarly assumed to be isotropic and homogeneous. The resulting equations are:<ref>{{citation |author=P. Ojeda and H. Rosu |date=2006 |title=Supersymmetry of FRW barotropic cosmologies |journal=[[International Journal of Theoretical Physics]] |volume=45 |issue=6 |pages=1191–1196 |doi=10.1007/s10773-006-9123-2 |arxiv=gr-qc/0510004 |bibcode=2006IJTP...45.1152R}}</ref>
:<math>\left(\frac{\dot a}{a}\right)^{2} + \frac{kc^{2}}{a^2} - \frac{\Lambda c^{2}}{3} = \frac{8\pi G}{3}\rho</math>
:<math>2\frac{\ddot a}{a} + \left(\frac{\dot a}{a}\right)^{2} + \frac{kc^{2}}{a^2} - \Lambda c^{2} = -\frac{8\pi G}{c^{2}} p.</math>
 
These equations are the basis of the standard [[big bang]] cosmological model including the current [[Lambda-CDM model|ΛCDM]] model. Because the FLRW model assumes homogeneity, some popular accounts mistakenly assert that the big bang model cannot account for the observed lumpiness of the universe. In a strictly FLRW model, there are no clusters of galaxies, stars or people, since these are objects much denser than a typical part of the universe. Nonetheless, the FLRW model is used as a first approximation for the evolution of the real, lumpy universe because it is simple to calculate, and models which calculate the lumpiness in the universe are added onto the FLRW models as extensions. Most cosmologists agree that the [[observable universe]] is well approximated by an ''almost FLRW model'', i.e., a model which follows the FLRW metric apart from [[primordial fluctuations|primordial density fluctuations]]. {{As of|2003}}, the theoretical implications of the various extensions to the FLRW model appear to be well understood, and the goal is to make these consistent with observations from [[Cosmic Background Explorer|COBE]] and [[WMAP]].
 
===Interpretation===
The pair of equations given above is equivalent to the following pair of equations
:<math>{\dot \rho} = - 3 \frac{\dot a}{a}\left(\rho+\frac{p}{c^{2}}\right)</math>
:<math>\frac{\ddot a}{a} = - \frac{4\pi G}{3}\left(\rho + \frac{3p}{c^{2}}\right) + \frac{\Lambda c^{2}}{3}</math>
with <math>k</math>, the spatial curvature index, serving as a [[constant of integration]] for the first equation.
 
The first equation can be derived also from [[Thermodynamics of the universe|thermodynamical considerations]] and is equivalent to the [[first law of thermodynamics]], assuming the expansion of the universe is an [[adiabatic process]] (which is implicitly assumed in the derivation of the Friedmann–Lemaître–Robertson–Walker metric).
 
The second equation states that both the energy density and the pressure cause the expansion rate of the universe <math>{\dot a}</math> to decrease, i.e., both cause a deceleration in the expansion of the universe. This is a consequence of [[gravitation]], with pressure playing a similar role to that of energy (or mass) density, according to the principles of [[general relativity]]. The [[cosmological constant]], on the other hand, [[Dark energy|causes an acceleration in the expansion]] of the universe.
 
===Cosmological constant===
The [[cosmological constant]] term can be omitted if we make the following replacements
:<math>\rho \rightarrow \rho + \frac{\Lambda c^{2}}{8 \pi G}</math>
:<math>p \rightarrow p - \frac{\Lambda c^{4}}{8 \pi G}.</math>
 
Therefore the [[cosmological constant]] can be interpreted as arising from a form of energy which has negative pressure, equal in magnitude to its (positive) energy density:
:<math>p = - \rho c^2. \,</math>
Such form of energy—a generalization of the notion of a [[cosmological constant]]—is known as [[dark energy]].
 
In fact, in order to get a term which causes an acceleration of the universe expansion, it is enough to have a [[scalar field theory|scalar field]] which satisfies
:<math>p < - \frac {\rho c^2} {3}. \,</math>
Such a field is sometimes called [[Quintessence (physics)|quintessence]].
 
===Newtonian interpretation===
The Friedmann equations are equivalent to this pair of equations:
:<math> - a^3 {\dot \rho} = 3 a^2 {\dot a} \rho + \frac{3 a^2 p {\dot a}}{c^2} \,</math>
:<math>\frac{{\dot a}^2}{2} - \frac{G \frac{4 \pi a^3}{3} \rho}{a} = - \frac{k c^2}{2} \,.</math>
 
The first equation says that the decrease in the mass contained in a fixed cube (whose side is momentarily ''a'') is the amount which leaves through the sides due to the expansion of the universe plus the mass equivalent of the work done by pressure against the material being expelled. This is the conservation of mass-energy ([[first law of thermodynamics]]) contained within a part of the universe.
 
The second equation says that the kinetic energy (seen from the origin) of a particle of unit mass moving with the expansion plus its (negative) gravitational potential energy (relative to the mass contained in the sphere of matter closer to the origin) is equal to a constant related to the curvature of the universe. In other words, the energy (relative to the origin) of a co-moving particle in free-fall is conserved. General relativity merely adds a connection between the spatial curvature of the universe and the energy of such a particle: positive total energy implies negative curvature and negative total energy implies positive curvature.
 
The [[cosmological constant]] term is assumed to be treated as dark energy and thus merged into the density and pressure terms.
 
During the [[Planck epoch]], one cannot neglect [[quantum mechanics|quantum]] effects. So they may cause a deviation from the Friedmann equations.
 
== Name and history ==
 
The main results of the FLRW model were first derived by the Soviet mathematician [[Alexander Friedmann]] in 1922 and 1924. Although his work was published in the prestigious physics journal [[Zeitschrift für Physik]], it remained relatively unnoticed by his contemporaries. Friedmann was in direct communication with [[Albert Einstein]], who, on behalf of Zeitschrift für Physik, acted as the scientific referee of Friedmann's work. Eventually Einstein acknowledged the correctness of Friedmann's calculations, but failed to appreciate the physical significance of Friedmann's predictions.
 
Friedmann died in 1925. In 1927, [[Georges Lemaître]], a Belgian priest, astronomer and periodic professor of physics at the [[Catholic University of Leuven (1834–1968)|Catholic University of Leuven]], arrived independently at similar results as Friedmann and published them in Annals of the Scientific Society of Brussels. In the face of the observational evidence for the expansion of the universe obtained by [[Edwin Hubble]] in the late 1920s, Lemaître's results were noticed in particular by [[Arthur Eddington]], and in 1930–31 his paper was translated into English and published in the [[Monthly Notices of the Royal Astronomical Society]].
 
[[Howard P. Robertson]] from the US and [[Arthur Geoffrey Walker]] from the UK explored the problem further during the 1930s. In 1935 Robertson and Walker rigorously proved that the FLRW metric is the only one on a spacetime that is spatially homogeneous and isotropic (as noted above, this is a geometric result and is not tied specifically to the equations of general relativity, which were always assumed by Friedmann and Lemaître).


Because the dynamics of the FLRW model were derived by Friedmann and Lemaître, the latter two names are often omitted by scientists outside the US. Conversely, US physicists often refer to it as simply "Robertson–Walker". The full four-name title is the most democratic and it is frequently used.{{Citation needed|date=September 2011}} Often the "Robertson–Walker" ''metric'', so-called since they proved its generic properties, is distinguished from the dynamical "Friedmann-Lemaître" ''models'', specific solutions for ''a''(''t'') which assume that the only contributions to stress-energy are cold matter ("dust"), radiation, and a cosmological constant.
(see <ref>Jim McLucas, Hartley oscillator requires no coupled inductors, EDN October 26, 2006 http://www.edn.com/article/CA6343253.html</ref>)


== Einstein's radius of the universe ==
== 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]].)


'''Einstein's radius of the universe''' is the [[Radius of curvature (mathematics)|radius of curvature]] of space of [[Einstein's universe]], a long-abandoned [[Static spacetime|static]] model that was supposed to represent our universe in idealized form. Putting
== Applications==
:<math>\dot{a} = \ddot{a} = 0</math>
[[Image:Scott310E hartley.gif|framed|Part of Scott 310E circuit diagram]]


in the Friedmann equation, the radius of curvature of space of this universe (Einstein's radius) is{{Citation needed|date=June 2011}}
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.
:<math>R_E=c/\sqrt {4\pi G\rho}</math>,


where <math>c</math> is the speed of light, <math>G</math> is the [[gravitational constant|Newtonian gravitational constant]], and <math>\rho</math> is the density of space of this universe. The numerical value of Einstein's radius is of the order of 10<sup>10</sup> [[light year]]s.
{{-}}


== Evidence ==
== See also ==
LC oscillators:
* [[Armstrong oscillator]]
* [[Colpitts oscillator]]
* [[Clapp oscillator]]
* [[Vačkář oscillator]]
Other (non-LC):
* [[Wien bridge oscillator]]
* [[Opto-electronic oscillator]]


By combining the observation data from some experiments such as [[Wilkinson Microwave Anisotropy Probe|WMAP]] and [[Planck (spacecraft)|Planck]] with theoretical results of [[Ehlers–Geren–Sachs theorem]] and its generalization,<ref>See pp. 351ff. in {{citation |last1=Hawking |first1=Stephen W. |last2=Ellis |first2=George F. R. |author2-link=George Francis Rayner Ellis |title=[[The large scale structure of space-time]] |publisher=Cambridge University Press |isbn=0-521-09906-4 |date=1973}}. The original work is Ehlers, J., Geren, P., Sachs, R.K.: Isotropic solutions of Einstein-Liouville equations. J. Math. Phys. 9, 1344 (1968). For the generalization, see {{citation |last=Stoeger |first=W. R. |last2=Maartens |first2=R |last3=Ellis |first3=George |author3-link=George Francis Rayner Ellis |title=Proving Almost-Homogeneity of the Universe: An Almost Ehlers-Geren-Sachs Theorem |journal=Ap. J. |volume=39 |date=2007 |pages=1–5 |doi=10.1086/175496 |bibcode=1995ApJ...443....1S}}.</ref> astrophysicists now agree that the universe is almost homogeneous and isotropic (when averaged over a very large scale) and thus nearly a FLRW spacetime.
== References ==
{{Reflist}}
*{{Citation
|inventor-first= Ralph Vinton Lyon
|inventor-last= Hartley
|inventorlink= Ralph Hartley


== References and notes ==
|title= Oscillation Generator
{{reflist}}
|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= }}


== Further reading ==
== External links ==
* {{citation |last=Friedman |first=Alexander |author-link=Alexander Friedman |title=Über die Krümmung des Raumes |date=1922 |journal=Zeitschrift für Physik A |volume=10 |issue=1 |pages=377–386 |doi=10.1007/BF01332580 |bibcode=1922ZPhy...10..377F}}<!-- Фридман, Александр Александрович -->
* [http://www.tpub.com/content/neets/14181/css/14181_81.htm Hartley oscillator], Integrated Publishing
* {{citation |last=Friedmann |first=Alexander |author-link=Alexander Friedman |title=Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes |date=1924 |journal=Zeitschrift für Physik A |volume=21 |issue=1 |pages=326–332 |doi=10.1007/BF01328280 |bibcode=1924ZPhy...21..326F}}<!-- Фридман, Александр Александрович --> English trans. in 'General Relativity and Gravitation' 1999 vol.31, 31–
* {{citation |last=Harrison |first=E. R. |title=Classification of uniform cosmological models |date=1967 |journal=Monthly Notices of the Royal Astronomical Society |volume=137 |pages=69–79 |bibcode=1967MNRAS.137...69H |doi=10.1093/mnras/137.1.69}}
* {{citation |author=d'Inverno, Ray |title=Introducing Einstein's Relativity |location=Oxford |publisher=Oxford University Press |date=1992 |isbn=0-19-859686-3}}. ''(See Chapter 23 for a particularly clear and concise introduction to the FLRW models.)''
* {{citation |last=Lemaître |first=Georges |author-link=Georges Lemaître |title=Expansion of the universe, A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulæ |date=1931 |journal=[[Monthly Notices of the Royal Astronomical Society]] |volume=91 |pages=483–490 |bibcode=1931MNRAS..91..483L |doi=10.1093/mnras/91.5.483}} ''translated from'' {{citation |last=Lemaître |first=Georges |author-link=Georges Lemaître |title=Un univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques |date=1927 |journal=Annales de la Société Scientifique de Bruxelles |volume=A47 |pages=49–56 |bibcode=1927ASSB...47...49L}}
* {{citation |last=Lemaître |first=Georges |author-link=Georges Lemaître |title=l’Univers en expansion |date=1933 |journal=Annales de la Société Scientifique de Bruxelles |volume=A53 |pages=51–85 |bibcode=1933ASSB...53...51L}}
* {{citation |last=Robertson |first=H. P. |author-link=Howard P. Robertson |date=1935 |title=Kinematics and world structure |journal=[[Astrophysical Journal]] |volume=82 |pages=284–301 |bibcode=1935ApJ....82..284R |doi=10.1086/143681}}
* {{citation |last=Robertson |first=H. P. |author-link=Howard P. Robertson |date=1936 |title=Kinematics and world structure II |journal=[[Astrophysical Journal]] |volume=83 |pages=187–201 |bibcode=1936ApJ....83..187R |doi=10.1086/143716}}
* {{citation |last=Robertson |first=H. P. |author-link=Howard P. Robertson |date=1936 |title=Kinematics and world structure III |journal=[[Astrophysical Journal]] |volume=83 |pages=257–271 |bibcode=1936ApJ....83..257R |doi=10.1086/143726}}
* {{citation |last=Walker |first=A. G. |author-link=Arthur Geoffrey Walker |date=1937 |title=On Milne’s theory of world-structure |journal=[[Proceedings of the London Mathematical Society]] 2 |volume=42 |issue=1 |pages=90–127 |doi=10.1112/plms/s2-42.1.90}}


{{Relativity}}
[[Category:Oscillators]]


{{DEFAULTSORT:Friedmann-Lemaitre-Robertson-Walker Metric}}
[[ca:Oscil·lador Hartley]]
[[Category:Coordinate charts in general relativity]]
[[de:Hartley-Schaltung]]
[[Category:Exact solutions in general relativity]]
[[es:Oscilador Hartley]]
[[Category:Physical cosmology]]
[[fr:Oscillateur Hartley]]
[[Category:Metric tensors]]
[[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]]

Revision as of 13:31, 11 August 2014

The Hartley oscillator is an electronic oscillator 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.

Operation

Schematic diagram

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 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 negative bias to limit amplification.

It is made up of the following:

  • Two inductors in series, which need not be mutual
  • One tuning capacitor

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).

Note that, if the inductance of the two partial coils and is given (e.g. in a simulator), the total effective inductance that determines the frequency of the oscillation is (coupling factor ):

(see [1])

History

Original Patent Drawing.

The Hartley oscillator was invented by 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 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."[2](The second half of the citation refers to Hartley's work in information theory which largely paralleled Harry Nyquist.)

Applications

File:Scott310E hartley.gif
Part of Scott 310E circuit diagram

The Hartley oscillator was extensively used on all broadcast bands including the FM 88-108 MHz band. An example is given of the Scott 310E RF oscillator for its FM section.

Benefits of Residing in a Apartment or Landed property in Singapore Property New Launches & Project Showcase In Singapore Many residential Singapore property sales involve buying property in Singapore at new launches. These are often homes underneath building, being sold new by developers. New Launch Singapore Property, 28 Imperial Residences Coming To Geylang Lorong 26 The property market is slowing down, based on personal property transactions in May Cell Apps FREE Sign Up Log in Property Brokers Feedback

Individuals all wish to be seen having the identical foresight as the experts in property investment or the massive names in their own fields. Thus the discharge of these tales works to encourage different buyers to observe suit. Bartley Ridge is the most popular new launch in district 13. Irresistible pricing from $1,1xx psf. Bartley Ridge is a ninety nine-12 months leasehold new condominium at Mount Vernon road, good next to Bartley MRT station (CC12). If you want to get more Rehda Johor chairman Koh Moo Hing said potential property consumers in the two areas Http://Modern.Dowatch.Net/Profile/Mic31K/Created/Topics are now adopting a wait-and-see attitude. How can I get the ebrochure and flooring plans of the new launch projects ? The Existing Mortgage on your HDB District 13, Freehold condominium District 11, Freehold Cluster landed house Sea Horizon EC @ Pasir Ris

FindSgNewLaunch is the main Singapore Property web site - one of the best place to begin your actual estate search whether you might be an investor, shopping for for own use, or searching for a spot to lease. With detailed details about each property, together with maps and pictures. We deliver you probably the most complete choice out there. No. For brand spanking new Singapore property gross sales, you possibly can withdraw at any time earlier than booking the unit, without penalty. On the preview, the agent will let you recognize the exact worth for you to resolve whether or not to proceed or not. Solely when you resolve to proceed will the agent book the unit for you. Pending for Sale Licence Approval All Pending for Sale Licence Approval New launch FREEHOLD condominium @ Braddell New launch condominium combined growth at Yishun PROJECT TITLE

To not worry, we'll hold you in our VIP Precedence list for future new launch VIP Preview. We'll contact you to establish your wants and advocate related tasks, both new launch or resale properties that probably match your standards. In case you're looking for resale property, such as these few years old, or just got Short-term Occupation Permit (PRIME), you might click on here right here for fast search and submit your shortlisted listings to us, we'll check and call you for viewing.

Oceanfront Suites, irresistible pricing for a 946 leasehold property with magnificent sea view. Dreaming of basking and feeling the warmth of pure sunlight is now just a click on away. Oceanfront Suites - Seaside residing no longer needs to remain an unattainable This Cambodia new launch, a mega development has also 762 residential models. Additionally located within this Oxley abroad property is a mega shopping center with 627 outlets and also up to 963 available workplace spaces and is surrounded by quite a few Embassy, resorts, Casinos and many vacationer relax space. Belysa EC @ Pasir Ris Esparina EC @ Sengkang Dell Launches World's first Gender-GEDI Female Entrepreneurship Index on 06/04/thirteen by Istanbul, Turkey. Paris Ris EC @ Paris Ris in search of indication of curiosity.

The developer should open a Venture Account with a financial institution or monetary establishment for every housing venture he undertakes, before he's issued with a Sale License (license to sell models in his development). All payments from buyers before completion of the challenge, and construction loans, go into the mission account. New launch rental LA FIESTA, an thrilling new condominium located along Sengkang Square / Compassvale Highway is a brief stroll to the bustling Sengkang City Centre the place the bus interchange, Sengkang MRT and LRT stations are located. Glorious location,Premium rental with Bayfront resort lifestyle theme and views ofwaterscape. Close to EC pricing - Worth for cash! Apr 02, 2013 Sengkang New Rental Launch, La Fiesta- Sengkang MRTstation at your gate.

As The Hillford property launch at Jalan Jurong Kechil may be very close to to beauty world mrt , the environment for the plot of land which belongs to World Class Land remains very upbeat as it is rather close to to Holland Village. Review now by visiting the brand new apartment pages on our website, each displaying complete particulars and the latest information of each new launch. You can even contact us directly to obtain quick & correct answers to all of your questions with high of the road service. An inevitable conclusion is that costs within the property market have just set new highs. The apparent connotation for potential buyers is to take motion now before prices bounce again. tract and points to his property line, marked by a big maple in a sea of Search SG Developersale.com

See also

LC oscillators:

Other (non-LC):

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

External links

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

  1. ↑ Jim McLucas, Hartley oscillator requires no coupled inductors, EDN October 26, 2006 http://www.edn.com/article/CA6343253.html
  2. ↑ Ralph V. L. Hartley, Legacies, IEEE History Center, updated January 23, 2003, http://www.ieee.org/organizations/history_center/legacies/hartley.html
Retrieved from "https://en.formulasearchengine.com/index.php?title=Main_Page&oldid=41540"