Talk:Parametric oscillator

Bad start

The present article covers Parametric amplifier quite well, and that IMO should be the main title. The redirection to a practically incoherent(?) introduction called Parametric oscillator is flawed and amateurish. Cuddlyable3 (talk) 06:11, 18 April 2008 (UTC)

Thank you, Cuddlyable; I'm glad you liked my parts! :) I'm inclined to agree with you about the additions, but the whole article could use some sprucing up, clarifying and referencing; I wrote it pretty early in my time here. I've been meaning to fix it up, for everyone who'd like to know how tree swings work; but I've been distracted with a few other projects in recent months. I'll try to come back soon, but you should also feel free to edit the article. :) Willow (talk) 08:49, 18 April 2008 (UTC)

Pump frequency

The pump frequency does not have to be twice the working frequency as the article states in the child swing example. The pump frequency can be twice, equal or lower than the resonance frequency. Helmut Wabnig (talk) 19:14, 27 February 2015 (UTC)

Parametric Amplifier section

I have translated the article for the German Wikipedia. While in the first parts of the article seemed to be quite well written, I had a few problems understanding the last part about the amplifiers. I don't know whether they are just unclear because I didn't understand them correctly or if there are parts that are really unspecific and even contradictory. I would appreciate if someone could comment on the following general remarks about the article in chronological order:

• For me the section "Parametric Resonance" just seems to be an unnecessary recapitulation of what has already been said before. Apart from the classical example that is given, everything has already been said before or is explained below. The differential equation is equivalent to the one above with the function f being replaced by a cos with some constant. I assume t represents the time as in the examples above. Why does the cos function not contain an angular frequency then? I guess one could use a nondimensionalised time, but for me it seems a bit odd and confusing, since I am used to see t in units of time which would cause a problem in this case.
• Now to the last paragraph in the "Introduction" of the amplifier section below. It might be totally correct and clear, but I am not too much of an electric engineer and therefor not familiar with the language, so I stumbled across the sentence containing "LC network with four eigenvectors with nodes at the connections". What exactly is meant by that and is the link to eigenvector correct? I only know eigenvectors in connection to matrices so I would assume some kind of eigenvalue problem for determining eigenfrequencies of a system, but I cannot figure out how to build an eigenvector into an electric circuit.
• Moving on to the next section. What exactly is meant by damping D? From what my intuition would tell me, it should be something like a Damping factor or a Damping ratio. The following constant alpha is even more mysterious. Since it is not introduced one might just assume it is some random rational number, but since t seems to be the time again one might just as well assume some kind of decay constant, so that the units would cancel and match those of the Damping factor or ratio. If t is indeed the time it would go from minus to plus infinity if alpha is constant and I just cannot make any sense of a "damping" that would fit in such an equation.
• I am not very impressed with the "rough" solution in general, but maybe with more explanation, one would be able to see something from it.
• Now to what is left of the explanation. First of all the usual question: What does h stand for? My suggestion this time is that it is the whole $h_{0}\sin 2\omega _{0}t$ part, the pumping function in the same way it is defined in the "Transformation of the equation" part above. "As $h_{0}$ approaches the threshold $2b$, the amplitude diverges." is certainly correct, but what does it mean with regards to the rough solution? I would say, that if the Amplitude of the driving force is close to a certain constant value, the output signal goes to plus or minus infinity, which only is a phase offset in this particular case and in case it gets even higher than 2b, the stronger the input signal gets, the weaker the output will be.
• Following up: "When $h\geq 2b$, the system enters parametric resonance and the amplitude begins to grow exponentially, even in the absence of a driving force $E(t)$". If h means h0, the above applies. If it is indeed the whole sinus term, it is either always below, or for a certain period above 2b. In any case it seems to be contradictory to "We assume that the damping D is sufficiently strong that, in the absence of the driving force E, the amplitude of the parametric oscillations does not diverge", therfore I assume it implies the absence of damping. Still, if one refers to the rough solution then for $E(t)\to 0$ one might as well write $E_{0}\to 0$, and in case $h_{0}\neq 2b$ the whole function will always be zero.
• Last point in the advantages section states that the parametric oscillator has the unique capability to operate without internal power supply. Even though it has got a reference it looks a bit odd to me. I had a look at the abstract of referred article and if I understood correctly, the absence of an internal power source means the inductive coupling of an external power source. For me that should be possible with any amplifier. I cannot see any "unique capability".

Sorry for the long and maybe a bit complicated explanation, but I would be very grateful if someone had any answers or could clarify some stuff.--Debenben (talk) 03:53, 23 January 2013 (UTC)

Another point: "damping" can be missunderstood since e.g. a swing without friction is described by the equation:

${\begin{aligned}{\ddot {\varphi }}+2{\frac {\dot {L}}{L}}{\dot {\varphi }}+{\frac {g}{L}}sin{\varphi }=0\end{aligned}}$

--Debenben (talk) 00:38, 30 January 2013 (UTC)

A Minor Opinion on Notation

In this article the parameter b is introduced as the time-averaged damping for the general time dependent damping beta(t). Omega(t) has an omega_0 as it's time-averaged counterpart, so does it not make sense to use a beta_0 for beta(t)? I'm not sure if b is a typical choice in the literature or not, but even if so I think Wikipedia is a great place to change that. To me, it makes more sense to have some symmetry to the notation. — Preceding unsigned comment added by I want a bear as a pet (talk • contribs) 03:18, 27 May 2017 (UTC)

I understand your point, but Wikipedia is not the place to change anything. See WP:RGW. Constant314 (talk) 05:14, 27 May 2017 (UTC)

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