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Q: equation and plot for transient LRC circuit input ( Answered ,   6 Comments )
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 Subject: equation and plot for transient LRC circuit input Category: Science Asked by: cereb-ga List Price: \$20.00 Posted: 10 Mar 2006 15:45 PST Expires: 09 Apr 2006 16:45 PDT Question ID: 705898
 ```For simulating some event that is unrelated to electronics or electricity, I found that the equations and variables involved in an LCR circuit responding to a transient have a charge/discharge curve of the type I need, together with the variables that drive it. As I envision it, the simulating circuit would be an inductor that creates a voltage when a magnet passes it, and through a diode feeds into a capacitor which, through a resistor, is connected to the other end of the inductor. All these components are basically in-line and both ends of the assembly are connected. There is a shunt resistor across the capacitor that can be adjusted to simulate leakage. The diode is inserted because if it did not exist, the inductor would serve as a low resistance conductor across the assembly R?s and the C. It only serves as a blocker to reverse current flow. The resulting curve reflects exponential charge and discharge, and the plot resulting from the component values selected should evidence a relatively sharp rise. By adjusting the variable I can then shape the resulting plot to reflect my simulated event. What I hope to receive is the equations that govern such circuit and a plot for that circuit with component values identified and ideally also the plot created by a Deadline, Winplot or Zgraph Program. I would appreciate someone responding constructively. An ASCII diagram might help and is shown below. ___________D1___________ | |____ | | | | C1 R1 | | | L1 ------ | | | R2 | | ---------------------------``` Request for Question Clarification by hedgie-ga on 11 Mar 2006 06:55 PST ```Circuit is simple, but depending on how much handholding is needed \$20 may not provide all you may expect. This phrase " the simulating circuit would be an inductor that creates a voltage when a magnet passes it" is somewhat hazy. 1) Can't we just apply some step or voltage polse to L2 terminals? 2) Are you familiar with Lapalce transform? 3) Would a link to a program which can solve/plot this be enough``` Clarification of Question by cereb-ga on 13 Mar 2006 02:57 PST ```Thank you, Hedgie - It is good to see you responding. The basic idea of it all is that this circuit will never be built - its sole purpose is to create visuals aids depicting stimuli and their decay over time to support the theme of a narrative on an entirely different subject matter. The magnitude of flux, its rate of change and the component values do not matter because I can adjust each as needed when plugged into the equations for the type of circuit illustrated. They would need to be explicit functions, sorry to say, because my math has shamefully deteriorated, as I found out when I started this project. I can change the syntax that may be required by any of the plotting programs I mentioned, however. For this particular task I do not see any need for handholding. I will need some more help later when it comes to combining plots and augmenting them with other constructs, but I will then define such tasks separately. Hope that helps. And again - thank you giving this a shot. And yes - if you know of some applet or online plotting program I could use - by all means.```
 Subject: Re: equation and plot for transient LRC circuit input Answered By: hedgie-ga on 13 Mar 2006 15:48 PST Rated:
 ```Cereb I understand that you just use the circuit to model response of a simple linerar system. We will use Lapalce method described here: RLC Circuits An Example of the Application of Laplace Transforms http://people.deas.harvard.edu/~jones/es154/lectures/lecture_0/Laplace/laplace.html%20 Your impedance is : Z(s) = R2 + Z1(s) 1/Z1(s) = 1/R1 + 1/s*C1 that can be transformed to Z(s) = R2 + R1*C1*s/( R1 + s*C1) =( R2* (R1 + s*C1) + R1 * C1 *s ) / ( R1 + s * C1) so that 1/Z(s) = (1 + C1/R1* s) / ( R2 + R2 *C1/R1 *s + C1 *s) when we do inverse transfrom reduces First a term reduces to a term proportional toapplied voltage Second to an exponetial, as shown in example 1; Now, clickingon link at the bottom of the page See Symbolic Inverse Laplace Transform Applet take you to the page which does the inverse and plots the response In my browser I do not see the [plot] button. Perhaps that step does not work. You cab use following to plot any simple function: Plotting applet http://www.pa.uky.edu/~phy211/graph_applets/plot_graph.html addtional references: http://math.fullerton.edu/mathews/c2003/LaplaceTransformBib/Links/LaplaceTransformBib_lnk_1.html Hedgie``` Request for Answer Clarification by cereb-ga on 14 Mar 2006 21:53 PST ```I mistakenly used the comment option when I replied to your answer. Basically, your answer was not responsive, and I ofered you choices. Perhaps you elect to respond?``` Clarification of Answer by hedgie-ga on 15 Mar 2006 01:11 PST ```Cereb I can understand that you are diappointed if you got 'a flat curve' I do not understand: "It is the result I needed, however." Did you mean: "It is NOT the result I needed, however." amd forgot the 'not'? In original question you said: "and ideally also the plot created by a Deadline, Winplot or Zgraph Program" I directed you to a web-based plotting applet, which can plot the exponential curve which is the solution I got for your circuit. Now it sounds like answer HAS TO use one of these three ploting programs you mentioned. It also feels like I am talking to a lawyer. I can help you your problem, but I am not willing to engage in arguments, for any amount of money. I do not think it would be expedient to try to introduce the zero star rating just for this ocassion. It would look good on my resume :-) I will simply withdraw my answer if the dialog will continue this way. So: There are some problems with the question as posed, (I am not convinced you really want a diode there- which makes the system nonlinear, and I do not see any inductor in the circuit) and with understanding the solution, and with plotting it. If you are willing and able to accept my expert asistence, I think those can be overcome by cooperative dialog. I am willing to give it another try, and as a first step I would like you to do this: Go to that plotting applet I suggested and see if you can plot function x^2 * sin(x) Describe what you get. This is a test, to see if the applet works on your machine. You can suggest a different plotting alternative, but at least you need to provide a link to such a program - You cannot assume evryone knows what Zline or whatever plotting ptogram is. And (if you want to work with me) they have to be multiplaform, like e.g. this one http://www.duke.edu/~hpgavin/gnuplot.html I do not have Winplot for Windows 95/98/ME/2K/XP (558K) (27 Feb 2006) on my machine and do not intend to install MS windows just to use that particular program. So, I am expecting your RFC, and please, do not try to enter that 0 star rating. If you cannot accept my terms for cooperation, just say so. I will withdraw the answer and write off the time I invested. That is one risk of the job. Hedgie``` Clarification of Answer by hedgie-ga on 15 Mar 2006 23:53 PST ```Cereb From what you say : "The inverse transform yielded a flat curve" I gather that you did not understand the answer. I have done the transform for you, and described result as having two terms. Restating that slightly, to make it more clear, I said " when we do the inverse transfrom, we get resulting current having two terms: First a term is proportional to the applied voltage Second term is an exponetial, same as the one shown in example 1 " The formula I gave you relates the value of your components (R1 R2 C1) to the time constant of the exponentional (the relaxation time of the circuit). Neither term is a 'flat curve' . I can clarify and explain the answer furher, but not without cooperation. As a minimum I would need clarification of the following I do not understand when you say: "It is the result I needed, however." Did you mean: "It is NOT the result I needed, however." amd forgot the 'not'? So, to sumarize: " If you do not respond to this request for clarification I will withdraw the answer. I will write off the time I invested so far." Hedgie``` Request for Answer Clarification by cereb-ga on 16 Mar 2006 11:40 PST ```Just as I was to insert my feedback I noticed your addtl. comment. I will still paste the reply I wrote offline. It offers a clear start so we can continue. First I wish to thank you for indicating your willingness to continue. You posed three questions: Re: plotting x^2*sin(x) - yes, the 2nd of the three links you listed gave me that plot Re: no inductor in the circuit - L1 was used in my sketch. It is at the extreme left in my sketch Re: diode - I 'envisioned' the diode as a solution - to preclude a flux-induced EMF and charge on C1 to dissipate back through L1. The desired condition is one where the R1C1 product shall determine the shape of the voltage decay. Since I am not building the circuit in can be ignored. Back to the task at hand - I can see the logic in your solution. I am satisfied that your answer is correct, even though I cannot follow it to the point where it demonstrably solves the task that I posted. I therefore propose that we close this task, with four stars given on faith, and that I write and post a new and more concise question. You then have the option to offer an answer of the type I will describe, or abstain from doing so. This would eliminate further handholding, provide for an honorable exit and also for a better defined new start. As to other comments you made: Re: HAS TO use one of the 3 plotting programs ---- I said that "if you know of some applet or online plotting program I could use - by all means. Re: missing "NOT" ---- Both forms effectively mean the same. The "however" I used was contrasting acknowledged effort with needed results. Re: engaging in arguments ---- I agree with your statement. Arguments have no place here specifically, and usually not anywhere. I did not find arguments in my feedback, however. Re: Zero star --- I was following your lead. You introduced handholding in connection with the offered amount. So I offered to add to the fee for continuing to completion, or if you decide not to, that I would accept that and pay the fee and rate the answer as non responsive. I welcome the choice you made.``` Clarification of Answer by hedgie-ga on 16 Mar 2006 19:48 PST `Thank you for your comments and rating. I will look at the new question.`
 cereb-ga rated this answer: ```I appreciate your effort, and patience - and will post a new question that is more explicit. I hope you will decide to respond to it```

 Subject: Re: equation and plot for transient LRC circuit input From: sorwin-ga on 11 Mar 2006 07:41 PST
 ```It appears to me that the question has nothing much to do with electricity, but rather concerns the mathematics of the Laws of Natural Growth and of Natural Decay. So far as I remember, the Law of Natural Growth is: v = V(1 - E^t/tor) and the Law of Natural Decay is: v = V * E^t/tor where v = instantaneous amplitude V = maximum amplitude E = exponential E t = time (in seconds) tor = time constant (in seconds) ^ denotes "to the power of" In electrical terms, tor = R * C (in seconds) where R = effective charging or discharging resistance (in Ohms) and C = capacitance (in Farads)```
 Subject: Re: equation and plot for transient LRC circuit input From: sorwin-ga on 11 Mar 2006 08:03 PST
 ```I made a mistake. For t/tor please read: -t/tor (or course).```
 Subject: Re: equation and plot for transient LRC circuit input From: sorwin-ga on 11 Mar 2006 14:27 PST
 ```Is this a better model of the schematic ?? Obviously, either Switch (growth) is ON and Switch (decay) if OFF, OR vice-versa. V ________ | Switch (growth) | R (growth) | -------------------- | | R (decay) | | C Switch (decay) | | | Ground ________________________```
 Subject: Re: equation and plot for transient LRC circuit input From: cereb-ga on 13 Mar 2006 03:15 PST
 ```Thank you too Sorwin - and I can see that you are sensing the direction I intend to follow - "sorta". I will subsequently deal along lines of the "Weber?Fechner law", but the phenomenon I am after right now is quite different. I do like the RCL circuit approach better, at least for now, because magnetic field strength (or induction), resistance and capacitance and even the diode serve additionally as suitable metaphores for what I have in mind. It is not that I wish to be evasive or secretive, but to explain what I need it for is just not possible, not here, anyway. I did not know about the "natural growth" model you cited - and will give this some thought in terms of its potential utility as I turn to somewhat related topics. So thank you for offering that comment.```
 Subject: Re: equation and plot for transient LRC circuit input From: cereb-ga on 13 Mar 2006 23:01 PST
 ```You invested effort. It is the result I needed, however. The link you offered made a general case for using LaPlace transforms for electric circuits. Ok, I recall from earlier days that this where it shines. The inverse transform yielded a flat curve. The steps to go from a general procedure to one where I can plug in particular values and see the resulting curve, that is what I needed, that is not what I saw. Specifically I asked: "an inductor that creates a voltage when a magnet passes it, and through a diode feeds into a capacitor which, through a resistor, is connected to the other end of the inductor. " A pulse generator, as hinted at in the links you offered, may simulate the induced EMF - it does not do so in terms of an equation that yields an EMF curve. I also said:" What I hope to receive is the equations that govern such circuit and a plot for that circuit with component values identified and ideally also the plot created by a Deadline, Winplot or Zgraph Program." None of that was offered. The "handholding" comment you first mentioned is something I could accept if we were on the same page. We are not. I am willing to pay you for the answer with 0 stars, if google accepts that, to reward your effort. Or we can get back to the question I posed, and if you can be responsive, I would offer another \$ 10.00. Otherwise I must reject your answer as being not responsive and decline payment. All said and done, I appreciate you trying. You decide.```
 Subject: Re: equation and plot for transient LRC circuit input From: sorwin-ga on 16 Mar 2006 15:16 PST
 ```The Question concerns how to plot the behaviour of an electrical circuit comprising FOUR independent variables and also a non-linear element. PLUS another unknown variable - the shape of the input signal. The notion of passing a magnet through a coil of wire amounts to a crude pulse generator. If we can tighten-up on this then a constructive step can be achieved. I suggest that the input signal should be represnted by an e.m.f of zero impedance in series with inductance L1. The e.m.f. comprises a single cycle of a bipolar sine wave. Hence it has a positive half-cycle followed by a negative half-cycle. This is pretty much what I would expect when a magnet passes through a coil. Due to the diode, ONLY the positive half-cycle is applied to the rest of the circuit. It follows that capacitor C1 has a charging period (via L1 and D1) followed by a discharging period (via R1). 1. During the DISCHARGING period, the voltage across the capacitor diminishes according to the Law of Natural Decay to which I have previously alluded. 2. During the CHARGING period the voltage across the capacitor increases, basically according to the Law of Natural Growth but modified by the series inductance L1 and by the SHAPE of the input voltage waveform. I am not able to suggest a mathematical analysis of the circuit during the charging period. Note that any such analysis must take account of the speed of the magnet's passage through the coil, hence of the period of the half-cycle of the sine wave. But I would caution against the "Irish Stew" approach to solving problems, whereby all variables are chucked into the pot, stirred-up and served without any understanding of what is happening and why.```