Electric Potential Damped Mass Spring System [Analog] - Page 1
Forum section: electronics / projects

author: jeffberhow
author_rank: Newbie
timestamp: May 09, 2014, 01:37:53 am
content: Hello everyone,I'm new here and this is my first post. I'm taking my first class in electrical circuits and we studied op amps for a chapter. Later on when discussing RLC circuits, this neat circuit comes up that can solve differential equations. I whipped it up with a few snags here and there and finally got a circuit working that mimics the differential equation of a damped spring and mass system.Check it out!I apologize for the vertical videoThanks for watching!

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 09, 2014, 02:31:38 am
content: Physical analogies abound. Any medium that can be expressed with a wave equation (ripples on water, E&M, quantum mechanics, even Relativity) will exhibit similar differential equations, and often, similar nonlinearities as well (shock waves for example -- given a suitable medium if necessary). It should be no surprise that the Fourier transform, and other transforms like it, are so physically relevant. This, and solving polynomial roots, largely accounts for a vast number of analytical, physical problems.Six op-amps is a, shall we say, academically large count to use; three passive components of course are sufficient for expressing the same (RLC) relation.An even cooler one uses a nonlinear element like a multiplier to make chaos (e.g., logistic map (add a multiplier and sample-and-hold) or Lorentz Attractor (two multipliers I think?)). This, by the way, is relevant to real circuits: there are some surprisingly common practical circuits which exhibit chaos, the peak-current-mode flyback converter being a prime example (being equivalent to the logistic map: the peak current comparator triggering is equivalent to a discrete time sampling event). Occasionally, you'll find much consternation in attempts to control circuits that exhibit unusual nonlinearities, and you'll find the circuit whining (limit cycles) or hissing (seemingly random) or spitting at you. Moral is, try to address the nonlinearities first, to avoid the chaos as well as possible. Then your circuit will be that much more stable.Tim

author: jeffberhow
author_rank: Newbie
timestamp: May 09, 2014, 05:36:07 am
content: Tim,Thank you so much for your response! It gives me a great amount to think about in my electrical engineering infancy. The Lorentz Attractor looks like so much fun, I think I will have my hands occupied for a while probing the idea. What you bring up about attempts at controlling the circuits is very true, but instead of a frustration I will try to keep a sense of awe and wonder; it's one of the reasons I want to go into control systems.The reason that I like the idea of op amps here (you're right, it is a bit over the top) is that I can model every little coefficient and derivative in the ODE: the spring constant, coefficient of friction, etc. It really feels like I can imagine the gears working in the circuit. Also, to pull of an oscillation this slow and for this long in an RLC circuit is beyond me, and beyond the actual components I have on hand.Jeff

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 09, 2014, 01:25:10 pm
content: Heh. I think I have some ~10H chokes in the box, but too much DCR to achieve anything more than a dull thud at low frequencies like that.You can synthesize an inductor using just one op-amp, however:http://en.wikipedia.org/wiki/File:Op-Amp_Gyrator.svgI guess the value would be, in an RLC circuit, the coefficients are mixed up, with terms of 1/LC and RL and so on, and it would be a good exercise to get familiar with the values and relations of real world component values. That was the thing that bothered me the most about Abstract Control Theory class: being abstract, not one single reference was ever made to real world component values. I knew these things, but I have to wonder if anyone else sitting there had any clue what was going on.Tim

author: jeffberhow
author_rank: Newbie
timestamp: May 09, 2014, 05:53:04 pm
content: 10 Henries! I haven't even seen an inductor that big even in a textbook problem, haha. That op amp gyrator seems really interesting: two 1000 Ohm resistors and a 100 uF cap already puts you at 100 H. In just an RL circuit, you could easily get time constants above a second with an inductor value of that size.You're absolutely spot on about the RLC circuit coefficients being all mixed up. I can yank out a Napier and resonant frequency fairly quickly depending on series or parallel construction, and then find the real part of the solution to control the damping and the imaginary part to control the frequency.If I was to try and match the RLC values in a series setup with the differential equation for a spring/mass, I could say 1/LC = k/M and R/L = myu/M wherek = 1/C = spring constantM = L = massmyu = R = coefficient of frictionJeff

author: ejeffrey
author_rank: Super Contributor
timestamp: May 09, 2014, 07:45:24 pm
content: Quote from: jeffberhow on May 09, 2014, 05:53:04 pmYou don't normally see inductors that big, but it would be a pretty reasonable value for the primary of a small 60 Hz transformer. The magnetizing current (primary current at zero load) of a transformer is just Vin / (2 * pi * f * Lp). If you want a magnetizing current of 30 milliamp at 120 V/60 Hz, you need 10 H. In europe where line voltage is 230 V/50 Hz, inductances would need to be even higher.QuoteTrue, but watch out. The gyrator's gain will also amplify non-ideal component behavior. With long time constants (10s of s) leakage may be a problem, especially if you are using electrolytic capacitors.

author: madshaman
author_rank: Frequent Contributor
timestamp: May 09, 2014, 08:04:06 pm
content: How would you guys manage DC drift, amplitude stability, phase distortion and jitter if you built an ultralow-frequency analog oscillator? (assuming high Q gyrators are used in place of inductors)I'm really just curious about methods to do this.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 10, 2014, 12:01:06 am
content: Quote from: jeffberhow on May 09, 2014, 05:53:04 pmI've heard of inductors up to, ah, think it was either 100H, or 1kH, or thereabouts. The aim was, improving the frequency response of a vacuum tube preamplifier stage -- the output impedance is on the order of 10kohms, and to get flat response below 20Hz requires over 80H. It's only required to handle 10mA, and DCR is not at all a problem (in fact, additional resistance is desirable, as it flattens and extends the frequency response). It just takes 5-10 thousand turns of extremely fine wire on a small laminated iron core.Probably, high impedance, high sensitivity or high voltage transformers have, from time to time, achieved much higher inductances, without it really being particularly important. The purpose of a transformer is to transform, not induct; ideally, the inductance should be infinite, and the energy storage null. (By this definition, the transformer used in a flyback converter should rather be called a "multi-winding inductor". In reality, it's understood that a transformer does have inductance, and if it is necessary to use that attribute for proper operation, that's fine -- as long as it's designed for it. Construction does vary a little as a result.)I also have some audio signal transformers which claim 500 ohm impedance primary (and several lower taps), 50kohm(!) secondary, 30-20kHz bandwidth, 8dBm maximum signal level. This suggests some 265H for the secondary! Inductance like this is not terrifically hard to achieve; these types use a mu metal core, which has extraordinarily high permeability. The side effect is, the magnetization current is vanishingly small, perhaps microamperes through the 50kohm winding, before saturation sets in. (Again, very little energy storage!) The 8dBm figure means 6.3mW, which, if this is referred to the 500 ohm winding, is all of 1.77V RMS. Which is a quite reasonable signal level. These transformers are mounted in a metal can about 7/8" dia. x 1-1/4" long, so the core and windings are not at all large.Such signal transformers are still relevant today, when isolating professional audio equipment to prevent ground loops.Tim

author: ejeffrey
author_rank: Super Contributor
timestamp: May 10, 2014, 02:14:40 am
content: Quote from: madshaman on May 09, 2014, 08:04:06 pmIf I wanted an ultra-low frequency oscillator I would use a quartz watch crystal to generate 65.536 kHz, then use a divider to generate whatever low frequency I needed. Of course it would be a square wave. If I needed a sine wave, I would use the crystal to clock a high resolution DAC and use DDS.

author: GK
author_rank: Super Contributor
timestamp: May 10, 2014, 02:25:25 am
content: The Heathkit EC-1 computer manual has some example simulations you might find interesting:http://ed-thelen.org/comp-hist/EC1-OP.pdfAlso check out the "library" at the Analog Computer Museum:http://www.analogmuseum.org/english/My implementation of the bouncing ball sim:Chaotic attractors:http://www.glensstuff.com/In analog simulation problems arescaled. Physical phenomenon which may have durations in hours can be simulated in a fraction of a second. I can't follow how discussion in this thread got to simulating 100H inductors with gyrators and 100uF capacitors.

author: jeffberhow
author_rank: Newbie
timestamp: May 10, 2014, 04:37:36 am
content: GK,Those are some really great resources, Thanks! Also, that bouncing ball is really impressive. After Tim brought up Lorenz Attractors, I've been scouring the internet for information on handling some of the math so I can try one myself. Is this glensstuff.com site yours?I agree, that the discussion should return to physical simulations, but those large inductors are fascinating and I think they came about due to thinking about the implementation of the circuit in the original post as an RLC circuit, hehe.Speaking of attractors: I'm really new on the forums here, but how often is math brought up when talking about engineering stuff? I know Dave doesn't go too in-depth with it in his videos.

author: madshaman
author_rank: Frequent Contributor
timestamp: May 10, 2014, 08:47:44 am
content: Quote from: ejeffrey on May 10, 2014, 02:14:40 amRight, but I was kind of asking about non-digital methods. Digital for low frequency is a no brainer because it gets around most of the issues I mentioned.

author: ejeffrey
author_rank: Super Contributor
timestamp: May 10, 2014, 05:31:54 pm
content: Quote from: madshaman on May 10, 2014, 08:47:44 amYou can then go and use the gyrator circuits discussed above -- that is a totally fine way to make a low frequency oscillator as a demonstration. You can use any of the classic oscillator circuits, but stabilizing is going to be hard -- an oscillator needs some non-linearity to stabilize the amplitude, and the time constant needs to be much slower than the oscillation frequency. You can get a square wave out of a 7555 (cmos 555) with big capacitors and inductors if that is analog enough for you. But when you start asking about noise and stability, the answer is to go digital.

author: IanB
author_rank: Super Contributor
timestamp: May 10, 2014, 06:23:01 pm
content: Quote from: jeffberhow on May 09, 2014, 01:37:53 amI just scanned the thread, but nobody mentioned specifically that "a circuit using op amps that can solve differential equations" is traditionally known as an analog computer?Back in the old days before digital computers were cheap and common, and when engineers used slide rules for calculations (before pocket calculators), then analog computers could be used to simulate dynamical systems.A traditional analog computer was like a plug board or breadboard on which you could wire up integrators, multipliers, adders, and other basic elements in the right combinations to solve your model equations. In effect your "program" was the pattern of patch cords used.Here's an interesting link with some history:http://www.networkworld.com/slideshow/107559/quick-look-10-cool-analog-computers.html

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 11, 2014, 12:06:07 am
content: Without using MSI, one could also tune a precision LC oscillator up at a normal frequency, say 500kHz, and divide it down with injection locked oscillators. It's still analog, but is also not direct synthesis...I think the best "direct" way would be to consider low noise amps (particularly low 1/f noise -- chopper amps seem like a good bet), high input impedance, and the best film capacitors you can find. The major sources of noise will be the resistors (since this is ultimately some variation on a Wien or Twin-T or other RC oscillator) and amps, and of long-term variation, the tempcos of the components. You'd also want to spend some time considering the AGC/clipping circuit, to minimize noise and distortion.Compensation might be interesting. Could an impedance (such as a capacitor) be inverted and used for an oscillator, so that it has an opposite tempco from the normal oscillator, then the outputs are combined with some kooky mixer/PLL frequency averaging? Would that not be necessary, is the gyrator already inverse? I'd have to look at the algebra.Keeping it stable (over days and years) would be really hard, at least as tedious as maintaining a traditional mechanical pendulum type clock. You know, a few pennies on the weight to speed it up when it's been falling behind, etc...tim

author: GK
author_rank: Super Contributor
timestamp: May 11, 2014, 12:27:17 am
content: Quote from: jeffberhow on May 10, 2014, 04:37:36 amYes, that site is mine, still under construction. The damped spring-mass system (along with the bouncing ball and missile trajectory) is a very common one in introductory analog computing texts. It's typically presented in the form of a car suspension system. Bernd Ulmann has a nice video of a car suspension system simulation in the examples section of his analog computer museum website.

author: GK
author_rank: Super Contributor
timestamp: May 11, 2014, 12:30:04 am
content: This is how you make a ULF oscillator with analog computer components (reply 48):https://www.eevblog.com/forum/projects/home-brew-analog-computer-system/msg192626/#msg192626You use either a comparator or summing amplifier configured with hysteresis coupled to an integrator with a low time constant (10's of seconds easily achievable). The triangle wave is then shaped with function generator module.