modelling circuits using differential equations

Discussion in 'Math' started by miketest, Nov 28, 2012.

  1. miketest

    Thread Starter New Member

    Nov 9, 2012
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    ok.. i need help in modelling a circuit using differential equations. Btw this is for a class project and our professor told us that to do this we can use kirchoff's laws or others. However i have no clue whatsoever on how to apply it in real circuits..


    can someone point me into the general direction on how to start this task?

    here is a picture of one of the schematic diagrams that i'm using( http://farm9.staticflickr.com/8317/8012534324_c64fb60f08.jpg ).. only that im using more led's in parallel with the led shown on the diagram. is it even possible to model it

    [​IMG]
     
    Last edited by a moderator: Nov 28, 2012
  2. Wendy

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    Mar 24, 2008
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    Major overkill in math. It can be done with simple algebra. Basically the 100KΩ has to be known value, then figure the equivalent voltage / resistance feeding the transistor B-E. From there it is simple Ic = β IB

    So why are you trying to use a differential equation for such a simple problem?
     
  3. miketest

    Thread Starter New Member

    Nov 9, 2012
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    well,... i don't know.. our professor told us that differentials can be used in kirchoff's laws where V=IR+L(dI/dt) etc... i dont really know how to apply that in my circuit... suppose that i added an inductor of about 5mH.. would i be able to apply it??
     
  4. Wendy

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    The moment you add reactance it becomes integration or differentiation, so then it would apply much better. Matter of fact, it is how analog computers work in many cases.
     
  5. WBahn

    Moderator

    Mar 31, 2012
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    There are a number of things that are all getting thrown in the pot together. None of the components in this circuit (with the possible exception of the photosensor) are modeled by a differential relationship between voltage an current. Now, if you use a high frequency model for the transistor, there is some capacitance that could be modeled by a differential equation.

    But even if you had some explicit capacitors and inductors, your circuit contains nonlinear elements (the transistor and the LED, if nothing else) and so your differential equation would be nonlinear and probably a royal pain to solve.

    What is normally done is to evaluate the DC bias condition of the circuit and then determine the small signal linear models for each nonlinear component for small changes about that DC bias point. You then determine the differential equation for the small signal circuit (or use transform methods, which simply apply the differential relationships and then take the Laplace/Fourier transform of the resulting differential equation without you having to fuss with the error-prone mechanics).
     
  6. miketest

    Thread Starter New Member

    Nov 9, 2012
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    thanks for the replies,, appreciate it..

    ok so what you guys are suggesting is to make small linear models for the components that are in a series (using kirchoff's law if i added a capacitor or inductor and just use V=RI if i don't)?? and then use laplace/fourier to transform that into a whole new differential equation that would model the circuit?

    can you guys give me an example on how to do it.?? i am really lost
     
  7. Wendy

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    Mar 24, 2008
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    First of all, merge B1 and the two resistors (the LDR and pot).

    Gotta go to the dentist, but I'll be back.
     
  8. miketest

    Thread Starter New Member

    Nov 9, 2012
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    ok... sorry if this sounds stupid... but how? do i do it in my real circuit or do i do it just math-wise... and how exactly do you merge them??? One is voltage and one is resistance... :(
     
  9. Wendy

    Moderator

    Mar 24, 2008
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    OK, I looked up an old illustration for another thread.

    http://forum.allaboutcircuits.com/showthread.php?t=63701

    [​IMG]

    The basic discussion was fairly different from this one, but the math doesn't change too much.

    Voltage dividers and Ohm's Law is pretty consistent with electronics in general. Most folk only need basic algebra to solve problems. This was good for me, I knew I was in trouble when I started Calculus I. The teacher had a bias against electronic examples, having had nothing but when he started his class. So of course, he went the other extreme. What Calculus I did absorb has long since dissipated.
     
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