Understanding an exercise

Discussion in 'Homework Help' started by drk, Nov 1, 2011.

  1. drk

    Thread Starter Active Member

    Mar 8, 2008
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    Hi, I have an exercise which tells me to consider the load's inductance high enough, so that the load can be considered a current source (constant current).

    I've simulated the circuit, and with a high inductance it does eventually ends up with a constant current.

    My problem is, how do I calculate that current?
    How to analyse the circuit?
     
  2. steveb

    Senior Member

    Jul 3, 2008
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    The approach is to consider average values in steady state conditions. The three sources with diodes will act as one source with the highest voltage getting through. This voltage will not be constant, but you can consider the average to be about 83% of the signal amplitude. Then subtract off the diode voltage. This average voltage will be across the resistor because the average voltage on the coil will be zero in steady state.
     
  3. Georacer

    Moderator

    Nov 25, 2009
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  4. steveb

    Senior Member

    Jul 3, 2008
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    Hmmm, not quite, but that's the right idea. Averaging requires dividing by the time. I obtained the 83% figure by the following integral.

    v_{avr}={{3\;v_{max}}\over{\pi}}\int_0^{\pi/3} \cos\theta d\theta={{3\sqrt{3}}\over{2\pi}}v_{max}\approx0.83\;v_{max}

    Then the diode voltage can be subtracted from this value.
     
  5. drk

    Thread Starter Active Member

    Mar 8, 2008
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    I'm getting the value of current +- what I get on the simulation.

    Thanks!
     
  6. Georacer

    Moderator

    Nov 25, 2009
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    Yeah, I forgot to average the integral. Thanks Steve.
     
  7. steveb

    Senior Member

    Jul 3, 2008
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    No problem. I tend to forget that too.

    Also, that pi/3 ratio being nearly equal to one has tricked my mind a few times. The difference is just small small enough that it does not allow our engineering judgement of "reasonableness" to detect the error. So, I came close to making the same mistake.
     
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