Solving a circuit in Freq Domain

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Discussion Overview

The discussion revolves around solving a circuit in the frequency domain, specifically addressing the behavior of currents and voltages in a circuit with a controlled voltage source. Participants explore various methods of analysis, including mesh analysis and Laplace transforms, while considering the implications of circuit parameters on steady-state behavior.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a mesh analysis leading to a complex current value for Ix, questioning its correctness and verification methods.
  • Another participant points out ambiguity in the polarity of the controlled voltage source, suggesting it affects circuit operation.
  • A later reply indicates that the circuit may not reach a steady state due to positive feedback, confirmed by a Spice simulation.
  • Some participants propose that the current can still be modeled sinusoidally using Laplace transforms, suggesting a different analysis method that does not assume steady state.
  • Concerns are raised about the validity of the problem being presented, as it diverges from typical steady-state problems encountered in class.
  • One participant mentions that reversing the polarity of the controlled source could alleviate the issue of positive feedback.
  • Another participant shares their own calculations for the amplitude and phase shift of Ix, indicating a steady-state case, while expressing uncertainty about extracting phase information from plots.

Areas of Agreement / Disagreement

Participants express differing views on whether the circuit reaches a steady state, with some asserting it does not due to positive feedback, while others believe the problem can still yield valid results under steady-state analysis. There is no consensus on the correct approach or outcome.

Contextual Notes

Participants note that the problem may contain a misprint regarding the controlled source's polarity, which could influence the circuit's behavior. The discussion reflects a range of assumptions and interpretations regarding circuit analysis methods.

phsyics_197
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Homework Statement



Question as in image:

rjnqx1.jpg


Homework Equations





The Attempt at a Solution



When I did Mesh, I got this:
-20j-20Ia+(Ia-Ib)2j=0
(Ib-Ia)2j-(Ib-5)j-(Ib-Ic)50=0
-(Ic-Ib)50-(Ic-5)8j-2(Ia-Ib)=0
2(Ia-Ib)-100Id=0
Ia-Ib=Ix
**This is done from Left to Right**

One thing I am not sure about is the Sin voltage source. I believe you convert it to Cos first? Then it should give you -20j.

Well, when I solved the above equations in Matlab, I got Ix = -6.4622 - 0.5310i.

I was wondering if that is correct, and how could I verify it?

Thanks
 
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The polarity of your controlled voltage source is a bit vague, and it will affect the operation of the circuit. Could you clarify it?
 
Yes, sorry about that. It should (+) on top and (-) on bottom.
 
phsyics_197 said:
Yes, sorry about that. It should (+) on top and (-) on bottom.

Hmm. In that case I think that the circuit won't reach a steady state; the current Ix is going to grow without bound as the controlled voltage grows while Ix does -- there's positive feedback occurring. (I just confirmed this with a Spice simulation).
 
But can't you still model the current sinusoidally?
 
phsyics_197 said:
But can't you still model the current sinusoidally?

Sure, but you'll need to use a slightly different analysis method; Solve for the current Ix as a function of time using Laplace transforms. This is mostly the same as the usual mesh method, only no assumptions about the circuit going to steady state are made. The voltage and current sources are replace with Laplace transform counterparts for sine and cosine driving functions. The expression for Ix(s) is found and a reverse Laplace transformation performed on it.

The result will be something like a sum of sine and cosine terms multiplied by an exponential that INCREASES with time, like e^{A t}.

[EDIT] BTW, the Spice simulation indicated that Ix would reach an amplitude of about 150 Million Amps in about 216 seconds.
[EDIT] Also note that this problem does NOT occur if the controlled voltage source has its polarity reversed (+ down, - up).
 
Last edited:
Are you 100% positive it does not reach steady state? Cause everything we have done in class has been for steady state problems. I find it hard to believe he is giving us a problem that we have never seen before.
 
phsyics_197 said:
Are you 100% positive it does not reach steady state? Cause everything we have done in class has been for steady state problems. I find it hard to believe he is giving us a problem that we have never seen before.

I believe what the simulation is telling me. Note that the problem could also be alleviated if the controlled source gain were -2 rather than +2. You might want to check that.
 
He specifically said that the (+) is on top. And when I worked it out by hand following his steps, I got what seems to be an appropriate answer.
 
  • #10
phsyics_197 said:
He specifically said that the (+) is on top. And when I worked it out by hand following his steps, I got what seems to be an appropriate answer.

Sometimes there is a world of difference between "seems" and "is" :smile:

If you have LTSpice on your PC (It's a free download, and practically an industry standard) I'd be happy to post the wirelist for you to run the simulation for yourself. You can see the difference if you change the gain from +2 to -2, effectively reversing the polarity of the controlled source.
 
  • #11
Sorry, I was playing around with PSpice and I know what you are saying.
 
  • #12
phsyics_197 said:
Sorry, I was playing around with PSpice and I know what you are saying.

So it looks like a misprint in the problem statement, or perhaps the person who created it didn't check for the positive feedback possibility.

The steady-state analysis method WILL yield a result in both cases, but it lacks the finesse to properly handle circuits that don't in fact have a steady state.
 
  • #13
Do you know the equation?

I was getting an amplitude of about 6, not sure how to extract the phase shift from the plot.
 
  • #14
I calculate a magnitude of 5.996A for Ix, with a phase shift (with respect to the current source 5cos(2t) ) of -144.107°. This is for steady-state case, of course.
 

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