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Zero Impedance in Oscillating current transformer

  1. Jul 28, 2014 #1

    I have read Steinmetz books and he has a very good example of OC phenomenon that is nothing like AC case. There are certain conditions under which an OC transformer has zero impedance. Also, on his chapter of long transmission lines, he says quarter wave resonance using abrupt pulses can add to gain high current and e.m.ff from small impulses. Anyone have experience or references? Anyone read any material similar to the title below? Thanks.

    Abnormal Voltages in Transformer - L. F. Blume AIEE 1919
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  3. Jul 28, 2014 #2


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    I do not have a copy of that book. Do you have a link to the text?
    Are you asking about the self resonance of transformer coils?

    I can understand a zero reactance, X, in an oscillating coil, when X_inductive + X_capacitive = zero.
    But unless it is superconducting, the ohmic resistance must always remain finite and positive.
    The vector sum of resistance and reactance is the impedance, Z = R + jX, which is non-zero.

    Unless you can present a more specific case, or provide a link to a web page, it will be hard to get answers to such a general question.
  4. Jul 28, 2014 #3
    Thanks for the response.


    That's a link to Steinmetz book. The example I discuss is on page 343 (or page 9 of PDF). I do not have a link for the Abnormal Voltages, but can find one. I am not sure if this is self resonance....I could use some clarifying as well. Steinmetz claims it is a phenomenon unique to OC systems, not happening in AC systems.
  5. Jul 28, 2014 #4


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    Actually, all that he has solved for is the resonant case of the RLC circuit. His oscillating current is a sine current that is exponentially decaying. So this has a built in "resistance" so to speak by virtue of the decay. When he solves for the zero impedance, he forces the decrement to be a function of the resistance. Note that he does the case where there is no resistance, then there is no decrement and you get the LC oscillation. You can also work out and find that his decrement and resonant frequency at zero impedance, given at the bottom of page 344, is exactly the same as if we solved an RLC circuit using traditional means. That is, his N is the damped frequency.

    So it all works out to be the same. He's just derived another way of solving for the RLC circuit without using Laplace analysis or differential equations.
  6. Jul 28, 2014 #5
    Interesting, but he says it is not a phenomenon encountered in AC, I wonder why not.

    Yes, he solves an RLC circuit, but the important part is the negative sign of the energy components. Also realize this: he finds it to have zero impedance when the resistance is non-zero, an incredible fact!

    Yes, he does an example later using zero resistance, but this is only a special case. The resistance need not be zero!
  7. Jul 28, 2014 #6


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    Probably has to do with the fact that he rigidly defined an AC signal to be monochromatic. The exponential decay in an RLC circuit means that the natural response is not monochromatic and so perhaps trying to solve it using a monochromatic frequency analsys (like the Fourier or Laplace transform) is difficult. Maybe the mathematical framework that we use to solve the problem today was not known back then. Again, this is from 1895! We shouldn't be surprised that this is not a new phenomenon but a well known one dressed up differently.

    But you have to understand, there is an impedance, it's in the fact that the oscillating current is dying out. At "zero" impedance, he is forcing a condition on the decrement that makes the exponential decay dependent upon the R, L and C of the system. The "zero" impedance is really a zero reactance with the resistance bound up in the conditions forced upon the decrement. When you remove the resistance, you end up with the LC circuit. When you add the resistance, the behavior is EXACTLY the same as an RLC circuit.

    EDIT: Also note, what would it mean for it to have zero impedance? That the current would become infinite or it would not die out. But he has defined that the current is going to die out in time, so he has built in this resistance into the oscillating current. So what he is solving for is behavior that is not going to be accounted for in this exponential decay, which in this specific case is simply the reactance of the circuit. He's basically started with the actual solution to the RLC circuit and solved for how we fit the known parameters, R, L, and C, into this solution.
    Last edited: Jul 28, 2014
  8. Jul 28, 2014 #7
    No, the zero impedance is the important quality. Yes, that means zero total impedance by the equation Z = R + jX ...in fact means the reactance can cancel out the resistance in effect. This is known, but not well discussed. Just like Steinmetz quote on long transmission lines:

    "...the effects of successive impulses add themselves, and large currents and high e.m.fs may be produced by small impulses, that is, low impressed alternating e.m.fs"

    Page 279 "Theory and calculation of transient electrical phenomenon and oscillations"

    This is not well known, but is known as quarter wave resonance, but rarely discussed.
  9. Jul 28, 2014 #8


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    For the Z to be zero, both R and X must be zero. That requires a source of energy such as a negative resistance = amplifier.

    The oscillation can only occurs on Open Circuit coils because when an AC system is connected it “terminates” the OC transformer terminals. The circuit is immediately changed and so immediately kills any internal oscillation between the OC terminals.

    I see this article is often referenced by the Tesla-ite community. The fascination could be with the superluminal phase velocities that are possible on OC helically wound coils of wire.

    The apparent superluminal velocity along the wire is due to the luminal speed of the magnetic field coupling the wire turns along the coil. The length of wire on any one turn must always be longer than the distance between two adjacent turns.

    Consider a water wave that arrives at a vertical wall, that is diagonally across it's path. The virtual point of contact between the wave and the wall will travel at a greater speed than the speed of the wave. When the wave and wall are parallel the velocity of that virtual point will be infinite. No matter what yo do at one point on the wall, the wave front cannot communicate that to another point on the wall faster than the wave moves towards the wall.

    The same concept applies to EM waves. The distinction is that “phase-velocities” are always super luminal, while “group velocities” are subluminal. The speed of light is the “group velocity”. Only the phase velocity can be superluminal. Communications must remain at the group velocity.
  10. Jul 28, 2014 #9


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    But if resistance is zero, then you have the normal lossless LC response as Steinmetz shows. When you have a non-zero resistance, the current has to exponentially decay regardless of Steinmetz's "zero" impedance condition. So you still have a resistive loss, what you do not have is a reactance.

    What he has done assume a specific solution to the current and solving the system under this solution. This solution incorporates a resistive loss. For example, let's say that I want to solve for a mass under the influence of gravity. Let's say that I define the potential energy to be PE' = mg(h-2). Now if I was to solve for how the ball falls starting at a height of 10 m to 2 m, then using PE' will get me the correct answer. However, I would say that the PE at 2 m is zero while most people would say that the PE at 2 m is 2mg. Yet if I let go of the mass at 2 m, it will still fall. I simply incorporated an offset into my definition of the potential energy. It doesn't change the solved behavior but can influence our intepretation of what will happen. The same thing is happening here in how Steinmetz defined the oscillating current to already be exponetially decaying. The current is already decaying so when we solve for the behavior, we are not going to see a "resistance" since it's already built in.

    None of this is new or rarely discussed. I work on a system that makes specific use of what you are describing. We have an antenna and a capacitor that forms an R, L, C circuit. We excite the antenna but use the capacitor to create an LC tank at the resonant frequency. By doing so, "...the effects of successive impulses add themselves, and large currents and high e.m.fs may be produced by small impulses, that is, low impressed alternating e.m.fs" occurs. That is, we first inject energy into the LC tank to start the resonance. Once the LC tank has been filled, we only need to inject small amounts of energy to compensate for the resistive losses. Thus, we maintain a high current and voltage in the antenna with only a small injection of energy. Without that capacitor, we would have to keep driving the high current and voltage into the antenna. RLC tank circuits are discussed in any low level electrical engineering class and you find them in many circuits.

    And if you think quarter wave resonators are rarely discussed then you've never sat in on an electromagnetic wave class. Quarter wave resonators are a huge topic in waveguide and transmission line theory.
    Last edited: Jul 29, 2014
  11. Jul 28, 2014 #10


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    It is very well understood. Standing waves with high voltages and current can be built up on resonant transmission lines, but only if they are driven by a source of energy at the resonant frequency. It is the energy fed in continuously by the driver that overcomes the resistive losses.

    The technical fields of coated optics, dipole antennas and pendulum clocks are based on that fundamental theory.
  12. Jul 29, 2014 #11


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    Attached is "Abnormal Voltages Within Transformers", L.F.Blume & Boyajian. AIEE. 1919.

    Attached Files:

  13. Jul 29, 2014 #12

    jim hardy

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    Leads right to the spark gap radio, does it not ?

    The way i read Steinmetz's text is that if
    the decrement is zero, and it's resonant, its impedance would be zero. Nothing wrong with that logic, even if it's just for a thought experiment.
    Then he toys with the algebra,
    Then he states that lightning falls in that category.

    Steinmetz was fascinated by lightning and studied it a lot, observing how it blew up his apparati and trying to capture and recreate lightning bolts in his laboratory. It was quite a mystery back then.
    Ionized gas exhibits negative resistance and he doubtless observed it - so i'm not surprised that he dabbled with the idea of zero resistance and ascribed the energy input instead to the reactive components. Remember - this was written before discovery of the electron. And he was among if not the very first to apply complex numbers to AC current analysis. They were just figuring things out then.

    You'd enjoy Steinmetz's biography "Modern Jupiter" published by ASME (How'd IEEE miss out on that one?)
    I went through a US engineering curriculum without ever hearing of Steinmetz.
    I can only speculate that he was removed from American textbooks at end of WW2 because of his avowed socialism.

    old jim
  14. Jul 29, 2014 #13


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    The Internet Archive has most of his books.
    https://archive.org/search.php?query=creator:"Charles Proteus Steinmetz"

    I downloaded a few to read on vacation as sometimes old texts give a slightly difference slant on things and I like his writing style using polar and rectangular coordinates.

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