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Circuits with Time Variant Reactance

MagAmp permeability inductance capacitance permittivity variactor diode

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#1 G4ΓΓ3ττ


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Posted 15 July 2013 - 09:42 PM

I thought I would create a space for anyone who would like to talk about electrical circuits that use time variant parameters to modulate a circuit’s electrical reactance, or alternatively—as the case may be—resistance.


This effect can be seen in the form of inductance and capacitance variation with respect to two signals; first, a primary signal passing through a device or circuit element; and second, an axillary signal applied to control the device or circuit element’s parameter—which can be considered as the “bias signal” or “control signal”. Ironically this happens all the time, and without anyone realizing it, that is, unless you’re an audiophile or radio engineer. For example a simple electrolytic capacitor can, among other types, vary its absolute magnitude of capacitance from the DC level at which it is operated at [1]. For audio this adds second order harmonics to the signal (read distortion), for radio, it adds unwanted frequency domain content. Returning to resistive devices, a solid-state circuit like a lambda diode falls under the category of a time variant resistance and most importantly, produces a negative slope for its V-I curve, while nearly all other resistive devices show a positive slope [2].


There are a lot of interesting uses for the above examples in real world applications. LF and RF oscillators can be (and are) made using the negative slope charictaristiscs of the lambda diode or gunn diode. Mainly, time-variant circuit elements are used in radio for frequency sweeping circuits. One of the most used for that purpose is the variactor diode, which changes effective capacitance based on the applied DC bias level [3]. In its usual application (frequency sweeping), a variactor diode's capacitance is changed at a rate that is very, very slow, with respect to the primary signal. When you start to increase the rate of change in the bias signal, and thus effectively changing the amplitude of effective capacitance in the circuit with respect to the applied input signal, strange things start to happen—or at least can theoretically happen given the right conditions.


Double frequency amplitude variation of circuit elemtent's reactance is what I personally will be covering in this thread. For anyone else who is interested, feel free to join in as well as talk about other applications and allied ideas related to the thread's theme. For the visual people out there, I've got pictures and diagrams coming soon. Arguments are welcome, but let's keep things about why something can or cannot work, as opposed to attacking people for what they think.


Foot Notes:


[1] CliftonLaboratories.com - Capacitance Change with Applied Voltage. (This is an awesome website for anyone who is interested in seeing fun experiments and judicious use of test equipment.)

[2] LambdaDiode.7zip (A collection of documents on negative resistance--negative slope V-I devices)

[3] Blackwell - Semiconductor-Diode Parametric Amplifier,1961

     Kaye - Circuit Techniques for Reflection-Type Parametric Amplifiers, 1966

     Penfield & Rafuse - Varactor Applications, 1962

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#2 Raui



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Posted 15 July 2013 - 11:52 PM

Great topic for discussion thanks for kicking this off Garrett. For those that aren't aware inductors share a similar trait as capacitors in that their ability to store energy isn't constant either. This is probably quite obvious to some but maybe not for others so I'll explain how I understand this works. The ability of a capacitor or inductor to store energy comes from two main factors, geometry and environment. When we apply power to a storage element the general scenario is that no significant change occurs to the geometry so we can rule this out as effecting our storage element while it's being powered and so it must be the environment.


The environment is signified by the permeability and permittivity of our element which both represent space's ability to store energy as an magnetic and dielectric fields. Since any real component has a finite permeability there is only so much field a space can contain. This is seen readily in the concept of saturation where an inductor stops behaving like it normally does because the space contains all the field it can.


As a quick side I think it's important to note that you don't need the parameter to change at twice the resonant frequency of the power circuit to see effects. I recall that towards the end of the year last year we were playing with inductors. I had a fairly large coil, can't recall the inductance but I'd say it would have been between 0.5 -> 1H. A DC field was applied and we observed the resulting voltages and currents traversing the coil. What was interesting is that if I removed the core quick enough I could actually get the voltage to go more negative than what it was positive with the core in place. Like for example say I applied 5V to the coil, if I quickly removed the coil the peak might've been at -8V. This for me confirmed that the magnetic induction 'laws' I'd been taught so far were incomplete and there was a term missing from it. Let's explore the concepts of induction for a moment to get a feel for what is happening.


In the most basic dimensional understanding a voltage is induced in a wire when the magnetic flux changes in time. Mathematically;

[LaTeX Error: One or more directories do not exist]


We know that [LaTeX Error: One or more directories do not exist] is given by

[LaTeX Error: One or more directories do not exist]


Where L is inductance and i is current. So if we expand this fully we get;

[LaTeX Error: One or more directories do not exist]


The first term in the expanded form [LaTeX Error: One or more directories do not exist] is well known as the reactance voltage and doesn't have anything to do with a changing inductance, only a changing current so that can't be what was causing the induction observed. The second term [LaTeX Error: One or more directories do not exist] is not much discussed yet was the form of induction used in the above DC solenoid experiment since we were dealing with a changing inductance.


One thing to note though is that it took work, and a fair bit of it, to remove the core from the inductor. This will always be the case for DC because the coils magnetic field will constantly be pulling the core into the coil as to maximize the inductance. In AC this isn't necessarily the case because with AC the force experienced by the core is changing continually. If the inductance changes at times when the core is feeling less force but you get the most induced emf then you've got a neat little situation. Now this is just my hunch, I won't try demonstrate this mathematically just yet, but perhaps running at twice the resonant frequency corresponds to this hotspot - parametric resonance.


Anyway this is just the start of a whole new avenue for exploration, pushing the boundaries of the known into the unknown. Exciting stuff, literally!

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#3 ColoradoSpringsFilms



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Posted 19 July 2013 - 01:35 PM

Thanks for the footnotes and other raw data. 


I am quite young but was directed to this forum and am quite proud I was shown it. Regarding the two posts above;


Thanks very much Garrett for the info and the footnotes. Very interesting stuff. This is now all coming together, as I've been reading a lot of Dollard's book, especially the Lone Pine Writing and Generalized Theory of Electric Waves. These two really helped my understanding of both the time variance factor in electrical circuits and the inadequacy of certain laws should we say. Versor math and the use of algebra as put forth in Generalized Theory of Electric Waves is now making much more sense to me than the first read. The relations of simple reactance, susceptance, admittance, conductance and others are now much more comprehensible. As mentioned by Garrett, the time variance factor really is important, as the set of these relations can be derived from a varying inductance and or capacitance. 


As for my experimenting, I have some small setups, nothing really noteworthy at all, but as time passes I hope to expand. My main project now is a basic transistor type setup that I use outside, allowing for plugging flouros into the ground; also utilizes an extra coil. I have not made a very efficient coil, as this one is rather tall, and its p or n factor I believe is too large. As Dollard mentions in Theory of Wireless Power, it should be around one; thus favoring shorter and more wide coils, as these are the ones I see too when looking at Tesla's Colorado Springs Notes. 


Regarding the setup, it is quite small, as in the future I plan to pick up an NST so that I can actually begin larger scale projects. My setup utilizes now a standard tip31c transistor in a common exciter circuit, with 12 V input. Scale up in the future soon... Adding the ground connection really helps the system and sometimes it won't start without this ground. My ground connection is a copper rod stuck about 4 ft in the ground in my backyard. I was wondering, because when I connect another coil to the ground with the correct capacitive top load, it too becomes excited. No ground-no power. Is this type of setup utilizing LMD waves to a greater extent with the ground connection do you believe for the extra coil? This of course leads me into earth batteries, which are for another thread...



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#4 Robert



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Posted 20 July 2013 - 11:50 PM

Newbie that I am, I have only just come across this subject of time variance of parameters, while catching up on the Eric Dollard threads over at energeticforums.com.


A thought that came to mind (and please correct me if it has already been thought of):


The Tesla bifilar pancake coil can have at least four topologies, as listed here (not my work, I simply came across it):



Although the diagram shows the four topologies as helical windings, I've verified to my own satisfaction that they can also be done as flat pancake coils.


My insight: With a suitable mechanical switch (one or two throw) one can turn any of the topologies into any other, and by so doing the values of resistance, capacitance and inductance would instantly change. And instead of using a rapidly alternating mechanical switch (which can wear out) one might use an equivalent electronic switch (that can switch much faster).


Does this make sense, and has anyone previously thought of doing this?

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#5 Raui



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Posted 26 July 2013 - 06:57 AM

I thought I'd add something new to this topic as it seems to have gone quiet. Steinmetz did experiment with circuits of varying reactance as is evidenced by his published writings in the 'On the Law of Hysteresis' series;
On the Law of Hysteresis Pt. 1
On the Law of Hysteresis Pt. 2
On the Law of Hysteresis Pt. 3

In this series starting in Pt 2 starting on pg 713 Steinmetz discusses a special type of dynamo he calls a 'humming bird'. Let me quote a few things he says on this device:

But the best proof is, that under circumstances, by the action of such a mechanical force, the magnetic loop made by the correspondence of L to F can be overturned, so that the rising curve of magnetization is higher than the decreasing, that is the cycle represents, not expenditure, but production of energy, here the action of mechanical force is plain. In rotating the keeper before the poles of an electroinagnet, magnetism. and inagnetizing current are mnade fluctuating, and in plotting the magnetism as a function of the M. M. F., we derive such an overturned loop.

To such overturned loops, based on actual tests made on an alternating dynamo of the " humming bird " type, are shown in Fig. 26.
Here simple mechanical energy has delivered not only the energy dissipated by molecular friction in the iron, but also the energy exerted by the varying magnetion upon the M. M. F., and while the M. M. F. does not expend, but receives energy, the mechanical force of rotation expends energy.

Attached File  Hysteresis1.png   97.69KB   0 downloads
Figure 26 - Overturned hysteresis loops

Here is another figure from the start of Pt 3 which shows a more pronounced overturned hysteresis loop.

Attached File  hysteresis2.png   59.68KB   0 downloads
Fig 3 - On the Law of Hysteresis Pt. 3


Obviously this gives us some idea of the hysteresis curve we are looking for in parameter variation devices.

Something to keep in mind is that the mechanical energy is being tranformed into electrical energy through the varying inductance voltage embodied in the expression mentioned in my post above. Roughly speaking the mechanical energy required will be proportional to the mass, inductance is not linearly related to mass. Eg; I could have a 1kg specimen of one core material and it could have less inductance than a 0.75kg specimen of a different core material. So therefore the change of inductance, and therefore the transformed electrical energy, isn't directly proportional to mechanical energy input. Obviously there will be drag but designs can be optimized. No doubt magnetic forces acting upon the rotor will exhibit some effect but I feel very strongly that this is an interesting avenue forward and one that definitely needs more research.

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#6 Leonardnit



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#7 Leonardnit



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