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Old 03-30-2012, 04:49 AM
garrettm4 garrettm4 is offline
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Lumped & Distributed Elements & Mutual & Self Inductions, Down the Rabbit Hole We Go


I hope this helps make more clear as to what Mr. Dollard was referring to in the quote you had of his in your post. While I can't speak for him, I can give you my understanding of it, in a round-about lecture of my own (if anyone finds something to be inaccurate or lacking in detail, please feel free to correct me).

Without further ado, here's my 2 cents on "The Four Distinct forms of Energy Stored in a Winding":

The various dielectric-metallic confines (or circuits) employed for the use of "electricity", create a myriad of conditions and settings for the two conjugate forces of the Electric Field. The magnetic and the dielectric. The most basic conditions are those of the LUMPED ELEMENTS. In the world of lumped element analysis, a resistor is just a resistor and a capacitor is only a capacitor, the employment and understanding of these conditions are only useful at LOW FREQUENCIES. A more advanced and very much more complicated condition is that of DISTRIBUTED ELEMENTS. Here a resistor is not only a resistor but an inductor and capacitor as well, the employment and understanding of these conditions are generally used at high frequencies and is the most accurate for calculation given ANY circuit condition.

Furthermore, beyond the lumped and distributed elements, we have TWO forms of the two inductions (dielectric & magnetic) these being in the context of SELF and MUTUAL relations. This is why we have C, K, L & M or a total of four circuit coefficients. C and L are self inductions, which means that if looked at from a lumped element point of view they can only store and return energy, THEY DO NOT TRANSFER ENERGY. K and M are mutual inductions, these if looked at from a lumped element point of view can be thought to only be able to transfer energy, they DO NOT STORE ENERGY.

Now if we combine both the SELF and MUTUAL inductions along with LUMPED and DISTRIBUTED ELEMENTS, we enter into a brave new world, one that will change your views on electrical circuits for the better. Here lies the "meat and potatoes" of what Mr. Dollard has been lecturing about. For now lets consider the specific employment of lumped elements, for example a common man, low frequency, 1:1 transformer utilizing a permeable core of soft iron.

Lets examine the LUMPED, MUTUAL and SELF Inductions of the Transformer. A transformer is wound to have almost NO SELF INDUCTION, this is because self induction CAN NOT TRANSFER ENERGY (it can only store and return energy), here MUTUAL INDUCTION IS EMPLOYED FOR USE. In the transfer of energy, mutual induction acts like an ADMITTANCE, whereas SELF INDUCTION (of a magnetic element) would act as an IMPEDANCE. When analyzing a transformers characteristics, ANY SELF INDUCTANCE (of the primary) IS CALLED "LEAKAGE INDUCTANCE". Both the Leakage Inductance L (of primary) and the Mutual Inductance M (between windings), in this simple case, are LUMPED ELEMENTS.

Now lets consider the DISTRIBUTED ELEMENTS in the transformer, time to go down the "rabbit hole". Interestingly, the transformer doesn't have a capacitor hooked up but it will still oscillate, why? Well sir, there CAN NOT be an OSCILLATION without the employment of a CONJUGATE FIELD OF INDUCTION, in the case of a transformer (a magnetic element) we need a DIELECTRIC ELEMENT to ALLOW for such an even to occur. This is quite the predicament for those, often unwitting, followers of the LUMPED ELEMENT MODEL, where is the capacitor? Well lets forget those guys and think outside the box, there must be a capacitance distributed throughout the coil, lets call this DISTRIBUTED (MUTUAL) CAPACITY and give it the letter K. This distributed capacity (K) is found IN-BETWEEN EACH TURN of the COIL and thus is CUT UP INTO SMALL LITTLE SELF CAPACITIES (C) that then constitute the whole of K. Next we have yet another DISTRIBUTED ELEMENT this being a SELF CAPACITY (C) of the entire winding to the transformer CORE or GROUND (generally a transformer core is directly connected to ground, so as to be at "zero or earth potential" for safety). Here the entire winding of the transformer can be looked at as a "metallic cylinder" or "capacitor plate" and the ground or transformer core as the other "capacitor plate", thus constituting a self capacity C between these two separate conductors. We will henceforth call this second distributed capacity, the Leakage Capacitance and give it the letter C.

As can be seen there are TWO DISTINCT DISTRIBUTED DIELECTRIC ELEMENTS in and around the transformer, one of self induction, Leakage Capacitance (C) and the other of mutual induction, Mutual Capacitance (K), each having a spatially distinct and separate path of propagation (orthogonal to one another). These being the most simple cases. NOTE, these distributed elements have almost no implications or effect at low frequencies, it is only at high frequencies that these distributed elements make them selves apparent to the naked eye (or oscilloscope screen) in the form of oscillations. A few examples of High Frequency Events, in which the distributed capacities would actually have physical meaning, would be, lightning discharges and arcing to ground or arcing from winding to winding. These HF events, along with the distributed elements of the transformer, cause (sometimes) disastrous oscillatory events in the high-power electrical distribution systems used by the utility companies.

To summarize our above transformer example, we can isolate two lumped magnetic elements, Leakage Inductance L (stored, un-transferable energy of primary) and Mutual Inductance M (transferred energy pri to sec), we also have two (UNINTENDED and often unwanted) distributed dielectric elements, Leakage Capacity C (to ground) and Mutual Capacity K (in-between turns of coil). If we go one step further, we can look at the directions of propagation of these four distinct inductions.

So with the above example and discussion given, lets examine the questions you gave pertaining to these four distinct inductions:

1) L, Leakage Inductance
Q - "The big magnetic fields that push our motors?"
A - My answer would be a resounding NO, leakage inductance can only store energy it CAN NOT TRANSFER ENERGY, thus it would only act as an IMPEDANCE and not as an ADMITTANCE required for the electrical to mechanical transfer of energy to create motion in a motor. The leakage inductance is the exact thing we try to get rid of when designing a motor, and is not something we usually want. There are times when a small leakage inductance can be helpful, this is only when there is a short circuit and the impedance of the leakage inductance prevents catastrophic failure by LIMITING the current of the short circuit.

2) M, Mutual Inductance
Q - "Energy stored in counterspace/innerspace?"
A - Magnetic energy as explained by Mr. Dollard is stored in Normal Space, not the "counter space" as explained by him. Mutual induction of the magnetic field is that which transfers energy in-between two separate coils, there is no storage of energy here, only the transfer of energy from one distinct coil to another. This topic can be found to yield many interesting and practical insights, but I will leave this subject for another time.

3) C, Leakage Capacitance
Q - "The field created by an electrostatic generator, or in a vacuum capacitor?"
A - Inside the vacuum capacitor there is NO LEAKAGE CAPACITANCE, this is normal SELF CAPACITANCE, although if at high frequency, when small capacities are physically meaningful, there is a leakage capacitance associated with the vacuum capacitors outer plate to ground (or any and all surroundings) (and on the topic of high frequencies, EVERYTHING has an associated leakage capacitance). Furthermore, only "quantum physicists" think a vacuum capacitor operates differently from any other capacitor type, at the end of the day there is little to NO difference, aside from the SPEED of DISCHARGE (which is due to permittivity affecting the manifest "velocity of light"). The electrostatic generator is a highly complex induction machine which converts mechanical energy (or seemingly this is the source) to electrostatic potential stored in a condenser. There may undoubtedly be a leakage capacitance associated with the electrostatic generators operation, but don't try to fool yourself into thinking that (leakage capacity) is the only thing going on during operation.

4) K, Mutual Capacitance
Q - "Energy stored in counterspace/innerspace?"
A -ALL DIELECTRIC ENERGY IS CONSIDERED AS A COUNTER SPATIAL ENERGY. Thus, the storage of dielectric energy is greater when there is MORE counter space for the energy to occupy. This can be looked at as the RECIPROCAL of SPACE or a "large space" divided into the "unit" (1) is an equally large "counter space". This is seen in the design of a capacitor, the closer the plates are the more "storage" or "capacity" the capacitor has, it's that simple.

5) Bonus Question on Capacity of a Wire
Q - "On a 20 secondary with spaced windings does approaching the coil with your hand increase its mutual capacity K, or its self capacity C??? but before you answer think what would happen if you had a long straight wire and could measure it's C. What would happen to the meter if you approached the wire?"
A - This is an interesting question and the answer is dependent upon perspective, how do you plan to measure the capacitance? This question answers your question but doesn't really give an answer, so lets work our way through this. First, ALL METALLIC SURFACES HAVE A DEFINITE CAPACITY REGARDLESS OF BEING REFERENCED WITH ANOTHER METALLIC SURFACE. When we measure a capacity we usually place TWO metallic surfaces of interest as close together as possible, we unwittingly try to make lumped elements. When considering a distributed capacity we generally can no longer use the methods and understanding of lumped elements, here lies the problem of measurement, how do we measure only one surface? Well there are techniques to do this but are beyond the scope of your question and my answer. So more to the point, the measurement of capacity is a problem of reference and THERE ARE MULTIPLE CAPACITIES ASSOCIATED WITH THE WIRE IN YOUR QUESTION and consequently multiple answers. An outstretched wire will have a greater "free-space capacity" while the coiled wire will have a greater self capacity to any-one object. Moving your hand closer increases C (leakage capacity) not K (mutual capacity). K is when there are multiple C's that are mutually connected with one another, or MULTIPLE separate metallic surfaces linked via dielectric flux, this in the secondary is seen in-between turns.

REFERENCE (for "bonus qustion"):
Fritz Lowenstein - Capacities [1916]

REFERENCES (for "common man transformer" discussion):
CP Steinmetz - Abnormal Strains in Transformers [1912]
JM Weed - Abnormal Voltages In Transformers [1915]
LF Blume & A Boyajian - Abnormal Voltages within Transformers [1919]
LV Bewley - Traveling Waves on Transmission Systems [1933]

To be continued in part 2

Garrett M

Last edited by garrettm4; 03-30-2012 at 11:42 PM.