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| From Exegesis. Historic. Catt on 27 May 1976. Page 1 , End of Page 1 ; Page 2 Page 3 , Page 4 , Page 5 , Page 6 , Page 7 , Page 8 , Page 9 , Page 10 , Page 11 , Page 12 , Page 13 , Page 14 , Page 15 , Page 16 Transcribed text. Page 1. Electromagnetic Theory. 27 May 1976/1 First, a brief, hurried summary of the latest developments in the subject. Details will be filled in later. Whereas usually the electric current is said to cause the fields within a (two wire) transmission line, Oliver Heaviside says "We reverse this"; the field (flux) travels down between the wires and causes an electric current in the wires. We shall call the normal theory, the conventional theory, that current flows sown the wires and causes the E-M field the Normal Theory, or Theory N. Heaviside's theory, that the field flows down between the wires and causes current in the wires we shall call Theory H. The third, most recent theory is a step beyond Theory H and is called the Catt Theory, Theory C. In this theory, the field (flux) flows down between the wires and THERE IS NO EL;ECTRIC CURRENT. Heaviside probably never got this far, although it will be necessary to research his latest writings to conrifm this [since confirmed - IC 2007]. It is noticeable that Gossick (and I think also Josephs) says that Heaviside went senile, and Gossick says his later writings should be dismissed. Gossick has [End of Page 1] dismissed the concept of Energy Current (the essence of Theory H) and so can Page 2 safely be classified as holding to Theory N. To a Theory N man, the assertion that these was no electric current would lead to the conclusion that the speaker or writer was senile. In general, what follows will be aspects of Theory C. 1. There is no electric current. 2. A capacitor is a transmission line. 3. An inductor is a transmission line. 4. A transformer is a transmission line. The velocity of an energy current in a perfect conductor is zero. That is, energy current cannot enter a perfect conductor. .... . . . . ( c = 1/ sq.rt. (mu.epsilon), and epsilon for a perfect conductor is infinity.) [See "The dielectric constant of copper." ] Capacitor. All capacitors behave as transmission lines in the manner described for parallel voltage planes in my paper, IEEE Trans. on Electronic Computers, Dec 1967, page 744. Because epsilon is very high, the outwards velocity of propagation is very slow. ESR is the initial chjaracteristic impedance of the transmission line. Page 3. Inductor. Single turn inductor, iron cored. [First diagram]............................................ Hi speed iron Waves leading to inductor ..............Inductor Zo approx. = 100 ohms ........................... mu very high c = co........................................................therefore Zo very high .............................................c=1/ (sq.rt(mu.epsilon) = very slow ................................................................since mu is so high Multi-Turn Inductor [Second diagram] .............................................................see ZoI Zo approx = 100ohms..............................IRON Wires leading to inductor.......................Inductor ............................................................mu very high "ZoI" is even larger than in single turn inductor as a result of crosstalk to other turns.
[Vertical text.] At this point use the approach in my opaper in IEEE 1967 referenced opverleaf to calculate wavefronts launched to the right. Page 4. Transformer. [Diagram] Zo approx. = 100ohms............IRON (hi speed)............Zo approx=100ohms c = 1/sqrt(muoepsilono) .....ZoTin very hi...........c = 1/sqrt(muoapsilono) ........................................................c very clo At P (and also at Q) reflections and crosstalk occur between primary and secondary and also between windings of the primary. Again, follow the method for xtalk between pairs of long wires described in my IEEE Dec 1967 paper. If Xformer core is air not iron, resistive paper analogy will work. For resistive paper, take a cross section perpendicular to the direction of transmission lines (i.e. in ya plane). Page 5. Real iron is not hi speed iron, so the full mu does not arise as the step, or wave front, passes the material. So with real iron the story is more complex, with new wave fronts being projected from behind the original wave front as the effective mu changes (as the magnetic material domains accelerate, gain velocity &c &c). Probably the best model to start with is an air cored Xformer of choke, get familiar with it and proceed from there to the more complex practical case of a slow (1usec) mu, that is a mu with finite frequency bandwidth. Discussion of Xformer on last page. As initial wave front step reaches P where it sees a change of impedance from Zo so that there is a reflection but some of the energy current continues towards Q. If mu > muo, the vleocity between P and Q is slower. At Q, reflections occur and also some of the wave front proceeds further to the right on the secondary (O/P) of the transformer. Page 6. Transmission lines can be cascaded. ia -ia ic -ic Assume no fringing (i.e. imagine a coax within a coax) Keep mu, epsilon the same for line AB and line BC. Project a step (wave front) down AB and at the same time project one down BC. It can be arranged that the first front has currents ia = -ib equal to those for the seocnd wave front ib = -ic Total current down B is then zero. Plate B can be removed and wave fronts are unaffected. This is if stress level ( ExH or Poynting Vector) and energy current [density] is the same. Therefore wave fronts can be cascaded laterally. Therefore the Xmission line wave front rules apply to one segment (tube) of energy current just as much as apply to the full Page 7 energy current. So we canapply ideas of energy current to a small volume. In a space with mu and epsilon, velocity of energy current is c = 1/sqrt(mu x epsiloin) (see my IEEE Dec 1967 paper). Discussion of Epsilon. High Epsilon means less voltage drop across for a given "displacement current", in the language of Theory N (Page 1).
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