Mutual coupling

As written, Eq. (52) depends on all the (infinite number of) adiabatic electi onic states. Fortunately, the inverse dependence of the coupling strength on energy separation means that it is possible to separate the complete set of states into manifolds that effeetively do not interact with one another. In particular, Baer has recendy shown [54] that Eq. (57), and hence Eq. (58) also holds in the subset of mutually coupled states. This finding has important consequences for the use of diabatic states explored below. 

While this derivation uses a complete set of adiabatic states, it has been shown [54] that this equation is also valid in a subset of mutually coupled states that do not interact with the other states. 

Designing the Mutually Coupled Forward-mode Filter Choke... 

More windings could be added to the mutually coupled filter choke core, but I highly recommend against this temptation. If the windings are not exact (to the turn), the supply will loose approximately 1 percent in efficiency for each turn in error on each output. Instead, use a mutually coupled filter choke for each complementary set of outputs, and use the output cross-sensing technique described in Section 3.9. 

These are wound on separate cores (not mutually coupled). 

For weakly guiding structures, the second term can be neglected, and we obtain the standard Helmholtz equation in which individual components of the electric field intensity vector E remain uncoupled. For high contrast waveguides this is clearly not the case. The second term in Eq. (2) in which the transversal electric field components are mutually coupled must be retained. 

From this brief description it is apparent that slice modes of both TE and TM polarizations are mutually coupled by the continuity conditions at the interfaces between slices. As a result, the mode fields of a channel waveguide have all components of the electric and magnetic field nonzero. In this way, the vectorial properties of mode fields are taken into account. 

Note that the TE and TM modes are now mutually coupled at the interface. The coupling is represented by the matrix X. 

It is interesting to note that if the matrix in Eqs. (40) and (48) is neglected, we obtain two independent sets of equations in which TE and TM modes of the slices do not mutually couple. They represent semivectorial approximations to the fully vectorial problem. 

The UV spectrum [/Imax 237,279 (sh), 288,327,344, and 359 nm] of murrayamine-K (135) indicated a 3-methylcarbazole, which was supported by the IR spectrum. The H-NMR spectrum resembled that of murrayamine-I (134). The only difference was that murrayamine-K has an unsubstituted carbazole C-ring, as concluded from the four, mutually-coupled protons at S 7.18, 7.31, 7.37, and 7.91. Based on these spectroscopic data and additional support by the C-NMR data as well as NOE experiments, structure 135 was assigned to murrayamine-K (130). 

Mutual inductance requires two parts the inductors (L) and the coupling between the inductors (K). We will illustrate the use of the coupling part K with two circuits. The first circuit will have three inductors with unequal coupling. The second circuit will have four inductors with equal coupling. Wire the circuit shown below. The dots on the inductors are critical since they indicate the polarity of the mutual coupling. Make sure the dots on your schematic agree with the ones on the schematic shown. 

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