Mutual impedance approach

Basically the approach is a combination of the plane wave expansion (spectral) and the mutual impedance approach as explained in Chapter 3 and also reference 62. 

Fig. D. 1 Evaluation of the array mutual impedance between the reference element in array q and all the other elements In array q by using the mutual impedance approach.

Generally, if the dipoles in an array are not parallel or coUinear, the computation for self- and mutual impedances is more difficult, and using the method of moments code is a more suitable approach. 

Table 1.3 shows the actual characteristic impedance of the horizontal line in Figure 1.27 for the vertical twin-circuit line illustrated in Figure 1.25. It is clear that the characteristic impedance is significandy frequency dependent. The variation reaches about 10% for selfimpedance and about 50% for mutual impedance in the frequency range of 100 Hz to 1 MHz. The characteristic impedance decreases as frequency increases and tends to approach the value as in the case of the perfecdy conducting earth and conductor. 

For lightning that struck the ground near a house, the simulation results in Figure 6.20 show close agreement with the measured results, and thus the proposed approach to use mutual impedance to protect equipment against a GPR is proved effective. 

If the distance between two impedance spectra measured on different frequency vectors is to be calculated, the impedance spectra need to be preprocessed. Therefore the impedance spectra are to be functional approximated, e.g. by utilizing smoothing and interpolation methods, e.g. roughness penalty approach. After that, the impedance spectra can be resolved on equal grids and the functional distance measure can be calculated over an mutual bandwidth. 

It is possible that the known anesthetic effect of the alkaloids of C. maculatum inhibits the mentioned fetal movements. In consequence, the tmigue obstructs the place where the shelves fuse together. Furthermore, the closure of the palatal shelves also depends on the separation of the fetal inferior jaw from the breast bone, which in turn depends on the fetal movements. If these movements are impaired, the lower jaw compresses the tongue against the upper part of the oral cavity, which impedes the mutual approaching of both palatal shelves [24]. 

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