Derivation of equation (16) equal to 0 yields $$\begin{aligned} \begin{array}{l} S^{\prime }=\frac{-n E[P] E[D]^{\prime }}{E[D]^{2}}=0 \\ E[D]^{\prime }=0 \end{array} \end{aligned}$$ (19) From the above equation, it can be seen that the optimal fixed CW ...
The first and second equations are combined to obtain the third equation. By inserting the known fields from above, we obtain the previous analytical result for C in a coaxial cable. More generally, these equations provide us with a method for obtaining the capacitance from the fields for any ...
The main contribution of this paper is the derivation of spatiotemporal Li茅nard-type models for expressing the dynamical behavior of a fluid transmission line. The derivation is carried out from a quasilinear hyperbolic system made of a momentum equation and a continuity one. An advantage of ...
Equation 1.56 shows Z0=L/C, which indicates that characteristic impedance of a lossless transmission line is only dependent on the unit inductance and capacitance of the transmission line, which are decided by transmission line dimension and substrate materials. Typical types of transmission line charac...
In order to account for variations of the outdoor temperature, a sine function with random noises as shown in Equation (12) is considered. FIGURE 7 Open in figure viewerPowerPoint The special-power-line supplied LVDN with multiple EHs under study. (12) In Equation (12), is the out...
designers must mathematically represent the line in circuit parameters such as resistance, inductance, capacitance, and conductance. In field theory analysis, equations should be written in terms of electric and magnetic fields. In both these analyses, we are solving the wave equation for a solution...
Interesting derivation showing how permittivity can make the electron look like a simple capacitor. The electron capacitance model permittivity epi=epi0*(1 + a/r)^2 also predicts bending of light correctly. Source of the fine line 137 constantis derivedfrom EM as spherical energylike the above ...
In Ref.13 a continuum approximation has been employed to derive an electromechanical wave equation, which for homogeneous parameters has the solution of decaying plain waves, propagating with a velocity v. This allows the derivation of the parametric dependence of the velocity v. This continuum ...
The luminance (Y) signal is computed from the first line of the equation, which approximates the response of the human visual system to each color. In order to make up the two color difference signals, the difference between Y and the R and B channels is taken, with the scaling factors...
Equation (3) is the general format of the time domain matrix form fully distributed parameter line model with frequency independent parameters. This equation is a matrix form PDE with constant parameters, and can be solved using numerical solution of matrix form PDE [43]. However, this matrix ...