A very short transmission line, such as those being considered here, in many situations will have no appreciable loss along the length of the line and the propagation constant can be considered to be purely imaginary phase constant, " i? " and the impedance expression reduces to,
42.
It would be ridiculously complicated to try to track a single molecule through multiple iterations of the water cycle, but it would be worthwhile to estimate the statistical time-distance propagation constant ( i . e . a molecule travels X miles in one week through evaporation, rain, ocean currents . . . etc ).
43.
As in any guiding structure, also in the NRD waveguide it is of basic importance to know the dispersion relation, that is the equation yielding the longitudinal propagation constant k _ { z } = \ beta-j \ alpha as a function of the frequency and the geometric parameters, for the various modes of the structure.
44.
Then, every unknown field is forced to have a form like U ( x, y, z ) = \ hat { U } ( x, y ) e ^ {-\ gamma z }, where the \ gamma term represents the propagation constant ( still unknown ) along the direction along which the waveguide extends to infinity.
45.
The "'propagation constant "'of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it two-port networks and their cascades, "'propagation constant "'measures the change undergone by the source quantity as it propagates from one port to the next.
46.
The "'propagation constant "'of a sinusoidal electromagnetic wave is a measure of the change undergone by the amplitude and phase of the wave as it two-port networks and their cascades, "'propagation constant "'measures the change undergone by the source quantity as it propagates from one port to the next.
47.
Note that " k " in equations ( 1.1 ) and ( 1.2 ) comes from the time derivative in Maxwell's equations and is the " free space " propagation constant ( actually, the propagation constant of whatever medium the metallic scatterers are embedded in ), proportional to frequency as we see in equation ( 1.3 ).
48.
Note that " k " in equations ( 1.1 ) and ( 1.2 ) comes from the time derivative in Maxwell's equations and is the " free space " propagation constant ( actually, the propagation constant of whatever medium the metallic scatterers are embedded in ), proportional to frequency as we see in equation ( 1.3 ).
49.
A "'closed waveguide "'is an electromagnetic waveguide ( a ) that is tubular, usually with a circular or rectangular cross section, ( b ) that has electrically conducting walls, ( c ) that may be hollow or filled with a dielectric material, ( d ) that can support a large number of discrete propagating modes, though only a few may be practical, ( e ) in which each discrete mode defines the propagation constant for that mode, ( f ) in which the field at any point is describable in terms of the supported modes, ( g ) in which there is no radiation field, and ( h ) in which discontinuities and bends may cause mode conversion but not radiation.
