Likewise, the radian frequency ([[omega].sub.n]) of the crack-free beam will vary with respect to [DELTA][[omega].sub.n], and the total radian frequency will be [[omega]'.sub.n] = [[omega].sub.n] + [DELTA][[omega].sub.n].
Therefore, the changes in the radian frequency ([DELTA][[omega].sub.n]) and natural frequency ([DELTA][f.sub.n]) can be obtained using (7) and (8), respectively.
The phase velocity of the propagated wave in the ring hybrid can be obtained by simply dividing the radian frequency
[omega] by the Bloch phase constant k ([v.sub.p] = [omega]/k).
Electric fields calculated through the exact and approximate SD Green's functions as functions of [ohm] for [T.sub.c] = 200 [micro]s and [T.sub.c] = 10 ns: (a) FD as functions of the radian frequency [ohm] and (b) TD as functions of t/[T.sub.c].
Electric and magnetic frequency-domain shielding effectiveness as functions of the radian frequency [ohm] for a time-harmonic electric line source.
It consists of the PD modeled by a subtractor with gain [k.sub.d], the loop filter which is modeled by a first-order low pass filter, proportion integral filter, with the s-domain transfer function F(s) = [V.sub.o](s)/[V.sub.d](s) = (1/s)(([[tau].sub.2]s + 1)/[[tau].sub.1]) to minimize the phase noise of the output of the PD, [V.sub.d](s), and a voltage control oscillator (VCO) tuned by [V.sub.d](s) to make the output phase [[theta].sub.o](s) closed to the input phase (s), which acts like a radian frequency
integrator as a result of [V.sub.d](s) = [DELTA]wt + [DELTA][phi], and have the s-domain transfer function V(s) = [[theta].sub.o](s)/[V.sub.c](s) = [k.sub.o]/s.
In these two equations, [Z.sub.0] is the terminal impedance, and [[omega].sub.c] and [[omega].sub.0] denote cut off radian frequency
and attenuation pole radian frequency
, respectively, which can be obtained from the EM simulation result.
Because the group delay, [t.sub.d], is equal to minus the rate of change of radian phase with respect to radian frequency
, the form
Based on a two ports network and using the methods mentioned in , the effective relative permittivity and permeability can be obtained from the complex refractive index n and wave impedance z (where k = [omega]/c, [omega] is radian frequency
, d is the slab thickness, and c is the speed of light.):
conductance [Omega] = the radian frequency
[T.sub.2] = the time-delay factor The time-delay factor is an additional optimizable variable, part of the Super Compact(*) model.
The parameters [omega.sub.1] and [omega.sub.2] are the radian frequency
limits of the pass band, and [omega.sub.x] and [omega.sub.y] are the limits of the image band.
The quality factor Q for each mode is the reciprocal of the product of the motional time constant and the radian frequency
of the mode.