Jim Kelley wrote:
Cecil Moore wrote:
Itot = Imax*cos(kx)*cos(wt)

Noting the linear variables and constants in there, and the absence of
anything that would change abruptly at certain particular values of x,
what would the expression for a standing wave on a shortened coil loaded
90 degree monopole have to look like?

Ideally, it would be of the form:

For x = 0 to top of coil,
Itot = k1*cos(k2*x)cos(wt)

For x = bottom of stinger to top of stinger,
Itot = k3*cos(k4*x)*cos(wt)

where k1-k4 are constants

Note: The above is a conceptual simplification as it
ignores the current "bulge" in a real-world loading
coil.

Note that at the coil/stinger junction:

Itot = k1*cos(k2*x)*cos(wt) = k3*cos(k4*x)*cos(wt)

- as required by the laws of physics. Remember, it is
always implied that we are considering only the real
part of the phasor. Thus a current phasor can undergo
an abrupt amplitude and phase shift without changing
the real value.

10*cos(0) = 14.14*cos(45) = 10

The above phasor has abruptly rotated its phase by
45 degrees and increased its amplitude by 41% with
no violation of the laws of physics.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com