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Tom Donaly wrote:
You and Gene also got the formula wrong, or at least you didn't get the complete formula for two waves passing in opposite directions deep in the night. What I posted was the equation for a pure standing wave. What you may be referring to is the omission of the real world traveling wave component that gets radiated. Since the radiated component amounts to only about 10% of the wave energy on a standing-wave antenna, it can be considered to be mostly negligible. The phase of that small traveling wave is completely swamped by the 90% wave energy that is in the standing wave on the 1/4WL standing-wave monopole. The components of a pure standing wave are two equal amplitude traveling-waves moving in opposite directions. Their phasors are equal in magnitude and opposite in direction of rotation. What is the phase of the sum of two equal amplitude phasors moving in opposite directions? Assuming each phasor has an amplitude of 1.0, here are some points in 1/4WL: Ifor + Iref = Itot 1.0 at 0 deg + 1.0 at 0 deg = 2.0 at 0 deg 1.0 at -15 deg + 1.0 at +15 deg = 1.9 at 0 deg 1.0 at -30 deg + 1.0 at +30 deg = 1.7 at 0 deg 1.0 at -45 deg + 1.0 at +45 deg = 1.4 at 0 deg 1.0 at -60 deg + 1.0 at +60 deg = 1.0 at 0 deg 1.0 at -75 deg + 1.0 at +75 deg = 0.5 at 0 deg 1.0 at -90 deg + 1.0 at +90 deg = 0.0 at 0 deg In 90 degrees of wire, the phase of the total (pure standing wave) current doesn't change. This makes the phase of the total current on a standing-wave antenna invalid for measuring the delay through the wire or through a coil. Note how the above values roughly correspond to the current amplitude and phase distribution on a 1/4WL monopole. From "Antennas" by Kraus: "It is generally assumed that the current distribution of a (thin wire dipole) is sinusoidal, and that the *phase is constant over a 1/2WL interval* ..." All illustrated on page 464 of the 3rd edition. -- 73, Cecil, IEEE, OOTC, http://www.w5dxp.com |
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