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Cecil, W5DXP wrote:
"Take a look at Figure 14-4 on page 465 of "Antennas For All Applications---third edition." Yes. If you don`t have a copy, you are truly deprived. Kraus corroborates the square phase diagram in the text. On page 463, he says: For each length the relative amplitude and phase of the current are presented for omega prime = 10 and omega prime = infinity corresponding to total length-diameter ratios (l/a) of 75 and infinity" (a very thin wire). What Kraus shows is a center-fed 5/4-wave dipole, 5/8-wave per side, for maximum gain without production of significant extra lobes. At 1/2-wave back from the open circuit ends of the dipole, phase moves up a vertical line from the zero-degree level to the 180-degree level. This is in the case of the extremely thin wire. For the l/a=75 wire, the phase change is much more gradual. Please look at Terman`s Fig. 4-5 on page 94 of his 1955 edition of "Electronic and Radio Engineering". Fig. 4-5 is: "Phase relations on a transmission line for two typical conditions. In these curves, the voltage of the incident wave at the load is used as the reference phase, and the line attenuation is assumed to be small." For the case of the complete reflection, the load is an open circuit as shown. The reflection coefficient is 1 (one) on an angle of zero. The reflected wave will be just as strong as the incident wave. The reflection causes the voltages of incident and reflected waves to have the same phase at an open circuit. They add arithmetically, and the total voltage across the open circuit (load) end of the line doubles. In this case the current of the two waves are equal and of opposite phase at the open circuit. Thus they add to zero at this point. At a distance of 1/4-wave back from the open circuit, the incident wave has advanced by 90-degrees from its phase position at the load, while the reflected wave has dropped back by the same 90-degrees. The line voltage from the forward (incident) and reflected waves at this point, one quarterwave back from the open circuit, are now 180-degrees out-of-phase. Their sum is nearly zero from a complete reflection on a nearly lossless line. The currents from the forward and reflected waves which were out-of-phase at the open circuit are now in-phase, at this point, 1/4-wave back from the open circuit. FROM Fig. 4-5(c), the phase line representing the case of a complete reflection, goes from zero-degrees for the voltages at the open circuit, and abruptly falls to a 90-degree lead with respect to the incident voltage at the open-circuit (load). AT 1/4-wave back from the load, the phase shifts instantly from 90-degrees lead to 90-degrees lag. At 1/2-wave back from the load, the phase shifts instantly from 90-degrees lag to 90-degrees lead. This flip-flop behavior continues each 1/4-wave of travel back from the reflection point. For the case shown for the reflection coefficient of 0.4, the phase oscillates between leads and lags of 40-degrees, not the 90-degree limits of the complete reflection case. The phase reversals in Kraus` Figure 14-4 are analogous to those in Terman`s figs. 4-5 and 4-7. All show abrupt 180-degree phase shifts alternating at regular intervals. Best regards, Richard Harrison, KB5WZI |
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