Antenna Voltage, Phase, Power and Impedance Distribution page 4

The results for the voltage and current distribution can now be used to find the power distribution along the length of the antenna using V x I = W.

Figure 13 Power Distribution

It can be seen that the power does not drop in a absolutely linear manner and that the majority of the power is in the INCIDENT direction. With an input power of 0.1614 W and 0.0589 W at the antenna tip, it is simple to calculate that there is 0.1614 - 0.0638 = 0.0976 W radiated or dissipated power in the INCIDENT direction compared to the 0.0638 W radiated or dissipated power in the REFLECTED direction. From this result it is easy to conclude that approximately 6/10 of the power is in the INCIDENT direction and 4/10 in the REFLECTED direction. This difference in powers becomes important in later antenna articles where it is shown to affect both radiated elevation and polarisation.

The voltage and current distribution results can also be used to calculate the impedance distribution as in figure 14 using simple Ohms law R = V / I.

Figure 14

As can be seen from the curve the result does not look right because the impedance in the REFLECTED direction, very close to the antenna input, is very high. Common sense would suggest that the impedance at this point where any returning current is entering a 50 Ω coaxial cable would be nearer to 50 Ω. What we are seeing is that as the remaining REFLECTED electrons reach the antenna base they still have a significant voltage but the current is very low, thus giving a high calculated impedance. It is clear that Ohms law does not apply to the conditions within a radiating object but the attempt to calculate the impedance has revealed that there is a deficiency of electrons in the REFLECTED direction at the antenna base which has an important significance that will be revealed in the Radiating Mechanism article.

6.1) Voltage Analysis

The measurement results have shown that the actual voltage distribution present is not the same a the old text books state. The classical explanation is displayed in figure 15 (which is figure 1(a) repeated here for convenience). A similar drawing convention is used in figure 16, which illustrates the measured vector sum voltage distribution, together with the measured difference current distribution as concluded in the previous Antenna Current Distribution article. Although there is virtually no difference between the current distribution curves, it is quite obvious that the voltage distribution curves are very different.

Figure 15 Classical Distribution

Figure 16 Measured Distribution

When the constituent parts of the sum and difference vectors are shown as the INCIDENT and REFLECTED voltages and currents respectively and with the same drawing convention, the major difference between the classical theory and reality becomes very clear as illustrated in figure 17 below.

Figure 17 Mathematically Processed Voltage and Current Distribution

6.2) Phase Analysis

If the phase distribution is plotted with the same convention as the classical current distribution and with the phase the same almost everywhere with the phase changes only occurring at current nulls, then a drawing as per figure 18 could result. Whereas is has been proven in this article that the vector sum measurement would look like figure 19 and when the INCIDENT and reflected phases are resolved, they appear as in figure 20. Again, the reality is very different to classical theory.

Figure 18 Classical Phase Distribution

Figure 19 Measured Phase Distribution

Figure 20 Mathematically Processed Phase Distribution

All of the voltage and current measurements have been made assuming that the phase change along the length of the antenna is linear. It can be seen from figure 21 that after an assumption of linear phase the voltage measurements are taken, and after this the voltage drop coefficient is estimated by curve matching. Then there is a subsequent calculations of INCIDENT and REFLECTED voltage which is used to generate a vector sum curve. The generated vector sum voltage curve is compared to the measured vector voltage sum curve and the comparison fed back in order to establish the correct voltage drop coefficient. The vector difference current calculations in the antenna current distribution study uses a similar process. Both of these are a 'circular calculations' that standing alone are not proof of linear phase. The i & r voltages are also used in order to calculate the vector sum phase. However, the additional data input from the phase measurement and the agreement of the generated vector sum phase with the measured vector sum phase shows that the original assumption of linear phase is almost certainly valid. As the original statements of phase being the same along almost all of the length of the antenna by Morecroft and Glasgow have no accompanying proof, it is reasonably safe to conclude that they were early assumptions and not actual measurements; these early assumptions should therefore be ignored if a full understanding of antennas is to be gained.

Figure 21 Measured and Mathematically Processed Voltage, Current and Phase Distribution Logic

6.4) Conclusions

By combining the knowledge gained in the voltage distribution and current distribution measurements, it is possible to understand the behaviour within the antenna and observe the fundamental process. It can be seen that as the INCIDENT signal passes along the antenna, both the current and voltage are reducing showing that power is being radiated all along the length and work is being done in order to radiate. The process in the REFLECTED direction is identical to the INCIDENT direction, except that the current and voltage are reduced. When the input of the antenna is reached by the current in the REFLECTED direction, there is still some voltage remaining that can be radiated even as the current is reaching zero.

The voltage is of course in phase with the current in each direction as can be seen in figure 17, which logically has to be right because both voltage and current are being carried on electrons in the form of charge. The illogical concept that the current and voltage are out of phase no longer has to be considered. It can also be seen that the phase changes linearly in both directions and the descriptions of the current being "everywhere in phase "as stated by Glasgow or being at "the immediate vicinity of the minimum, which is where substantially all of the phase change takes place" as suggested by Terman are obviously wrong.

The nature of the voltages and currents that really exist within the antenna could easily be incorporated into a computer program in order to simulate a more realistic behaviour than is presently achieved with simulations. However, it would be very wise to also incorporate the real radiation mechanism and actual behaviour of the radiation outside of the antenna that will gradually be revealed as this series of articles progresses, because the old text books are also wrong about several elementary principles of radiation.

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First Published by William J Highton on 5/7/2015

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