4.4) Comparing phases of measured difference current with a theoretical instantaneous difference current

The resulting measured current curve can now be compared with a theoretical instantaneous difference current curve as in figure 18 and it can be seen that there is a phase difference between the two. This is partially due to the electrical length of the Toroidal Ferrite Probe as illustrated in figure 19 below.

Figure 18 Current Phase Comparison

The horizontal line in figure 19 represents the length of the antenna and the point D the current detection point of the probe. The probe is positioned at point B on the antenna in order to measure current at point B. However, it can be seen that when the INCIDENT current travels from left to right it is sensed at the point B and arrives at the detector (point D) after travelling the length of the probe (B to D). When the sensed signal arrives at the probe (point D) the main signal has arrived at point C along the length of the antenna. So, the signal detected at point D has the phase of point C with the current of point B (ignoring probe losses), thus causing phase error. The REFLECTED signal has a similar behaviour and when the REFLECTED arrives at the detector (point D) it has the phase of point A with the current of point B. There is therefore, a total phase error introduced of twice the phase shift along the probe (B to D) .

Figure 19 Phase Comparison

The fact that the phase shift in the probe is causing phase error can be proven in a simple way. An antenna of twice the length of the original is constructed and the measurements repeated. The frequency is now halved in order to obtain the antenna matched centre frequency. This means that the phase shift along the probe is halved because its electrical length remains constant. The phase shift error in measurement should also be halved (this was in fact more than halved because some other minor errors e.g. mechanical positioning of the probe and radiation have also been reduced) and produce an improved curve match. The result of the longer antenna can be seen in figure 20 below and it can be seen that the phase shift error is greatly reduced and there is little point in making further measurements.

Figure 20

4.5) Calculation of INCIDENT and REFLECTED Currents

Now that a curve similar to a sinusoidal wave as stated in the text books has been obtained, it is possible to prove the theory further by mathematically separating the difference current into the INCIDENT and REFLECTED components.

Figure 21 Longer Antenna

It can be seen from Figure 21 that a linear reduction of current along the the length of the antenna together with changing instantaneous currents due to the changing phase relationships of the two signals produces an instantaneous difference current curve almost identical to the measured curve and from this it can be assumed that if the INCIDENT and REFLECTED current drops are not exactly linear, they are almost so. There is an interesting lecture on adding waves of different phases or 'superposition' on YouTube which gives a mathematical understanding of how two individual waves add but in this calculation we have two waves that subtract together with a linear loss along the length of a λ/4 antenna in both directions which make this a very special case. However, the lecturer does demonstrate at 5.52 minutes that the instantaneous INCIDENT to REFLECTED current difference at any one point is a constant which makes the resulting calculations simpler.

Now that we have matched the measured curve to the theoretical curve, we can examine the simple equations used. As the current drops in a linear manner along the length of the antenna in both directions, we can now state that the peak current at any point in a well matched quarter wave antenna is:-

Where I_{in} is the peak input current in Amps

|B-E| is the phase change or 'distance' of measurement point (B) from the end of the antenna (E) in degrees (See Figure 19)

In order to find the Instantaneous Difference Current at point B the phase change along the length of the antenna has to be taken into account:-

Where θ is a the phase at measurement point (B) in degrees (See Figure 19)

I_{in} is the peak input current in Amps

I_{i} is the peak INCIDENT current at point (B) in Amps

I_{r} is the peak REFLECTED current at point (B) in Amps

|B-E| is the phase change or 'distance' of measurement point (B) from the end of the antenna (E) in degrees (See Figure 19)

The equation 6 can be simplified:- Since sin - θ = - sin θ

In Equation 6:- - sin - θ can be reduced to + sin θ

So, after the measurements and the calculations it is proven that the Instantaneous Difference current curve is in fact sinusoidal but is made from two separate linearly decreasing currents. This fact, that there are two currents, will be used as the basis in this series of articles to gain a full understanding of the real mechanisms involved in antenna radiation.

How Does an Antenna Work Index

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