Antenna Voltage, Phase, Power and Impedance Distribution page 1

1.1) Introduction

 Traditionally, antennas have been studied from the perspective of current distribution. However, in order to fully understand the radiation mechanism of an antenna it is necessary to have an appreciation of the voltage, power and impedance distribution. In this article the voltage distribution is measured and from these results and the previous current distribution results the power and phase distribution calculated and the impedance distribution studied. In classical antenna theory the voltage distribution is sometimes discussed but rarely, if ever, included in calculations or explanations of operation. It is also sometimes mentioned that the voltage at the end of an antenna can be very high and it is sometimes stated that this could approach a theoretical infinite voltage. This rather disturbing idea does not seem to be included in any formulas published for antennas nor are there any explanations as to how this could occur. From the previous study of 1.1) Understanding Coaxial RF Transmission Lines by Measurement and Calculation it is clear that the voltage in an open circuit does not measure as being more than twice the applied voltage and is in fact two samples of the same applied voltage dynamically added by the measuring instrument. With this in mind, the rather difficult task of measuring voltage along the length of a grounded monopole is performed.

1.2) Conventional Voltage Distribution

 The traditional voltage (and current) distribution for a quarter wave antenna is described in Principals of Radio Engineering by R S Glasgow M.S., McGraw-Hill, 1936.   Glasgow appears to have based the current and voltage distribution of an antenna on the observed behaviour of transmission lines, much the same as other respected authors have done for decades. The following is an excerpt from the book,  page 416.

"169. Current and Voltage Distribution in an Antenna - An antenna possess distributed inductance and capacitance and is electrically similar in behaviour to a long transmission line, such as a telephone line with the distant end an open circuit. A system of standing waves may be produced on such a circuit by impressing an alternating voltage of the proper frequency on the system. Under these conditions the line is in resonance with the impressed frequency. ---

 The current and voltage distribution in the case of a vertical antenna when the lower end is grounded is shown in figure (1). By adjusting either the length of the wire or the frequency of the applied voltage to obtain resonance, a stationary wave of current is produced, as in (a), which is everywhere in phase. The current is at a maximum at the base and the distribution will be sinusoidal if the inductance and capacitance per unit length are the same throughout the structure. In this case the length of the wire required will be exactly a quarter wave length. In practice the actual length of wire required to produce resonance at a given frequency is found to be less than λ/4 - usually about λ/4.5 - because L and C are not uniform. This causes the current to deviate from a sinusoidal distribution."


[Glasgow's current & voltage distribution drawing]

Fig 1(a)- Current and voltage distribution of grounded antennas.

1.3) Classical Voltage Curves

 A somewhat similar curve is shown for voltage in Principles of Radio Communication by J. H. Morecroft, John Wiley and Sons, 1927 page 872 Fig. 62.  An extension of this is shown on the same page in Fig. 61. and this has one and three quarter wavelengths all following the 'classical standing wave' pattern as per figure 2. It seems very clear that the early antenna engineers believed that antenna current and voltage followed the classical transmission line theory.

[Morecroft's current & voltage distribution drawing]

Fig 2- A possible form of excitation of an antenna at a frequency much higher than its natural frequency.

 There is very little mention of voltage distribution in the text books after the 1930's.  This may due to the fact that it would cause confusion and allow argument in relation to classical transmission line theory but this is only conjecture. If there really was virtually no voltage and maximum current at the input of the quarter wave antenna, then the input would present a very low impedance which is not the case. The impedance at the matched frequency (in the previous distributed current measurement it was proven that antennas do not resonate) is designed to match the impedance of the feeder and this is now generally implemented at 50 Ω with a coaxial cable. Of course it could be argued that the impedance at the end of the antenna becomes many MΩ and the voltage nearly infinite but as the following measurements will show, this is not the case.

 There is also the comment by Glasgow about the current along the length of wire " which is everywhere in phase" that should not be ignored. This is not reality and as these articles and measurements reveal, the real behaviour of antenna is that the INCIDENT current passes along the antenna, reflects at the end and passes back along the antenna length. The phase therefore changes along the length of the antenna and this linear phase shift is fully confirmed by a direct measurement with a VNA and an active low capacitance probe.

2.1) Antenna Voltage Distribution Measurements

An antenna is made from a  length of enamelled copper wire soldered into an SMA connector (in this case a 506 mm length of 1.25 mm) wire and is preferably the same antenna as used for the previous current distribution measurements.  This measurement suffers from the same problem as the current distribution measurements in as much as there is a tendency for the probe to pull the antenna matching off frequency. Therefore, a constant frequency measurement is likely to have significant error, and it is preferable to use a frequency sweep to find the antenna matched frequency on the VNA with an S11 measurement, thus ensuring that the results are always representative of an antenna used at the matched frequency. The test circuit used for all of the current distribution measurements are as per figure 3. This arrangement with an in house version of the VHF 300 MHz amplifier ( giving an antenna input of up to +20 dBm) was more than adequate to drive the active low capacitance probe and ensure that the Tx level was above any interfering signal level.  The RF bridge is an in house tandem transformer type. The tandem transformers also ensure that there is no d.c. present at the bridge output and that there is no chance of static discharge from the antenna that may damage the voltage probe. Another possible cause of probe damage can be a local high power transmission which happens to be at a frequency that the AUT responds to and it is advisable to avoid the use of high cost probes if the tests are not performed in an anechoic chamber.

Figure 3 Antenna Voltage Measurement Test Circuit

[Voltage measurement test set up]


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