Restricted Space Antennas
Now that we've gotten some preliminaries out of the way, we can start to look at some actual antennas. It seems that most antenna texts start out with dipole antennas, so that must be a pretty good starting point.
What is it? A dipole antenna is simply a straight section of wire fed with an RF signal. Normally it is fed in the center and is resonant, as indicated in the diagram. In these notes we will consider a dipole to be near resonant. If it's not resonant or nearly so, we'll call it a "doublet". In the literature, there doesn't seem to be a consistent nomenclature, though.
Length. A resonant dipole is very close to 1/2
wavelength long. It's not quite 1/2 wavelength because the speed of light,
"c", is a little slower in copper or aluminum than in free space. There is
also a reduction in the velocity due to stray capacitance from insulation
or corrosion on the wires. The resonant length is also affected somewhat
by the conductor diameter, with larger diameters giving somewhat shorter
antennas. For practical purposes, the length of a resonant dipole can be
estimated as 95% of the length of a half wave in free space. The formula
L (m) = 142.5/F(MHz)
L (ft) = 468/F(MHz)
Here's a question: What is the length of a center fed resonant dipole for the 6 meter band (50.1 MHz)?
Current and Voltage. The antenna has nearly zero current at the ends. It's not quite zero due to capacitive end effects, but if it's not very close to zero, you'll see arcing! It also has a current maximum at the center. The voltage distribution on the dipole is nearly opposite that of the current distribution. The minimum voltage is at the center, while the ends have a very high voltage.
Impedance. Remember that impedance is defined as the ratio of voltage to current. From Ohm's Law, Z = E/I. That means that the impedance of the dipole is minimum at the center and maximum at the ends. The high impedance at the ends means that it may be very hard to feed the antenna at the ends. Since the impedance is nearly infinite, it acts like an open circuit and little power is transferred. In order to feed a dipole at the ends, special matching provisions will be needed.
In free space, the impedance of a center-fed half wave resonant dipole is about 72 ohms. That is a near perfect match for 75 ohm coax and quite acceptable for 50 ohm coax, too. Unfortunately, the impedance in the real world depends on the height above ground and the ground quality.
Conductor Diameter. The figures above, computed using MultiNEC, show the effect of conductor diameter on the resonant length and impedance of a 40m dipole at 7.1 MHz. Note that the formula says that the resonant length would be 468/7.1 = 65.9 ft. In most cases the NEC predicted length in free space is somewhat longer, but the effect of insulation, ground and other factors is not accounted for. It is recommended that when you construct a dipole, cut the wires a little longer than required, then trim the antenna to resonance. It's easier to cut than to splice additional wire.
Note that for diameters larger than about 1 in, there is no perceptable affect of wire diameter and the antenna performs as if it were made with no losses. The biggest difference between the zero loss and copper wire cases occurs when the wire diameter is 0.25 in or less. Although the resonant length is a little smaller with copper wire, the major effect is an increase in impedance. This increase is mainly due to the wire resistance which increases in proportion to 1/D because of the skin effect. The following figure shows the effect on the antenna gain.
What can we learn from this simple exercise? First, as far as a 40m dipole is concerned, there's no reason to use a conductor larger than about 1 in, but that's still too large for most installations, space limited or not. If we take 72 ohms as the radiation resistance, then the difference in impedance represents losses in the wire. To stay above 95% efficiency, we want the impedance to be less than about 72/0.95 = 76 ohms. From the graphs, that happens whenever the wire diameter is larger than about 0.03 inches, which corresponds to roughly AWG #20 wire. As long as the wire is larger than that, the effect is not going to be noticeable.
We can cross check the results from the impedance calculation with the antenna gain results. Note that 95% efficiency is equivalent to 10 log(0.95) = 0.22 dB drop in gain. Since the free space gain of a lossless dipole is about 2.14 dBi, we are at 95% efficiency when the gain drops to about 1.92 dBi. That happens with a wire diameter less than about 0.03 in, confirming the earlier evaluation. These results can be scaled for other frequencies. For 80m, the limit will be approximately double the wire diameter or on the order of #14 AWG wire.
Effect of Ground. The effect of a ground does several major things to a dipole antenna. First, it causes the signal to be reflected which modifies the radiation pattern. (We haven't talked about that yet, but we will.) Second, the reflected signal influences the antenna and changes the impedance. Third, the ground will absorb some of the signal, decreasing the efficiency. The following figures show the effect of ground on a 7.1 MHz dipole made from #14 copper wire with various ground conditions.
First, notice that the resonant length and impedance both vary quite a bit depending on the ground conditions, which we normally have no control over. The resonant length can vary from 66 to 68 ft, with the larger variations over a perfectly conducting ground. The impedance also will vary from very low to around 100 ohms, with the perfect ground showing the larger variations. Therefore, in building a dipole, we shouldn't be too concerned about exactly estimating the resonant length or the impedance. We'll always have to adjust the length for resonance and the impedance will generally be in an acceptable range, unless we are over a perfect ground.
But what about gain and perfomance? As the above figures show, there are also variations in the gain and the take off angle. First, notice that at heights below about 30 ft, the take off angle is 90 degress - straight up. That means that most of the radiation is going vertically upward, so the antenna will be less than optimum for DX contacts. If we want to obtain a low angle of radiation, say 20 to 30 degrees, then we better invest in some tall towers! Surprisingly, the poorer ground shows the lower takeoff angles at lower heights, so that may be good.
Notice in the gain graph that the curves for less than ideal ground conditions are lower than that for a perfect ground. The model for a perfect ground has no ground losses - all energy is reflected. The difference between the curves shows the loss due to real world ground conditions. As can be seen, there is at least a 1 dB loss from perfect to average ground and another 1 dB loss from average to poor ground. Remember that each dB represents about 20% loss of the radiated power. But worse for limited space conditions is the situation at low heights. At heights less than about 30 ft, losses can be on the order of 4 to 6 dB. That amounts to losing about 60 - 75% of the radiated power warming the ground, while most of the rest of the power warms the clouds overhead!
L = 492/F(MHz) = 468/50.1 = 9.34 ft or 9 ft 4 in, approximately
Due to conductor size, etc., the actual length will vary