Elevation angle discrimination is a possible mechanism allowing
this vertical stack to reduce
frequency dependent nulls, presumably a result of multipath. Elevation angle discrimination depends on the elevation beam width of the combined antennas. The antenna’s elevation pattern also depends on height above ground.
Elevation angles of reception have importance in that signals from distances beyond the horizon can arrive at different angles with respect to the horizon. Communications research indicates, in general, lower angles near the horizon are favored for long distance reception. This may particularly apply to long distance TV reception because broadcast transmit antennas are designed to ensure maximum radiation is below the horizon (negative elevation angles). In general, full-power broadcast antennas have a narrow vertical beam width and also incorporate downward beam-tilt. With narrow vertical beam patterns and beam-tilt, the transmitted signal strength decreases rapidly for angles above the horizon.
At the receiving antenna, the effects of the ground reflections cause great attenuation at an angle of zero elevation degrees. This is due to the reflected signal being 180 out-of-phase with respect to the direct signal, and cancellation occurs.
Two conditions are necessary for a vertical stack of receiving antennas to achieve both a low angle and narrow elevation beam width:
A. Height above ground of several wavelengths
B. Large stacking separation
Computer simulations with
4NEC2 software provides for graphing the vertical beam pattern of antennas. The horizon is shown on the 4NEC2 graphs as 90 degrees. The image below shows on the left, the upper half-pattern in free space of a
single long-Yagi; overlaid is a
stack at 89 inches.
The second pattern, on the right side, shows the response of one long-Yagi at 64 feet that is overlaid with a stack at 60.5 feet (60.5 feet is the average height of the stack). This pattern shows multiple nulls or minimas, these arise from ground reflections being out of phase with the direct signals. The presence of ground also produces additional ~6dB antenna gain at vertical angles where the reflection adds in phase with the direct signal.
It can be seen that the antenna stack has increased gain at lower angles. This could help the problem of frequency selective fade. The rationale is; for both tropospheric scatter (tropo) signals as well as 2-Edge signals (if the nearest edge is relatively far away), the major signals arrive at lower angles. Since the troposphere reaches to ~6 miles in height, tropo can have many paths, with some signals arriving at higher angles. For higher angles, the signal must travel greater distances and may be out of phase with the low-angle & earlier signals. The stacked antennas provide some angle-of-arrival discrimination for elevation angles greater than about 1.2 degrees (88.8 degrees on the graph).
To estimate how much rejection may be required to improve a deep signal fade (null). The sum of two signals can be calculated using vector addition. It can be visualized that the sum two equal vectors at, or near, 180 degrees out of phase with respect to each other, add to near zero.
Suppose the desired, or direct, signal had amplitude of +1 Volt, and a multipath signal had equal or lesser value of amplitude, but was 180 degrees out of phase (-1) with the desired signal.
As examples, to the direct signal add decreasing magnitudes of a multipath signal:
+1 added to –1 = 0
+1 added to –0.95 = 0.05 (26 dB below a Voltage of 1 Volt)
+1 added to –0.90 = 0.10 (20 dB below a Voltage of 1 Volt)
In above, dB=20 x [Log10(Volts)]
Changing the multipath signal magnitude from 0.95 to 0.90 results in a ~6 dB improvement in the combination. In terms of dB rejection relative to desired:
Magnitudes of Multipath and dB Rejection
0.95 = 0.45 dB (relative to desired),
0.90 = 0.92 dB (relative to desired)
Difference = -0.47 dB
A multipath reduction of 0.47 dB, relative to desired signal, improved combined signal ~6 dB (26 dB to 20 dB).
As the amplitude of one of the vectors becomes smaller than the other, then the magnitude of their combination rapidly increases. The image below graphically shows the result of combining two signals arriving; one of them 180 degrees out-of-phase with respect to the other.
In the graph, as an example observe the curve at 25 dB. A 25 dB null can occur if the reflected signal has amplitude that is only ~0.5 dB lower than the direct signal. The greater the difference in amplitudes of the two signals, then the shallower the null will be. For example if the multipath signal is about ~10 dB weaker than the direct signal, then the combination may be reduced about 3 dB.
It can be seen that the deep nulls (say 25 dB) are sensitive to small changes in amplitude of the direct and multipath signals. The image below shows sensitivity to multipath signal changes of 0.25 dB relative to the direct signal.
In the chart immediately above, for an initial ~ 25 dB combined cancellation or null, if one could decrease the multipath signal by 0.25 dB, there could be an improvement in the combined signal of ~3 dB. If the initial combined null depth is ~10 dB, this improvement diminishes to ~0.5 dB improvement for a 0.25 dB multipath amplitude reduction. That is more than a 2 for 1 reduction in destructive interference for every 0.25 dB rejection of the out-of phase (multipath) signals. So, it appears that relatively modest amounts of signal discrimination can result is appreciable improvement for the combined (desired) signal.
In this case, the low angles are of most interest. The image below shows an expanded view of the elevation patterns shown in the first image above. The stacked antennas have increased gain, but in order to compare vertical patterns responses, the single antenna and the stacked antennas are shown with both patterns normalized. For convenience, the vertical angle is shown as degrees above the horizon.
It can be seen that for angles above about 2 degrees, the stack has at least 0.5 dB discrimination compared to the single antenna. On average, higher angle-of-arrival signals above 2 degrees are rapidly decreased due to the narrow elevation response of the stack.
Summary
If an appreciable fraction of multipath signals arrive at higher angles than the desired (often most direct path) then a relatively small rejection of multipath can yield an appreciable improvement in multipath null depth. It follows that vertically stacked antennas at sufficient height (AGL) and relatively wide spacing could be advantageous for rejection of multipath signals.
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