The half-lambda T-antenna is a specific implementation of the T-antenna. The overall view of the antenna is shown in the picture below. The picture contains formulas as well.
The quick modeling gave the same result as the previously described T-antenna. The top hat is a simple capacitive load allowing us to drastically shorten the overall height of the antenna - it can be lowered as much as to 0.1 lambdas. We all know that shortening of the transmitting antennas lowers their radiation resistance. The very short antennas can have the radiation resistance as low as 1 Ohm and even less. This makes the antenna very inefficient and requires the output power to be increased significantly.
Below is some number of screenshots of the modeling application. I tried to design the model of the T-antenna for the 20 meters band. According to the formulas above, the 2L element should be 10.2 meters, the L element - 5.1 meters.
The calculation has shown the very high active and reactive resistances.
I expected this and was not very curious. The next step is to add the coil at the feed point. This had to increase the electrical length of the antenna which should lead to lowering the reactance. Short playing with the table of loads has brought the more or less good result - the reactive part of the antenna reactance was moved very close to zero. In this particular case, the coil was only 275 uH.
The SWR remains very high because the active resistance does not match the 50 Ohms cable.
Changing the R to 1200 has brought the excellent result - the SWR become perfect!
To sum up. On the higher bands, the antenna can be as much effective as the corresponding quarter-wave monopole, yet shorten. On the lower bands, the T-antenna is a drastically shortened version of the full-size quarter-wave monopole, therefore it is much less effective. The reason of usage of this antenna on the lower bands is the very long wavelength, which makes the creation of the quarter-wave monopoles almost unmanageable task. For example, you can build the antenna for the Top Band and have it as high as 10 meters. The capacitive hat is 51 meters long. Not so small, but folding the wires of the hat should allow you to build the antenna even on the small private garden in the center of the city. For these dimensions, the coil should be changed by the 5000 pF capacitor. The radiation resistance is only 6 Ohms. Although you could match the active resistance to the required 50 Ohms, the efficiency of the antenna will be quite low. Also, the very low height of the antenna makes it very narrow. The 10 meters high Top Band antenna has SWR range by 2:1 only 24 kHz.
Below are two models. The first is for 20 meters, the second is for 160 meters. Both models are designed for the real bad ground. The 160 meters band antenna feed point is located directly on the ground, whereas 20 meters band antenna is raised up by 2 meters.
20 meters
-----------
*
14.15
***Wires***
3
0.0, 0.0, 0.0, 0.0, 0.0, 5.1, 8.000e-04, -1
0.0, 0.0, 5.1, 5.1, 0.0, 5.1, 8.000e-04, -1
0.0, 0.0, 5.1, -5.1, 0.0, 5.1, 8.000e-04, -1
***Source***
1, 0
w1b, 0.0, 1.0
***Load***
1, 1
w1b, 0, 275.7, 0.0, 0.0
***Segmentation***
800, 80, 2.0, 2
***G/H/M/R/AzEl/X***
2, 2.0, 0, 50.0, 120, 60, 0.0
160 meters
-----------
*
1.825
***Wires***
3
0.0, 0.0, 0.0, 0.0, 0.0, 10.0, 8.000e-04, -1
0.0, 0.0, 10.0, 26.0, 0.0, 10.0, 8.000e-04, -1
0.0, 0.0, 10.0, -25.0, 0.0, 10.0, 8.000e-04, -1
***Source***
1, 0
w1b, 0.0, 1.0
***Load***
1, 1
w1b, 0, 0.0, 5000.0, 0.0
***Segmentation***
800, 80, 2.0, 2
***G/H/M/R/AzEl/X***
2, 0.0, 0, 6.0, 120, 60, 0.0
The quick modeling gave the same result as the previously described T-antenna. The top hat is a simple capacitive load allowing us to drastically shorten the overall height of the antenna - it can be lowered as much as to 0.1 lambdas. We all know that shortening of the transmitting antennas lowers their radiation resistance. The very short antennas can have the radiation resistance as low as 1 Ohm and even less. This makes the antenna very inefficient and requires the output power to be increased significantly.
Below is some number of screenshots of the modeling application. I tried to design the model of the T-antenna for the 20 meters band. According to the formulas above, the 2L element should be 10.2 meters, the L element - 5.1 meters.
The calculation has shown the very high active and reactive resistances.
I expected this and was not very curious. The next step is to add the coil at the feed point. This had to increase the electrical length of the antenna which should lead to lowering the reactance. Short playing with the table of loads has brought the more or less good result - the reactive part of the antenna reactance was moved very close to zero. In this particular case, the coil was only 275 uH.
The SWR remains very high because the active resistance does not match the 50 Ohms cable.
Changing the R to 1200 has brought the excellent result - the SWR become perfect!
The radiation pattern is nice - it is very similar to the full-size quarter-wave monopole.
The antenna is quite wide-band. The SWR by 2:1 is about 470 kHz.
To sum up. On the higher bands, the antenna can be as much effective as the corresponding quarter-wave monopole, yet shorten. On the lower bands, the T-antenna is a drastically shortened version of the full-size quarter-wave monopole, therefore it is much less effective. The reason of usage of this antenna on the lower bands is the very long wavelength, which makes the creation of the quarter-wave monopoles almost unmanageable task. For example, you can build the antenna for the Top Band and have it as high as 10 meters. The capacitive hat is 51 meters long. Not so small, but folding the wires of the hat should allow you to build the antenna even on the small private garden in the center of the city. For these dimensions, the coil should be changed by the 5000 pF capacitor. The radiation resistance is only 6 Ohms. Although you could match the active resistance to the required 50 Ohms, the efficiency of the antenna will be quite low. Also, the very low height of the antenna makes it very narrow. The 10 meters high Top Band antenna has SWR range by 2:1 only 24 kHz.
Below are two models. The first is for 20 meters, the second is for 160 meters. Both models are designed for the real bad ground. The 160 meters band antenna feed point is located directly on the ground, whereas 20 meters band antenna is raised up by 2 meters.
20 meters
-----------
*
14.15
***Wires***
3
0.0, 0.0, 0.0, 0.0, 0.0, 5.1, 8.000e-04, -1
0.0, 0.0, 5.1, 5.1, 0.0, 5.1, 8.000e-04, -1
0.0, 0.0, 5.1, -5.1, 0.0, 5.1, 8.000e-04, -1
***Source***
1, 0
w1b, 0.0, 1.0
***Load***
1, 1
w1b, 0, 275.7, 0.0, 0.0
***Segmentation***
800, 80, 2.0, 2
***G/H/M/R/AzEl/X***
2, 2.0, 0, 50.0, 120, 60, 0.0
160 meters
-----------
*
1.825
***Wires***
3
0.0, 0.0, 0.0, 0.0, 0.0, 10.0, 8.000e-04, -1
0.0, 0.0, 10.0, 26.0, 0.0, 10.0, 8.000e-04, -1
0.0, 0.0, 10.0, -25.0, 0.0, 10.0, 8.000e-04, -1
***Source***
1, 0
w1b, 0.0, 1.0
***Load***
1, 1
w1b, 0, 0.0, 5000.0, 0.0
***Segmentation***
800, 80, 2.0, 2
***G/H/M/R/AzEl/X***
2, 0.0, 0, 6.0, 120, 60, 0.0
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