When I was a kid and became interested in antennas, it bothered me that so much power was dissipated in the terminating resistor in rhombics. I wondered if it could be recycled somehow. I recently took up the task of trying to recycle this power. It seemed that it might be possible to feed back the energy to the input, so that is exactly what I decided to try—and it works.
The model
For modeling purposes I began with a rhombic with the following specifications:
1. Frequency = 3.5 GHz.
2. Wire radius is 0.080 inch perfect conductor.
3. Leg length is 3 wavelengths.
4. Height of the antenna is one wavelength over average ground.
These specifications were chosen to be the same as Cebik’s in “LongWire Antennas Part 4: Rhombic Arrays and Beams” [1]. The antenna analysis program I used is nec based 4nec2, available for free [2]. All simulations were done using 10 segments per half wave.
The simulations
Figure 1 shows a simulation of the antenna described above. The results are in the Table below. The result agrees with Cebik’s simulation [1]. His simulation data can be found in the table below his Fig 8.
Figure 2a shows a similar antenna but with the termination resistance replaced by a transmission line [3] from the output to the input. Since I had no idea what the length and impedance of the transmission line should be, or whether or not the leg length needed to be different from three wavelengths, I let 4nec2’s genetic evolver look for these values. I used the following weights: Gain 100, fronttoback 5, reactance 1. Figure 2b shows the resulting radiation pattern of the antenna it found, and the Table below tabulates the result.
Actually 4nec2 found two solutions. In the second solution the radiation is in the reverse direction. Figure 2c shows the resulting radiation pattern, and the Table below tabulates the result.
Discussion of results
Several things are important to note. First the leg length is approximately 25/8 = 6.25/2 = 3.125 wavelengths long instead of 3 wavelengths, and the transmission line length is about 23/4 = 5.75 wavelengths long. In fact further investigation shows that the leg length w for a feedback rhombic is
w = (lambda/8)(2n + 1) where lambda is the wavelength and n is an integer.
The length t of the transmission line is
t = (lambda/4)(2n – 1).
(Actually the length of the transmission line can be any multiple of a wavelength greater than t)
The total path length is 2w + t = n*lambda. For this antenna, n = 12, so the total path length is 12 wavelengths at 3.5 MHz. One way to see this is to sweep the antenna over a wide frequency range and see performance peaks at n = 12 (frequency = 3.5), n = 13 (frequency = (13/12)*3.5 = 3.79), n = 14 (frequency = (14/12)*3.5 = 4.08), etc.
The long feedback loop necessarily leads to a narrowband antenna. The approximate bandwidths for the n = 12 feedback rhombic are:
SWR 1%
G1 dB 1%
10dB f/b 0.5%.
The impedance of the antenna is high, approximately 2100 ohms for the forward radiating version and 1200 ohms for the backward radiating version. These transmission lines are too high to fabricate directly (see Cebik “Some (Old) Notes on HomeBrew Parallel Transmission Lines” [4]), but can be brought down with a quarter wave transformer. Likewise the feedback impedances are also high, but can also be brought down using quarter wave transformers.
Build it?
If you plan to build this antenna, I have the following suggestions.
1. Use an antenna modeling program so you can model your specific version of this antenna. Scaling and guessing won’t work very well with a narrowband antenna.
2. Use a higher segmentation density than 10 per lambda/2 for your final design. 40 will probably be adequate.
3. Include wire conductivity and transmission line loss in your simulation.
4. Still be prepared for some cutandtry.
The 4nec2 program listings for these antennas can be found here.
http://home.comcast.net/~ross_anderson/PLFBR.htm
If you do make this antenna, you’ll be the first person to do so.
Ross Anderson W1HBQ ross_anderson@comcast.net October 6, 2007
[1] http://www.cebik.com/wire/lw4.html
[2] http://home.ict.nl/~arivoors/
[3] Cebik discusses modeling transmission lines in “3. Transmission Lines as Lines” http://www.cebik.com/load/loadtl3.html
[4] http://www.cebik.com/trans/par.html
My homepage “Ross’s Antennas”, with links to my other pages, is http://home.comcast.net/~ross_anderson
Table 
Gain(dBi) 
f/b(dB) 
Feedback Impedance 
Feedpoint Impedance 
Cebik Model 
16.03 
41.2 

864 + j25 ohms 
Forward FB Rhombic 
19.88 
33.2 
1345 ohms 
2152 – j116 
Reverse FB Rhombic 
19.88 
38.5 
730 
1183 + j69 
Figure 1 Rhombic with 3 wavelength legs and 850 ohm terminating resistor.
Figure 2a Feedback Rhombic with 3 1/8 wavelength legs.
Figure 2b Forward radiating Feedback Rhombic with 3 1/8 wavelength legs.
Figure 2c Reverse radiating Feedback Rhombic with 3 1/8 wavelength legs.