The Feedback Rhombic

 

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 “Long-Wire 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, front-to-back 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%

     G-1 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 Home-Brew 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 cut-and-try.

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

Notes, References, and Links

[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.