## The Half Rhombic

#### Directional

The directional characteristics of the half rhombic antenna are derived by the addition of the two horizontal lobes as shown in **Figure 1.** Both of the two vertical lobes are out of phase with the other and thus, cancel out each other. This directional characteristic is made possible by the termination resistor that is located at the far end of the antenna.

Again, as in the case of the Beverage Antenna (* antenneX*, June 1989) signals that are flowing from the equipment end toward the termination are absorbed, preventing any energy that is not radiatedfrom being reflected back along the antenna. As a result of using the termination resistor, the lobes, as in

**Figure 1**are being radiated back towards the transmitter and absorbed, resulting in a uni-directional pattern. Conversely, by not terminating the far end, a bi-directional pattern is generated. This is shown in

**Figure 2**.

#### Too Large for Most Bands

For the most part, the half rhombic would be too large to be used on most of the ham bands because the supporting mast would be too tall. For an example, a half rhombic for 3.5 to 18.5 MHz would have a linear dimension of 620 feet (189m) and an apex height of 225 feet (69m). That is a bit much since the mast has to be made of a non-conductor such as wood, and the guying system also has to be made of a non-conductor. A very expensive undertaking.

#### AIM at Repeaters

Where the half rhombic can come into good use is in the 28-54 MHz range and higher as it can be aimed at a particular area and give good coverage in that area. Another use applies to someone located a good distance from a specific area populated with a number of repeaters. By aiming a half rhombic at the repeater area, coverage can be maintained without using a beam. It would be a simple matter to aim several antennas at specific areas and switch them. On two meters an enormous amount of gain can be obtained with this antenna without requiring so much real estate. One of these antennas could be put on the roof of most houses and the expense would not be too great. Of course, the uni-directional pattern must be directed at the area of interest.

#### Design Information

It is desirable to make the legs of the half rhombic as long as possible in order to obtain maximum gain and directivity. However, in the real world of houses, yards and natural obstructions, this is not always possible. For satisfactory performance, each leg of a half rhombic must be at least one wavelength at the lowest frequency of operation. In general practice, a leg length of a minimum of two wavelengths is generally used, and on VHF and UHF, this would not be hard to manage. Yes, this wire antenna can be used on VHF and UHF. Again, the half rhombic is limited to a size that will fit on the property and still be aimed at the area of interest.

#### Covers a 4:1 Range

The frequency range of the half rhombic enables it to cover a 4 to 1 range with ease. As an example, a half rhombic designed for 10 MHz is capable of operating as high as 40 MHz. Depending on how much change in gain and directivity can be tolerated, the frequency range can be extended a lot farther. This would enable you to use one of these antennas on 10/6 and 2 meters with suitable changes in matching networks.

#### Tilt Angle

Once you have decided how long the leg length should be, the next thing is to figure out the tilt angle for the leg length to be used. The tilt angle is going to be a compromise between two conditions:

- The tilt angle must have a value so the lobes of maximum radiation from both legs are in exactly the same direction. This is necessary to allow the two forward lobes to combine and produce the uni-directional pattern. This value is 90 degrees less than the wave angle.
- The tilt angle must have a value so the radiation in the forward lobe of one leg can combine in phase with the radiation of the forward lobe from the other leg in order to create the uni-directional pattern. This usually means that the projection of either leg of the half rhombic is going to be a half wavelength shorter than the actual length of the leg. Therefore, the tilt angle wil be smaller than the original value. In actual practice the tilt angle will be a compromise between the two values.

Here is a table that shows the value of tilt angles for use with various leg lengths. Antenna length is expressed in wavelengths. To convert these lengths to feet this formula can be used:

**(1)**

## Length (feet) = 492(H-0.05)/F(MHz)

Where **H** is the number of half-wavelengths

An easier formula is this one:

**(2)**

## Length (feet) =984(N-0.025)/F(MHz)

Where **N** is the number of full wavelengths on the antenna.

Since the length is not especially critical, and there is not very much end effect on long antennas, the 0.025 factor can be dropped from the formula. If you need the value of the angle between the two legs of the half rhombic, just double the tilt angle for the angle.

**Antenna Length in Wavelengths**

1

2

3

4

6

8

10

12

**Tilt Angle in Degrees**

30

50

57

62

67

70

71

73

Once the tilt angle and the leg lengths are known, then the height of the apex of the antenna and the length of the counterpoise can be calculated if you are using a counterpoise.

In **Figure 3**, a right triangle is formed by one of the legs of the antenna (L) and the height of the apex above ground (H) and 1/2 the length of the counterpoise (1/2C). The tilt angle (T) is one of the angles in the right triangle. The ratio of the height to the leg length is equal to the cosine of the tilt angle (cosT). Now assume the leg is two wavelengths long and the tilt angle is 50 degrees using values from the table.

The following relationships can be written:

**(3)**

**(4)**

**(5)**

## cos T = H/L

## cos 50° .= H/2

## .6427 = H/2

H = 1.286

So, rounding off of the answer gives 1.3 wavelengths above ground for the apex. To convert this to feet, a simplified version of Formula 2 is used:

**(6)**

## Length (feet) = 984N/F(MHz)

Where **N** is the number of full wavelengths.

The ratio between one half of the length of the counterpoise (1/2) and the leg length **(L)** is equal to the sine of the tilt angle **(T, sine T)**. This allows the counterpoise length to be calculated easily as shown in the following example:

**(7)**

## sineT = 1/2C/L

**(8)**

## sine 50 = 1/2C/2

**(9)**

## 0.766 =1/2C/2

1/2C = 1.532 or 1.5

C = 1.5*2 = 3

So, the counterpoise needs to be three wavelengths long.

The following table will give the height of the apex and counterpoise lengths needed in terms of wavelengths at the operating frequency.

**Leg Lengths1234681012**

**Apex Heights0.0871.31.61.92.32.73.33.5**

**Counterpoise Lengths135711151923**

A practical antenna for 10 meters with a leg length of six wavelengths on 29 MHz would have a leg length of 193.5 feet (59m), an apex height of 74 feet (22.6m), an apex angle of 67 degrees and a counterpoise length of 355 feet (108.2m). This would require a tall support and some acreage of land. It would be 10 wavelengths for a leg on 50 MHz. The apex height would be a little above optimum at 3.96 wavelengths, but should bum a path to the area of interest.

#### Experimenters’ Delight

On two meters the leg length would be 29.76 wavelengths, with an apex height of nearly 10.95 wavelengths. There would have to be a matching network at the feed point to match the antenna impedance to the 50 ohm output of the transmitters. The gain of this antenna would be very high on 10 meters, and go up as the frequency does. Gain figures for a military half rhombic with a leg length of a 1 1/2 wavelengths on 30 MHz with a 30-foot (9.1m) mast are 4-5 dBd at 30 MHz and nearly 10 dBd at 70 MHz. So you can see that a monster with a leg length of six wavelengths would have a jot more than that. For a ham living in areas of tall trees, such as the pine forests of Georgia and other similar areas, this type of antenna would be ideal.

#### The Non-Terminated Half Rhombic

The half rhombic can also be used as a non-terminated antenna, as shown in **Figure 2**, by removing the terminating resistor at the far end. This changes the antenna characteristics in the same manner as removing the terminating resistors on a terminated rhombic. The antenna impedance varies over the frequency range of interest and all of the other characteristics also change as well.

The gain is cut in half since the pattern becomes bi-directional, with equal division of transmitted power between the front and rear of the antenna as the antenna becomes bi-directional along the axis of the antenna Matching becomes a problem because the antenna will have a varying VSWR over the useable range. The range of frequency coverage will be reduced too and the antenna radiation pattern will vary causing the reception of undesired noise and interference.

These antennas are capable of doing a fine job on the higher frequency ham bands. A half rhombic for 10 meters with two wavelengths on a leg will need only 132 feet (40.2m) of antenna wire, and an apex height of 43 feet (13.1m), with a tilt angle of 50 degrees. If you decide to use a counterpoise, the wire length will be 99 feet (30.2m). This should fit on most residential lots leaving only the problem of aiming the antenna in the correct direction.

#### Good Project for Wooded Areas

As a possible project for someone in a heavily wooded area, how about an antenna farm that consists of half rhombics hung from trees? The counterpoise must be kept high enough where it can’t be snagged by the antlers of a passing moose or elk. You could have an antenna farm consisting of half rhombics aimed in all desired directions. Such a configuration would require much less maintenance and money than a beam.

If you consider that a 14 MHz half rhombic with a leg length of two wavelengths can cover all of the bands to 10 meters without gaps in frequency coverage and with more gain than a tri-bander, things really get interesting. Such an antenna would have an apex height of about 86 feet (26.2m), a tilt angle of 50 degrees and a counterpoise length of 198 feet (60.4m). Hanging several of these antennas from tall trees, aimed where you want them, the system should put out a very healthy signal on all bands from 20 meters to 10 meters, without the expense of a beam and a tower. By switching antennas, it would be possible to have excellent coverage of all the areas desired.

Originally posted on the AntennaX Online Magazine by Richard Morrow, K5CNF

*Last Updated : 27h April 2024*