E9A02 (D)
What antenna has no gain in any direction?
A. Quarter-wave vertical
B. Yagi
C. Half-wave dipole
D. Isotropic antenna

E9: ANTENNAS AND TRANSMISSION LINES

E9A Basic antenna parameters: radiation resistance, gain, beamwidth, efficiency, beamwidth; effective radiated power, polarization

Antenna gain is one of the most misunderstood topics in amateur radio. There are several reasons for this, including:

  • Antennas dont really have gain in the same way that an amplifier has gain. When you use a linear amplifier, you get more power out than you put in. Since transmitting antennas are passive devices, there’s no way to get more power out than you put in.
  • It’s not easy to measure antenna gain. There is no antenna gain meter that you can simply hook up to an antenna to measure its gain.

So, what is meant by antenna gain? Antenna gain is the ratio of the radiated signal strength of an antenna in the direction of maximum radiation to that of a reference antenna. (E9A07) What this means is that when you talk about antenna gain, you have to know what kind of antenna you’re comparing it to.

When talking about antenna gain, antenna engineers often refer to the “isotropic antenna.” An isotropic antenna is a theoretical antenna used as a reference for antenna gain. (E9A01) An isotropic antenna is an antenna that has no gain in any direction. (E9A02) That is to say it radiates the power input to it equally well in all directions.

Let’s take a look at a practical example. The 1/2-wavelength dipole antenna is the most basic amateur radio antenna. The dipole actually has some gain over isotropic antenna. The reason for this is that it is directional. The signal strength transmitted broadside to the antenna will be greater than the signal strength transmitted off the ends of the antenna.

The gain of a 1/2-wavelength dipole in free space compared to an isotropic antenna is 2.15 dB.

Sometimes, you’ll see this value as 2.15 dBi, where dBi denotes that an isotropic antenna is being used for this comparison.

Since the isotropic antenna is a theoretical antenna, some think it’s better to compare an antenna to a dipole antenna. An antenna will have a gain 3.85 dB compared to a 1/2-wavelength dipole when it has 6 dB gain over an isotropic antenna. (E9A12) You obtain this value by simply subtracting 2.15 dB from the 6 dB figure: Gain over a dipole = gain over an isotropic antenna - 2.15 dB = 6 dBi - 2.15 dBi = 3.85 dBd

Sometimes, the gain over a dipole is denoted as dBd.

Similarly, an antenna has a gain of 9.85 dB compared to a 1/2-wavelength dipole when it has 12 dB gain over an isotropic antenna. (E9A13):  Gain over a dipole = gain over an isotropic antenna - 2.15 dB = 12 dBi - 2.15 dBi = 9.85 dBd

Antennas that are said to have gain are really focusing the energy that is input to them. The higher the gain, the narrower the focus, or beamwidth. The beamwidth of an antenna decreases as the gain is increased. (E9A06)

Effective radiated power

When you use an antenna that has gain, you are increasing the effectiveness of the power input to it, at least in the direction the antenna is pointing. The term that describes station output, taking into account all gains and losses is effective radiated power. (E9A18) The effective radiated power is not just the input power times the gain of the antenna. You also have to take into account losses in other parts of the antenna system.

This is especially true for VHF and UHF repeater systems, where losses in the feedline, duplexer, and circulator can be significant. The power that reaches the antenna may be substantially lower than the power output of the transmitter.

For example, the effective radiated power relative to a dipole of a repeater station with 150 watts transmitter power output, 2 dB feed line loss, 2.2 dB duplexer loss, and 7 dBd antenna gain is 286 watts. (E9A15) To calculate the answer, you have to first subtract the losses from the gain, as expressed in dB to get the total gain of the system:

total system gain = 7 dB – 2 dB – 2.2 dB = 2.8 dB.

Now, recall that 3 dB corresponds to a power ration of 2:1, as shown in the table below. 2.8 dB would then be slight less than that. In fact, 2.8dB corresponds to a power ratio of approximately 1.905, so the effective radiated power is the transmitter output power times the total system gain:

effective radiated power = 150 W x 1.905 = 268 W.

Let's look at another example. The effective radiated power relative to a dipole of a repeater station with 200 watts transmitter power output, 4 dB feed line loss, 3.2 dB duplexer loss, 0.8 dB circulator loss, and 10 dBd antenna gain is 317 watts. (E9A16). In this case, the total gain of the system is 10 dB – 4 dB – 3.2 dB – 0.8 dB, or 2.0 dB. 2.0 dB corresponds to a power ratio of approximately 1.585, and the effective radiated power equals 200 W × 1.585 = 317 W. In this system, high feedline and duplexer losses are almost completely negating the benefit of using such a high gain antenna.

Finally, the effective radiated power of a repeater station with 200 watts transmitter power output, 2 dB feed line loss, 2.8 dB duplexer loss, 1.2 dB circulator loss, and 7 dBi antenna gain is 252 watts.

(E9A17) In this example, the total gain of the system is 7 dB – 2 dB – 2.8 dB – 1.2 dB, or 1.0 dB. 1.0 dB corresponds to a power ratio of approximately 1.26, and the effective radiated power equals 200 W

× 1.26 = 252 W.

Feedpoint impedance, antenna efficiency, frequency range, beamwidth

Other antenna parameters are also important, of course. One of the most basic antenna parameters is the feedpoint impedance. Why would one need to know the feed point impedance of an antenna? To match impedances in order to minimize standing wave ratio on the transmission line. (E9A03) The reason that it’s important to minimize the standing wave ratio, or SWR, is that if you’re using coaxial cables, minimizing the SWR will also help you minimize losses. If you minimize losses, you’ll radiate more signal.

Many factors may affect the feed point impedance of an antenna, including antenna height, conductor length/diameter ratio and location of nearby conductive objects. (E9A04)

For example, we say that the feedpoint impedance of a half-wavelength, dipole antenna is 72 Ω, but that’s only really true if the antenna is in free space. When it’s closer to the ground than a quarter wavelength, then the impedance will be different. That’s why you have to tune the antenna when you install it.

Radiation resistance

Another antenna parameter that’s frequently discussed is radiation resistance. The radiation resistance of an antenna is the value of a resistance that would dissipate the same amount of power as that radiated from an antenna. (E9A14) Radiation resistance plus ohmic resistance is included in the total resistance of an antenna system. (E9A05)

If you know the radiation resistance and the ohmic resistance of an antenna, you can calculate its efficiency. You calculate antenna efficiency with the formula (radiation resistance / total resistance) x 100 percent. (E9A09)

Vertical antennas are sometimes criticized as being inefficient antennas. Soil conductivity is one factor that determines ground losses for a ground-mounted vertical antenna operating in the 3-30 MHz range. (E9A11) If soil conductivity is poor, ohmic resistance will be high, and the antenna's efficiency will be low. One way to improve the efficiency of a ground-mounted quarter-wave vertical antenna is to install a good radial system. (E9A10)

The frequency range over which an antenna satisfies a performance requirement is called antenna bandwidth. (E9A08) Normally, the performance requirement is an SWR of 2:1 or less. In fact, you’ll sometimes hear this parameter referred to as the 2:1 SWR bandwidth.

 

BY KB6NU DAN ROMANCHIK

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