## Antenna Scaling

Electromagnetic waves have a characteristic length which is related to their frequency, as discussed in a previous section. Since antennas are made to radiate and receive electromagnetic energy, it can be shown that their perfomance depends not on their physical size, but on their dimensions relative to the wavelength.
One fundamental implication of this is that antennas can be scaled from one frequency to another by expressing their dimensions in terms of wavelengths. Thus if we have an antenna design for one frequency, it is easy to convert the design to any other frequency simply by making the antenna the same size in terms of wavelength.

It should be noted that for the procedure to work exactly, all dimensions must be scaled. That includes wire or conductor diameters and height above ground, as well as the lengths of any elements or wires. Normally the lengths are easily scaled, but scaling the height above ground and the wire diameters is difficult in practice. Fortunately the effect of the wire diameter on performance is normally not overly important, as we will see in later sections. The height above ground, however, can have an important effect on the radiation pattern. Generally speaking, scaling an antenna to a lower frequency (ie. longer wavelength) will make the antenna larger and higher above the ground. If we cannot actually raise the antenna, the lower height will probably decrease performance. Conversely, scaling to a higher frequency generally means smaller antennas and we can lower the antenna and still maintain the same performance.
Since we can scale any antenna design to any frequency, it may be much easier to experiment and prototype antennas at very high frequencies, which correspond to short wavelengths and smaller antenna structures. It is much easier to try an antenna designed for the 2 meter band, where a wavelength is less than 7 feet, rather than the 80 meter band, where the wavelength is more like 270 feet.
Scaling Procedure. There often seems to be a lot of confusion over how to actually go about scaling an antenna to a different frequency. Actually the procedure is very straight forward and can be summarized in the following steps:

• Calculate the wavelength WLold of the design frequency.

• Calculate the wavelength WLnew of the new frequency.

• Calculate the length scale factor by dividing WLnew by WLoldSF = WLnew / WLold

• Note: Since wavelength is inversely proportional to frequency, the scale factor can also be calculated directly from SF = Fold / Fnew

• Multiply every dimension in the original design by the scale factor SF to determine the actual antenna dimensions at the new frequency. Xnew = Xold * SF

Let's try a simple example to illustrate the procedure. Assume we have a quarter wave ground plane antenna that works great for the 2 meter band (146 MHz), so we want to try the same antenna on 80 meters (3.6 MHz). The 2 meter ground plane antenna has the following dimensions:

Antenna Design for 2 meters
ElementSizeDescription
Vertical Element19.5 inchesLength
Vertical Element0.5 inchesDiameter
Height10 feetAbove ground

We proceed by first calculating the wavelength of the original antenna at 146 MHz and determine that WLold = 984 / 146 = 6.7397 feet. Similarly we can calculate the wavelength at the new frequency WLnew = 984 / 3.6 = 273.3333 feet. The scale factor is therefore SF = 273.3333 / 6.7397 = 40.56. Multiplying all of the dimensions by the scale factor gives the following antenna dimensions for our 80 meter version:

Antenna Scaled for 80 meters
ElementSizeDescription
Vertical Element790.84 inches = 65.9 feetLength
Vertical Element20.28 inches = 1.7 feetDiameter