Practical_Antenna_Handbook_0071639586

C h a p t e r 1 2 : T h e Y a g i - U d a B e a m A n t e n n a 283
is 33 ft 3½ in. When the wire is replaced with 1-in aluminum tubing, the dipole resonates
at 33 ft 2½ in. The difference, 1 in, is probably inconsequential to the overall operation
of the dipole.
Example 12.2 A three-element Yagi of a certain design and having elements of 1-in
aluminum tubing meets the following specifications at 14.1 MHz:
• Forward gain = 8.25 dBi
• Feedpoint impedance = 13.8 + j0 Ω
• Front-to-back ratio = 31 dB
• Front-to-side ratio = 25 dB
With the use of a simple 4:1 balun, the input impedance becomes 55 Ω, and the 2:1
VSWR bandwidth using 50-Ω coaxial cable is 220 kHz.
Now suppose we replace all the aluminum elements with #12 copper wire of exactly
the same length. The performance of the resulting beam at 14.1 MHz becomes:
• Forward gain = 7.5 dBi
• Feedpoint impedance = 24.2 – j17.0 Ω
• Front-to-back ratio = 16.3 dB
• Front-to-side ratio = 16.3 dB
In short, every important performance parameter of our three-element beam has been
compromised by blindly ignoring the effect of element diameter on the design
dimensions. And simply to obtain a reasonable SWR at the design frequency, we must
switch to a 2:1 balun to obtain a transformed input impedance of 48.4 – j34 Ω. This
corresponds to an SWR of 1.9:1, but it is the best we will see unless we adjust the driven
element for zero reactance at 14.1 MHz.
If we launch a more thorough attempt to bring the wire beam up to the level of
performance of the original beam, we find we can get closer, but we’re not able to
perfectly equal the original. For comparable front-to-back (F/B) and front-to-side (F/S)
ratios and a feedpoint impedance that is a good match for the 4:1 balun, we can obtain
about 8 dBi forward gain. But the resulting 2:1 SWR bandwidth is only 125 kHz—one
consequence of making the element diameter much smaller. In the process, we have
had to lengthen the director by 3 in and slightly shorten the reflector for this particular
design.
Element diameter comes into play another way, as well. Once a Yagi design has
been developed for one frequency or band, that same design can be “translated” to
other frequencies by scaling all the important dimensions—including element diameter—in
accordance with the change in wavelength. Unfortunately, in the process of scaling
a good design to another center frequency, the resulting element diameter(s) may be