Electronics Demystified, 2nd edition

Stan Gibilisco

Explanations for Quiz Answers in Chapter 12

1. If we place two half-wave dipoles parallel to each other and feed them 90º (1/4 of a cycle) out of phase, we'll get an optimized unidirectional radiation and response pattern. Engineers call this type of system a unidirectional end-fire array. Choice C represents the best answer here. Technically, we'll "sort of" get a unidirectional pattern if we follow the instructions in choice A or choice B, but the antenna won't work at its best. If we build the system described at D, we won't get a unidirectional pattern. Referring to the chapter text, it's clear that we should use the design described in choice C.

2. To determine the efficiency Eff_% of an antenna (in percent) when we know the radiation resistance R_R and the loss resistance R_L (both in ohms), we can use the formula

Eff_% = 100 R_R / (R_R + R_L)

In this case, R_R = 73.5 ohms and R_L = 26.5 ohms, so

Eff_% = 100 x 73.5 / (73.5 + 26.5)
= 7350 / 100
= 73.5%

The correct choice is B.

3. Let's recalculate the efficiency with the new radiation-resistance value R_R = 735 ohms. We have

Eff_% = 100 R_R / (R_R + R_L)
= 100 x 735 / (735 + 26.5)
= 73,500 / 761.5
= 96.5%

The correct choice is D.

4. When a radio-frequency (RF) transmission line has a standing-wave ratio (SWR) of 1:1, we observe the same RF voltage-to-current ratio at every point along the line; this ratio equals the characteristic impedance of the line. The only way that we can guarantee this ideal situation is to make certain that the antenna's radiation resistance equals the characteristic impedance of the line, and also that the antenna has no net reactance at the point where the line feeds it. We must fulfill all three requirements stated in the choices A, B, and C. (Choice C is redundant in this context; it will inevitably turn out true if both A and B hold true.) The correct choice is D, "More than one of the above."

5. We can improve the directivity of a dish antenna by increasing the operating frequency, feeding it with a horn antenna pointed back toward the paraboloidal reflector, or using a reflector with a larger diameter. Of course, for these modifications to yield good results, we must design the feed dipole or horn for the correct frequency, and also ensure that the reflector has the correct paraboloidal shape. We must also keep the feed dipole or horn at the focal point of the paraboloidal reflector. The correct choice is D, "Any or all of the above."

6. The conductor not connected directly to the feed point constitutes a parasitic element. The conductor connected to the feed line forms the driven element. In this case, the driven element measures a few percent longer than the parasitic element, so we know that the parasitic element is meant to work as a director. The answer is B.

7. If the driven element in a Yagi is meant to function as a half-wave radiator and comprises metal tubing, we can assume that the velocity factor equals 0.90. We can approximate the optimum frequency f_MHz (in megahertz) for a half-wave open dipole measuring 4.81 meters from end to end as

f_MHz = 150 x 0.90 / 4.81
= 135 / 4.81
= 28.1 MHz

The correct choice is A.

Do you suspect that the foregoing calculation is an oversimplification, because the exact length of the half-wave driven element in a two-element Yagi must differ slightly from the length of an open dipole without the presence of a parasitic element? If so, you're right! However, the difference won't amount to much. In any case, none of the other choices come anywhere near the correct value. If we operate the antenna described here at 28.1 MHz, it should work pretty well.

8. To calculate the free-space wavelength of a wireless signal in meters when we know its frequency in megahertz, we can divide 300 by the frequency. In this case, that gives us 300 / 24.0 = 12.5 MHz. The correct choice is A.

9. When we want to build a half-wave dipole antenna using ordinary wire, we can divide 467 by the intended frequency (in megahertz) to obtain the optimum end-to-end length L_ft (in feet). In this case, we want to construct the dipole for use at 3.535 MHz, so

L_ft = 467 / 3.535
= 132 ft

The correct choice is C.

10. A full-wavelength loop antenna radiates and receives the best in directions perpendicular to the plane containing the loop. The correct choice is B. Of course, for this question and answer to make any sense, we must assume that the loop lies entirely in a single plane, and isn't "twisted" into some weird or complicated three-dimensional shape!