CRAC Class B (2025) — Questions 661–670
U0865. To make a half-wave dipole antenna operating at frequency f (in MHz). The length of each element arm (in meters) is approximately:
制作工作频率为f（单位：兆赫）的半波长偶极天线。每边振子 的长度（单位：米）约为：
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Each arm of a half-wave dipole is a quarter wavelength. With λ = 300/f (m) and the ~0.95 shortening factor, one arm ≈ (300/f)/4 × 0.95 ≈ 71.3/f meters (A). 48.8/f (B) is the 1/4-wave- in-coax length (with velocity factor); 142.6/f (C) is the full dipole; 150/f (D) is the free-space full wavelength.
U0866. The propagation speed of radio waves in a medium is lower than the speed of light; its ratio to the speed of light is called the "velocity factor", the reciprocal of the square root of the dielectric constant. Polyethylene dielectric coaxial cable is the most commonly used. Its velocity factor is approximately:
电波在介质中的传播速度低于光速，其与光速的比值称为"速度 因子"，是介电常数平方根的倒数。聚乙烯介质同轴电缆我们最 为常用。其速度因子约为：
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Velocity factor = 1/√(εr) and is always ≤ 1. Solid polyethylene has εr ≈ 2.3, giving VF ≈ 0.66; the question's accepted value is about 0.65 (A). Values above 1 (B, C) are impossible for a passive dielectric, and 1.0006 (D) is essentially air.
U0867. To build a certain phased antenna array operating at frequency f (in MHz), a coaxial cable of 1/4 wavelength is needed; its approximate length (in meters) should be:
制作工作频率为f（单位：兆赫兹）的某相控天线阵列需要长度 为1/4波长的同轴电缆，大致长度（单位：米）应当为：
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Quarter wavelength in coax = (75/f) × velocity factor. For solid polyethylene VF ≈ 0.65, that is 75 × 0.65 / f ≈ 48.8/f meters (A). 75/f (C) is the free-space quarter wave; 71.3/f (D) is a dipole arm; 149.8/f (B) is a half wave in coax. The coax quarter-wave with VF gives 48.8/f.
U0868. If a dipole antenna is to have low input impedance when resonant at the operating frequency, the total length of the elements can be:
如需偶极天线谐振于工作频率之时具有低输入阻抗，振子的总 长度可以是：
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A center-fed dipole has a low feed-point impedance at resonance when its total length is an odd multiple of λ/2 (λ/2, 3λ/2, …) (A). At even multiples (full wavelengths, λ, 2λ) the center becomes a current node and the impedance is very high (C is wrong). Option B includes even multiples, so it is not specifically "low impedance".
U0869. The necessary and sufficient condition for a dipole antenna to resonate at the desired operating frequency is:
偶极天线谐振于所需工作频率的充分和必要条件是：
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A dipole resonates whenever its total (both arms) electrical length equals n·λ/2 (n = 1, 2, 3, …) — this covers half-wave, full-wave, 3/2-wave, etc. (A). Restricting to odd multiples only (C) or to whole wavelengths (D) is too narrow; 1/4 multiples (B) describes a monopole over ground, not a dipole.
U0870. Which of the following resonant dipole antennas has peak gain in the direction perpendicular to the element?
下列哪种谐振偶极天线在垂直于振子的方向上具有峰值增益：
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A half-wave dipole (element = λ/2) radiates maximum field broadside — perpendicular to the element (A). A full-wave (λ, =2 half-waves) dipole develops a figure-8 with nulls broadside and peaks off the ends; the 3/2-wave (D) is also end- fired/lobed, not broadside-peaked. 1/8 and 1/4 wavelengths (B, C) are electrically short and inefficient, with no clean broadside peak.
U0871. The method to raise a dipole antenna's resonant frequency is:
提高偶极天线谐振频率的方法是：
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Resonant frequency is inversely proportional to electrical length. Shortening the elements lowers the electrical length and raises the resonant frequency (A). Lengthening (C) lowers it; adding a loading coil (B) or capacitance hat (D) adds electrical length and lowers the frequency.
U0872. Between the antenna and feed line a component commonly called a "balun" is often inserted. The origin of "balun" is:
在天线和馈线之间常会接入一个俗称"巴伦（BALUN）"的部 件。"巴伦"的由来是：
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"Balun" is a portmanteau of BALanced and UNbalanced (A). It is not a person's name (B, C) or a brand (D).
U0873. Between the antenna and feed line a component commonly called a "balun" is often inserted. Its main function is:
在天线和馈线之间常会接入一个俗称"巴伦（BALUN）"的部 件。它的主要功能是：
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A balun's job is to interface a balanced load (e.g., a dipole, both legs symmetric) with an unbalanced line (coax, one conductor grounded), transferring RF while choking common- mode/parasitic currents (A). It is not primarily an automatic matcher (B), bandwidth extender (C), or SWR reducer per se (D) — though a proper balun can improve the measured SWR by eliminating feed-line radiation.
U0874. A dipole whose two arms each have an electrical length of 1/4 wavelength, with the center broken and fed via a balun, measures resonant frequency f and input impedance Z. If the total length is unchanged but the break/feed point is shifted 1/8 wavelength to one side, the most obvious change in the antenna's characteristics is:
一副两臂电气长度各为1/4波长的偶极天线，断开中点，通过巴 伦馈电，测得谐振频率为f，输入阻抗为Z。如果总长不变，但 是将断开的馈电点向一侧偏移1/8波长，则天线特性的最明显变 化是：
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Moving the feed point away from the current antinode (center) toward a higher-current region reduces the symmetry and places the feed at a point of lower current / higher voltage, so the input impedance rises sharply (A). Total length is unchanged, so the resonance frequency f stays about the same. This is the principle behind "off-center-fed" (OCF) dipoles, which present a higher, often usable impedance.