May 04, 2009 -------------------------------------------------------------------------------- These are typical problems a ham might encounter over the course of normal operations. How long, how high, how heavy -- all are part of getting that radio gear working and keeping it working. Don't despair, all of the necessary formulas and conversion factors are in The ARRL Handbook or on the Web. ------------------------------------------------------------------------------- 1) What is the reactance of a 0.001 µF capacitor at 60 Hz? 1 kHz? 1.82 MHz? 2) The free-space wavelength of a 146.34 MHz signal is how many meters? Feet? Inches? Centimeters? 3) In order to keep your self-supporting tower upright at the maximum expected wind-load, you need a base that weighs 15000 pounds. If concrete weighs 150 pound per cubic foot, how many cubic yards are required? Cubic meters? 4) Using a velocity factor of 66 percent, what is the length of the following transmission lines in feet? a. 1/4-wavelength at 3.550 MHz b. 1/2-wavelength at 443.5 MHz c. 1 wavelength at 14.350 MHz 5) A counterweight for the new Zepp antenna needs to be at least 30 pounds to keep the wire taut. All you have is a pile of 1 kilogram weights. How many are required? 6) The weekend project is to put up a 1/4-wavelength sloper for the State Emergency Net on 3975 kHz. How long is the antenna in feet, assuming a 95 percent velocity factor? If it's attached to your tower at a height of 55 feet and the lower end must be at least 8 feet above the ground, how far from the tower base will the end be? 7) Calculate the VSWR for the following combinations of forward (Pf) and reflected (Pr) power: a. Pf = 95 W, Pr = 5 W b. Pf = 1400 W, Pr = 65 W c. Pf = 10 W, Pr = 0.15 W d. Pf = 800 W, Pr = 22 W 8) The finest subdivision of the Maidenhead Grid Square system are the 5'×2.5' sub-squares. Assuming 60 nautical miles per degree, what are the dimensions of the sub-squares in kilometers? 9) Willy's new rotor is rated to operate properly to -40° C. Billy just bought one rated to -40° F. Whose will operate at the colder temperature? 10) A tuned circuit must resonate at 10.105 MHz. Choose the proper value of inductance or capacitance that completes the circuit: a. 680 pF b. 4.7 µH c. 220 pF d. 1.5 µH 11) The wattmeter shows 1200 W going into the dummy load. What is the peak voltage appearing across the load? 12) A power tube requires 25 cubic feet per minute of cooling air, but you only have a squirrel-cage blower rated to deliver 1 cubic meter per minute. Will it suffice? 13) What is the length in both feet and meters of half-wave wire dipoles at the following frequencies, assuming a 95 percent velocity factor? a. 1.850 MHz b. 7040 kHz c. 24.900 MHz d. 50.120 MHz 14) Convert the following between linear ratios and dB: a. A loss of 1 dB equals a loss of how many percent? b. A power gain of 8 is a gain in how many dB? c. What is the voltage ratio corresponding to 6 dB? 15) A full-wave loop antenna for 3.6 MHz is 278 feet in circumference. If the loop is to be formed into an inverted triangle with a 120 foot horizontal section that is 75 feet above the ground and the remaining two sides are equal, by how much will the apex clear the ground? Bonus: What is the speed of light in furlongs per fortnight? Answers 1) 2.65 MO, 159 kO and 87.4O 2) 2.05 meters; 6.72 feet; 80.7 inches, and 205 cm (wavelength in meters = 300/f [MHz]) 3) 3.7 cubic yards or 2.83 cubic meters (15000/150 = 100 ft3 with 27 cubic feet/cubic yard 4) (a) 45.7 ft (b) 0.73 ft (c) 45.24 ft 5) 13.6, so use 14 weights at 2.2 lb/kg 6) 35.5 feet. The antenna is 58.9 feet long with a vertical drop of 47 feet, so the horizontal run is v(58.92-472) 7) (a) 1.6: 1; (b) 1.55:1, 1.28: 1; (c) 1.4:1 (use the formulas in the Transmission Lines chapter of The ARRL Handbook) 8) The sub-squares are 5.75×2.88 miles or 9.26×4.63 km. 9) Trick question -- both rotors are rated exactly the same. -40° C and -40° F are equal temperatures. 10) (a) 0.36 µH; (b) 53 pF; (c) 1.13 µH; (d) 165 pF 11) 346.4 V peak; 244.9 V rms. 12) Yes. Divide cubic meters by 0.028316 to get cubic feet. The fan can deliver 35.3 cfm. 13)(a) 253 feet or 77.1 meters; (b) 66.5 feet or 20.3 meters; (c) 18.8 feet or 5.73 meters; (d) 9.34 feet or 2.85 meters. Length in feet = 468/f (MHz) 14) (a) 20.6 percent; (b) 9.03 dB; (c) 2 15) The 120 foot flat top leaves 79 feet on a side. Each half of the loop becomes a right triangle with a hypotenuse of 79 feet and one side of 60 feet, leaving v(792-602) = 51.4 feet of vertical drop so that the ground clearance is 75-51.4 = 23.6 feet. Bonus: 1.803×1012 furlongs/fortnight. A furlong is 40 rods, a rod is 16.5 feet and a fortnight is 14 days.