# News

## Amateur Radio Quiz: Calculation Calisthenics

05/01/2009

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?

1) 2.65 MΩ, 159 kΩ and 87.4Ω

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 √(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 √(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.

H. Ward Silver, N0AX
Contributing Editor

Back