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When two impedance vectors don t lie along a single line, you must use vector addition to be sure that you get the correct net impedance. In Fig. 16-3, the geometry of vector addition is shown. Construct a parallelogram, using the two vectors Z1 = R1 + jX1 and Z2 = R2 + jX2 as two adjacent sides of the figure. The diagonal of the parallelogram is the vector representing the net complex impedance. (Note that in a parallelogram, pairs of opposite angles have equal measures. These equalities are indicated by single and double arcs in Fig. 16-3.)

344 Transformers and impedance matching 11. An advantage of a toroid core over a solenoid core is: A. The toroid works at higher frequencies. B. The toroid confines the magnetic flux. C. The toroid can work for dc as well as for ac. D. It s easier to wind the turns on a toroid. 12. High voltage is used in long-distance power transmission because: A. It is easier to regulate than low voltage. B. The I2R losses are lower. C. The electromagnetic fields are stronger. D. Smaller transformers can be used. 13. In a household circuit, the 234-V power has: A. One phase. B. Two phases. C. Three phases. D. Four phases. 14. In a transformer, a center tap would probably be found in: A. The primary winding. B. The secondary winding. C. The unbalanced winding. D. The balanced winding. 15. An autotransformer: A. Works automatically. B. Has a center-tapped secondary. C. Has one tapped winding. D. Is useful only for impedance matching. 16. A transformer has a primary-to-secondary turns ratio of 2.00:1. The input impedance is 300 resistive. What is the output impedance A. 75 . B. 150 . C. 600 . D. 1200 . 17. A resistive input impedance of 50 must be matched to a resistive output impedance of 450 . The primary-to-secondary turns ratio of the transformer must be: A. 9.00:1. B. 3.00:1.

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Qiiz 345 C. 1:3.00. D. 1:9.00. 18. A quarter-wave matching section has a characteristic impedance of 75.0 . The input impedance is 50.0 resistive. What is the resistive output impedance A. 150 . B. 125 . C. 100 . D. 113 . 19. A resistive impedance of 75 must be matched to a resistive impedance of 300 . A quarter-wave section would need: A. Zo 188 . B. Zo 150 . C. Zo 225 . D. Zo 375 . 20. If there is reactance at the output of an impedance transformer: A. The circuit will not work. B. There will be an impedance mismatch, no matter what the turns ratio of the transformer. C. A center tap must be used at the secondary. D. The turns ratio must be changed to obtain a match.

Formula for Complex Impedances in Series Suppose you are given two complex impedances, Z1 = R1 + jX1 and Z2 = R2 + jX2. The net impedance, Z, of these in series is their vector sum, given by the following formula:

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DO NOT REFER TO THE TEXT WHEN TAKING THIS TEST. A GOOD SCORE IS AT least 37 correct. Answers are in the back of the book. It s best to have a friend check your score the first time, so you won t memorize the answers if you want to take the test again. 1. A series circuit has a resistance of 100 and a capacitive reactance of -200 . The complex impedance is: A. 200 j100. B. 100 j200. C. 200 j100. D. 200 j100. E. 100 j200. 2. Mutual inductance causes the net value of a set of coils to: A. Cancel out, resulting in zero inductance. B. Be greater than what it would be with no mutual coupling. C. Be less than what it would be with no mutual coupling. D. Double. E. Vary, depending on the extent and phase of mutual coupling. 3. Refer to Fig. TEST 2-1. Wave A is: A. Leading wave B by 90 degrees. B. Lagging wave B by 90 degrees. C. Leading wave B by 180 degrees. D. Lagging wave B by 135 degrees. 346

Z = (R1 + jX1) + (R2 + jX2) = (R1 + R2) + j(X1 + X2) Calculating a vector sum using the formula is easier than doing it geometrically with a parallelogram. The arithmetic method is also more exact. The resistance and reactance components add separately. Just remember that if a reactance is capacitive, then it is negative imaginary in this formula.

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