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) Ans: vo 10 sin !t V for 0 t < T=2, 0 for T=2 t < 3T=4, and 10 1 sin !t V for t ! 3T=4 Four diodes are utilized for the full-wave bridge of Fig 2-48 Assuming that the diodes are ideal and that vS Vm sin !t, (a) nd the output voltage vL and (b) nd the average value of vL Ans: a vL Vm j sin !tj V; b VL0 2Vm = A shunt lter capacitor (see Example 213) is added to the full-wave recti er of Problem 250 Show that the ripple factor is given by Fr 2= 4fRL C 1 % 1=2fRL C Add a 470 F lter capacitor across points a; b in the full-wave recti er circuit of Fig 2-48.

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The adjacency matrix and the adjacency list are shown in Figure 15.63 on page 318. a. The breadth-first search visits ABDECHFIGKLJMONPQ; its spanning tree is shown on the left in Figure 15.64 on page 318. b. The depth-first search visits ABCFEIHDKLMJGNPQO; its spanning tree is shown on the right in Figure 15.64 on page 318.

If RL 1 k p and vS 120 2 sin 120 t V, use SPICE methods to determine (a) the magnitude (peak-to-peak) of the output ripple voltage and (b) the average value of output voltage (Netlist code available at author website) Ans: a vL 2:79 V; b VL0 168:34 V The level-discriminator circuit (Fig 2-49) has an output of zero, regardless of the polarity of the input signal, until the input reaches a threshold value Above the threshold value, the output duplicates the input Such a circuit can sometimes be used to eliminate the e ects of low-level noise at the expense of slight distortion Relate vo to vi for the circuit Ans: vo vi 1 A=jvi j for jvi j > A, and 0 for jvi j A.

This appendix summarizes mathematical topics used in the study of data structures THE FLOOR AND CEILING FUNCTIONS The floor and ceiling functions return the two nearest integers of a given real number The floor of x, denoted by x , is the greatest integer that is not greater than x The ceiling of x, denoted by x , is the smallest integer that is not smaller than x Here are the main properties of these two functions (The symbol stands for the set of all integers) Theorem A1 Properties of the Floor and Ceiling Functions 1 x = max{m | m x}, and x = min{n | n x} 2 x x < x + 1, and x 1 < x x 3 x 1 < x x x < x + 1 4 If n and n x < n + 1, then n = x .

Fig. 2-48

8.5 Here are the schemas for a few more of the tables in one implementation of the antique store database: Item Item_ID | Type | Description | Cost | Consignment_Seller_ID | Price_Sold

If n and n 1 < x < n, then n = x 5 If x , then x = x = x 6 If x , then x < x < x 7 x x and x = x 8 x + 1 = x and x + 1 x LOGARITHMS The logarithm with base b of a positive number x is the exponent y on b for which b y = x For example, the logarithm of 1000 base 10 is 3 because 103 = 1000 This is written log10 1000 = 3 The logarithm with base 2 is called the binary logarithm and is written lg x = log 2 x For example, lg 8 = 3.

Fig. 2-49

CHAP. 2]

As a mathematical function, the logarithm is the inverse of the exponential function with the same base: by = x y = log b x For example, 3 = lg 8 because 23 = 8..