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Multiply by (x l)2 (x 2), 3x + 1 = A1 (x 1)(x 2) + A2 (x 2) + A3 (x 1)2 Letting x = 1, 4 = 0 + A2 ( 1) + 0 Letting x = 2, 7 = 0 + 0 + A3 (1) or A3 = 7 The remaining numerator, A1 , is determined by the condition that the coef cient of x 2 on the right side of (2) be zero (since it is zero on the left side). Thus, A 1 + A3 = 0 or A1 = A3 = 7 or A2 = 4 (2) A3 3x + 1 A1 A2 + + = x 1 (x 1)2 x 2 (x 1)2 (x 2)

Execute hPrb10_15.CIRi and use the Probe feature of PSpice to plot the waveforms of Fig. 10-15.

Fig. 10-15

[More generally, we use all the roots of D(x) to determine some of the A s, and then compare coef cients of as many powers of x as necessary to nd the remaining A s.]

2 Endorsement in full Endorsement in full states that the check can be cashed or transferred only on the order of the person named in the en dorsement 3 Restrictive endorsement A restrictive endorsement limits the re ceiver of the check as to the use he or she can make of the funds collect ed Usually this type of endorsement is done when checks are prepared for deposit Reconciliation Each month, the bank forwards to the depositor a statement of his or her account showing the beginning balance, all the deposits made and other credits, any checks paid and other charges (debits), and the ending bal ance Included in this envelope with the statement are the paid or canceled checks and any other deductions or addi tions to the account.

10.16 Determine the smallest value of inductance that could have been used for the buck converter of Example 10.5 and the inductor current remain continuous. Ans: L Lc 50 H

Find the values of Imax and Imin for the buck converter of Example 10.5 if the value of L Lc 50 H, as determined in Problem 10.16. Ans: Imax 2:4 A; Imin 0

Now the antiderivatives of f (x) will consist of terms of the form ln |x a| plus at least one term of the form A B dx = j (x a) (x a) j 1 Case 3: D(x) has irreducible quadratic factors, but none is repeated. In this case, each quadratic factor x 2 + bx + c contributes a term x2 to the partial fractions representation. EXAMPLE

Use the procedure of Problem 10.3 to nd an expression for the current gain GI I2 =I1 for the ideal boost converter of Fig. 10-4. Ans: GI 1 D

Use Problem 10.6 as a guideline to derive expressions for Imax and Imin shown on the boost converter waveforms of Fig. 10-5. Ans: Imax V2 V D 1 ; 1 D RL 2 fs L Imin V2 V D 1 1 D RL 2 fs L

n 9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 65

0 The actual gain GV for the boost converter with inherent inductor resistance was determined in Problem 0 10.11. Determine cycle D Dp for which GV has a maximum value. p the duty Ans: Dp 1 Rx =RL