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The negotiability of a note receivable based upon its maturity value, en ables the holder to receive cash from the bank before the due date. This is known as discounting. Once the interest to be paid has been determined, the procedure for discounting a note is quite simple. The maturity value of a note is: 1. Maturity value = face of note + interest income where the face is the principal and interest income is computed as before. The holder of a note may discount it at the bank prior to its due date. He or she will receive the maturity value, less the discount, or interest charge imposed by the bank for holding the note for the unexpired portion of its term. In other words, 2. Discount = maturity value discount rate unexpired time, and 3. Net Proceeds = maturity value discount. For example, Mr. Ed holds a $400, 90-day, 12 percent note written by Mr. Bill on April 10. It is discounted at 12 percent on May 10. The in terest on the note amounts to $12. Hence: 1. Maturity value = $400 + $12 = $412 Since at the time of discounting, Mr. Ed has held the note for only 30 days, the bank will have to wait 60 days until it can receive the matu rity value. The discount charge is then 2. Discount = $412 (12/100) (60/360) = $8.24 and Mr. Ed receives 3. Net proceeds = $412 $8.24 = $403.76

(b) The Laplace-domain transfer function (7) is of the form T s Kb s 2 s 1 1 s 1 3 s 1

4.6 Show that the line y = x makes an angle of 45 with the positive x-axis (that is, POQ in Fig. 4-14 contains 45 ).

1 1 1 25 rad=s 1 CC RC RL 10 10 6 4000 1 1 1 50 rad=s !2 2 RE CE 100 200 10 6 1 hfe 1 RE Ri hie 101 100 100 1000 !3 509:1 rad=s CE RE Ri hie 3 200 10 6 100 1100 !1

Since there is at least a decade of frequency (in which the gain can attenuate from its midfrequency value) between !3 and the other (lower) break frequencies, !3 must be the low-frequency cuto !L . Then fL (c) !3 509:1 81:02 Hz < 100 Hz 2 2

Let P be the point on the line y = x with coordinates (1, 1). Drop a perpendicular PQ to the positive x-axis. Then PQ = 1 and OQ = 1. Hence, OPQ = QOP, since they are base angles of isosceles triangle QPO. Since OQP contains 90 ,

As in Problem 8.12, Ib 0 if vi is deactivated; a driving-point source replacing RL would then see a frequency-dependent output impedance given by Zo Zdp RC 1 sCC 8

Assume that the coupling capacitors in the CS MOSFET ampli er of Fig. 4-25 are identical. Determine the voltage-gain ratio (a) for any frequency and (b) for midfrequency operation.

Note!

Fig. 4-14

(a) The equivalent circuit is drawn in Fig. 8-21. By voltage division, where RG R1 kR2 R1 R2 R1 R2 1 RG sRG CC Vgs V V RG 1=sCC i sRG CC 1 1 Current division at the drain node yields IL from which Vo RL IL sgm RD RL rds CC = RD rds V sCC RD rds = RD rds RL 1 gs 3 sCC RD rds = RD rds gm Vgs RD krds g V RD krds 1=sCC RL m gs sCC RD rds = RD rds RL 1 2

1 2T

Consider each quadrant separately. In the rst quadrant, |x| = x and |y| = y. Hence, the equation becomes x + y = 1; that is, y = x + 1. This yields the line with slope 1 and y-intercept 1. This line intersects the x-axis at (1, 0). Hence, in the rst quadrant our graph consists of the line segment connecting (1, 0) and (0, 1) (see Fig. 4-15). In the second quadrant, where x is negative and y is positive, |x| = x and |y| = y, and our equation becomes x + y = 1, or y = x + 1. This yields

3 2T

Fig. 1-22 (a) The integral in (1.20) is simply the area under the f t curve for one period. average current as 1 T T 4 1 2:5 A T 2 2 We can, then, nd the

Fig. 4-15

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