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Example 4.7. In the triode ampli er of Fig. 4-14, VGG 4 V, VPP 300 V, RL 10 k , and RG 2 k . The plate characteristics for the triode are given by Fig. 4-13(b). (a) Draw the dc load line; then determine the quiescent values (b) IGQ ; c VGQ ; d IPQ , and e VPQ . (a) For the given values, the dc load line (4.11) has the iP intercept VPP 300 30 mA RL 10 103 and the vP intercept VPP 300 V. characteristics of Fig. 4-13(b). (c) (e) These intercepts have been utilized to draw the dc load line on the plate

(b) Since the polarity of VGG is such that vG is negative, negligible grid current will ow IGQ % 0 . For negligible grid current, (4.10) evaluated at the Q point yields VGQ VGG 4 V. Projection of Qn onto the vP axis of Fig. 4-13(b) gives VPQ 220 V. (d) The quiescent plate current is read as the projection of Qn onto the iP axis of Fig. 4-13(b) and is IPQ 8 mA.

CHAP. 14]

Voltage vgs will swing along the dc load line of Fig 4-6(b) (which is now identical to the ac load line) from point a to point b, giving, as extremes of iD , 3.1 mA and 0.4 mA. The corresponding extremes of vS iD RS are 6.2 V and 0.8 V.

15,000 7,500 7,500 15,000 15,000

For the MOSFET ampli er of Example 4.5, let VGSQ 6:90 V. Calculate IDQ from the analog of (4.2) developed in Section 4.8.

14.10 The distance by bus from New York to Boston is 225 miles. The bus driver gets paid $12.50 per hour, while the other costs of running the bus at a steady speed of x miles per hour amount to 90 + 0.5x cents per mile. The minimum and maximum legal speeds on the bus route are 40 and 55 miles per hour. At what steady speed should the bus be driven to minimize the total cost 14.11 A charter airline is planning a ight for which it is considering a price of between $150 and $300 per person. The airline estimates that the number of passengers taking the ight will be 200 0.5x, depending on the price of x dollars that will be set. What price will maximize the income 14.12 Suppose that a company can sell x radios per week if it charges 100 0.1x dollars per radio. Its production cost is 30x + 5000 dollars when x radios are produced per week. How many radios should be produced to maximize the pro t, and what will be the selling price per radio 14.13 A box with square base and vertical sides is to be made from 150 square feet of cardboard. What dimensions will provide the greatest volume if: (a) the box has a top surface; (b) the box has an open top 14.14 A farmer wishes to fence in a rectangular eld, and also to divide the eld in half by another fence (AB in Fig. 14-6). The outside fence costs $2 per foot, and the fence in the middle costs $3 per foot. If the farmer has $840 to spend, what dimensions will maximize the total area

From the drain characteristics of Fig. 4-9(b), we see that VT 4 V and that IDon 5 mA at VGSon 8 V. Thus,

CHARACTERISTICS OF FIELD-EFFECT TRANSISTORS AND TRIODES VGSQ 2 6:90 2 IDQ IDon 1 5 10 3 1 2:63 mA 4 VT (Compare Example 4.5.)

By a method called self-bias, the Q point of a JFET ampli er may be established using only a single resistor from gate to ground [Fig. 4-5(b) with VGG 0 : If RD 3 k ; RS 2 k , RG 5 M , and VDD 20 V in Fig. 4-5(b), and the JFET characteristics are given by Fig. 4-6, nd (a) IDQ ; b VGSQ , and (c) VDSQ .

Fig. 14-6

(a) On Fig. 4-6(a) we construct a transfer bias line having a vGS intercept of VGG 0 and a slope of 1=RS 0:5 mS; the ordinate of its intersection with the transfer characteristic is IDQ 1:15 mA. (b) The abscissa of the Q point of Fig. 4-6(a) is VGSQ 2:3 V. (c) The dc load line from Example 4.2, already constructed on Fig. 4-6(b), is applicable here. The Q point was established at IDQ 1:15 mA in (a); the corresponding abscissa is VDSQ % 14:2 V.