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thereby keeping earnings from being greatly distorted by any uctuating increases or de creases in prices. Yet it sometimes allows too much maneuvering by managers to change net income. For example, if prices are rising rapid ly and a company wishes to pay less taxes for that year, management can buy large amounts of inventory near the end of that period. These higher inventory costs, because of prices, under LIFO immediately be come an expense, and thus result in the nancial statement showing a lower net income. Conversely, if the rm is having a bad year, manage ment may want to increase net income to garner favor with stockholders. This can be done by delaying any large purchase of high-cost inventory until the following period by keeping the purchase out of the Cost of Goods Sold section for the current year, and thus avoiding any decrease in net income. In a rising market, certain tax advantages are gained through LIFO because it yields a lower pro t because of its higher cost of goods sold. This can be shown by using the data while assuming sales of $20,000 for the year. FIFO Sales $20,000 Cost of Goods Sold Goods Available for Sale $6,100 3,130 Less: Ending Inventory Cost of Goods Sold 2,970 Gross Pro t $17,030 LIFO $20,000 $6,100 2,430 3,670 $16,330

The following treatment echoes that of Section 6.2 For the usual case of negligible grid current, (4.7) degenerates to iG 0 and the grid acts as an open circuit. For small excursions (ac signals) about the Q point, iP ip and an application of the chain rule to (4.8) leads to ip iP % diP where we have de ned 1 v gm v g rp p 7:8

CHAP. 7]

the distance OA is assumed to be 1, so that the coordinate of A is 1. The point B is two units away from O; therefore, B has coordinate 2. Every positive real number r is the coordinate of a unique point on L to the right of the origin O; namely, of that point to the right of O whose distance from O is r. To every point Q on L to the left of the origin O,

@vP vP @iP Q iP Q @i i Transconductance gm P P @vG Q vG Q Plate resistance rp

7:9 7:10

Under the condition iG 0, (7.8) is simulated by the current-source equivalent circuit of Fig 7-9(a). The frequently used voltage-source model of Fig. 7-9(b) is developed in Problem 7.19.

we assign a negative real number as its coordinate, the number QO, the negative of the distance between Q and O. For example, in the diagram

This information shows LIFO produces (in a rising price market): a low er ending inventory, a higher cost of goods sold, and a lower gross prof it. FIFO will produce the opposite. The IRS will permit companies to use LIFO for tax purposes only if they use LIFO for nancial reporting purposes. Thus, if a business uses LIFO for tax purposes, it must also report inventory and income on the same valuation basis in its nancial statements, but it is allowed to report an alternative inventory amount in the notes to the nancial statements. This is permitted because it affords true nancial analysis in comparing, on a similar basis, one business with another. It should be noted that a

_ K (a)

_ K (b)

the point U is assumed to be a distance of one unit from the origin O; therefore, the coordinate of U is 1. The point W has coordinate 1 , which means that the distance WO is 1 . Clearly, every negative real number is the coordinate of a 2 2 unique point on L to the left of the origin. The origin O is assigned the number 0 as its coordinate. This assignment of real numbers to the points on the line L is called a coordinate system on L .

(a) For the JFET ampli er of Example 4.2, use the drain characteristics of Fig. 4-6 to determine the small-signal equivalent-circuit constants gm and rds . (b) Alternatively, evaluate gm from the transfer characteristic.

(a) Let vgs change by 1 V about the Q point of Fig. 4-6(b); then, by (7.3), 3 iD 3:3 0:3 10 1:5 mS gm % vGS Q 2 At the Q point of Fig. 4-6(b), while vDS changes from 5 V to 20 V, iD changes from 1.4 mA to 1.6 mA; thus, by (7.4), vDS 20 5 rds % 75 k iD Q 1:6 1:4 10 3 (b) At the Q point of Fig. 4-6(a), while iD changes from 1 mA to 2 mA, vGS changes from 2:4 V to 1:75 V; by (7.3), 3 iD 2 1 10 1:54 mS gm % vGS Q 1:75 2:4

Choosing a different origin, a different direction along the line, or a different unit distance would result in a different coordinate system. 1.2 ABSOLUTE VALUE For any real number b de ne the absolute value |b| to be the magnitude of b; that is, |b| = b b if b 0 if b < 0

Derive the small-signal voltage-source model of Fig. 7-1(b) from the current source model of Fig. 7-1(a).

2