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(a) If capacitor CK appears as a short circuit to ac signals, then application of KVL around the plate circuit of Fig. 4-30 gives, as the equation of the ac load line, VPP VGQ iP RL vP . Thus, the ac load line has vertical and horizontal intercepts VPP VGQ 300 4 25:5 mA RL 11:6 103 as shown on Fig. 4-31. (b) We have vg vS ; thus, as vg swings 2 V along the ac load line from the Q point in Fig. 4-31, vp swings a total of 2Vpm 213 145 68 V as shown. The voltage gain is then Av 2Vpm 68 17 2Vgm 4 and VPP VGQ 296 V

where the minus sign is included to account for the phase reversal between vp and vg . (c) Applying (7.9) and (7.10) at the Q point of Fig. 4-31 yields vP 202 168 4:86 k rp iP vG 4 15 8 10 3 i 15:5 6:5 10 3 4:5 mS gm P vG vP 180 3 5 Then, gm rp 21:87, and Problem 7.21, yields Av RL 21:87 11:6 103 15:41 R L rp 11:6 4:86 103

(35.4)

LIFO 1. Yields the highest amount of COGS 2. Yields the lowest amount of gross pro t 3. Yields the lowest amount of ending inventory Weighted Average Yields results between FIFO and LIFO for all three concepts being re viewed.

The input admittance to a triode modeled by the small-signal equivalent circuit of Fig. 7-9(b) is obviously zero; however, there are interelectrode capacitances that must be considered for highfrequency operation. Add these interelectrode capacitances (grid-cathode capacitance Cgk ; plategrid, Cpg ; and plate-cathode, Cpk ) to the small-signal equivalent circuit of Fig. 7-9(b). Then (a) nd the input admittance Yin , (b) nd the output admittance Yo , and (c) develop a highfrequency model for the triode.

(a) With the interelectrode capacitances in position, the small-signal equivalent circuit is given by Fig. 7-24. The input admittance is Yin IS I I2 1 VS VS VS sCgk VS 1=sCgk VS Vo sCpg VS Vo 1=sCpg 1

We know that Dx x r = rx r 1 for any rational number r. Now the formula can be extended to arbitrary exponents. If, in Theorem 35.2, we replace x by r and a by x (thereby making x positive), we get x r = er ln x . Hence, Dx x r = Dx er ln x = er ln x Dx r ln x = er ln x r Thus, we have the following: Theorem 35.5: For any real number r and all positive x, Dx x r = rx r 1 1 x = xr r 1 x = rx r 1 [by the chain rule]

(2) (3)

CHAP. 7]

(a) e2 ln x = eln x = x2 (b) ln e2 = 2 (c) e(ln u) 1 =

Fig. 7-24