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(a) If an asymptotic Bode plot of Av j! is made, over what values of frequency (in the midfrequency range) is the gain constant in amplitude (b) Find the midfrequency gain in decibels if Ks 108 . (c) Within 2 percent accuracy, over what range of frequencies is the exact gain constant Ans: a 100 ! 105 rad=s; b MdbM 60 db; c Mdb ! 58:8 db for 500 ! 5 104 rad/s 8.25 In Problem 8.19, the gain of the FET ampli er does not depend on the Miller capacitance CM ; however, the situation changes if the source resistance is nonzero. (a) Add a source resistance Ri to Fig. 8-26, and nd an expression for the voltage-gain ratio. (b) Evaluate the gain for Ri 0 and for Ri 100 if Cgs 3 pF, Cds 1 pF; Cgd 2:7 pF; rds 50 k ; gm 0:016 S; RL RD 2 k ; RG 1 M ; and f 50 MHz. Ans: a b 8.26 Av s gm RG = Ri RG s Cds Cdg gds GD GL s RG kRi Cgs CM 1

Since v Ri, the maximum voltage must be 5 10 50 V. In Fig. 2-10 the plots of i and v are shown. The identical nature of the functions is evident.

If two angles of one triangle are congruent respectively to two angles of another triangle, the remaining angles are congruent.

An inductance of 2.0 mH has a current i 5:0 1 e 5000t (A). Find the corresponding voltage and the maximum stored energy.

For Ri 0; Av 10:348j131:538; for Ri 100; Av 3:49j61:268

Fig. 4-38

AC power in resistors, inductors, and capacitors, is summarized in Table 10-1. We use the notation Veff and Ieff to include the phase angles. The last column of Table 10-1 is S VI where S is called apparent power. S is discussed in Section 10.7 in more detail.

PRINCIPLE 3:

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Consider the high-pass lter circuit of Fig. 8-15(a). (a) Show that as ! becomes large, the amplitude ratio Mdb actually approaches 20 log RL = RL RS as indicated in Fig. 8-15(b). (b) Show that jM 2 j!L j, where !L 1=C RL RS , has the value 1 jM 2 j1 j 1 RL = RL RS 2 . 2 2 In the high-pass lter circuit of Fig. 8-15(a), the source impedance RS 5 k . If the circuit is to have a high-frequency gain of 0.75 and a break or cuto frequency of 100 rad/s, size RL and C. Ans: RL 15 k ; C 0:5 F In the circuit of Fig. 3-20, replace VS with a sinusoidal source to give the small-signal circuit of Fig. 8-6. (a) If the impedance of the coupling capacitor is not negligible, nd the current-gain ratio Ai s IL =IS . (b) Determine the low-frequency cuto point. Ans: a Ai hfe RB = RB hie ; b the gain is independent of frequency down to f 0 Show that the RC network of Fig. 8-29 is a high-pass lter. Ans: Determine its low-frequency cuto point. !L R1 R2 R3 R1 R2 R3 C3

EXAMPLE 10.6 Find the power delivered from a sinusoidal source to a resistor R. Let the e ective values of voltage and current be V and I, respectively. p p pR t viR V 2 cos !t I 2 cos !t 2VI cos2 !t VI 1 cos 2!t RI 2 1 cos 2!t Thus, PR V2 1 cos 2!t R Q 0

Fig. 4-39

R3 _

Table 10-1 p v V 2 cos !t Veff V 08 p i I 2 cos !t Ieff I 8 P VI cos ; Q VI sin and S VI (apparent power) Z R L C R jL! j C! i p V 2 cos !t R p V 2 cos !t 908 L! p V 2C! cos !t 908 Ieff V 08 R V 908 L! VC! 908

PRINCIPLE 4:

V2 L! V 2 C!

C3 _

The measure of each exterior angle of a triangle equals the sum of the measures of its two nonadjacent interior angles.

The instantaneous power entering a resistor varies sinusoidally between zero and 2RI 2 , with twice the frequency of excitation, and with an average value of P RI 2 . v t and pR t are plotted in Fig. 10-5(a). EXAMPLE 10.7 Find the ac power entering an inductor L. p p pL t viL V 2 cos !t I 2 cos !t 908 2VI cos !t sin !t VI sin 2!t L!I 2 sin 2!t Thus, V2 sin 2!t L! P 0 Q VI V2 L!I 2 L!

Fig. 8-29

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