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23. (a) 150; (b) 204; (c) 39; (d) 64 22; (e) 160 24. (a) 4; (b) 7; (c) 18 and 9; (d) 9 and 6; (e) 10 and 5 25. (a) 17 and 9; (b) 23 and 13; (c) 17 and 11; (d) 5; (e) 13 26. (a) 36; (b) 381; (c) 12 23; (d) 12x2; (e) 120; ( f ) 96; (g) 18; (h) 2 27. (a) 737; (b) 14; (c) 77 28. (a) 10; (b) 12 and 9; (c) 20 and 10; (d) 5; (e) 210 29. 12 34. (a) 1:49; (b) 49:4; (c) 1:3; (d) 1:25; (e) 81: x2; ( f ) 9:x; (g) 1:2 35. (a) 49:100; (b) 4:9; (c) 25:36; (d) 1:9; (e) 9:4; ( f ) 1:2 36. (a) 10:1; (b) 1:7; (c) 20:9; (d) 5:11; (e) 2:y; ( f ) 3x:1; (g) 23:2; (h) 1: 22; (i) x: 25; ( j ) 2x:4 37. (a) 6:5; (b) 3:7; (c) 23:1; (d) 25:2; (e) 23:3 or 1: 23 38. (a) 100; (b) 121; (c) 12; (d) 100; (e) 105; ( f ) 18; (g) 20 23 2 39. (a) 12; (b) 63; (c) 48; (d) 21; (e) 45 2

CHAP. 8]

EXAMPLE 8.12 Express Z s for the circuit shown in Fig. 8-17 and observe the resulting magnitude scaling. Km Cs K Ls R 1=Cs Z s Km Ls m K R 1=Cs Km R m Cs Km R

49 2 22;

Fig. 8-17

(d) Equation (8.15) can be rearranged to give Av s hfe RC RL RC RL hie hfe 1 RE sRE CE 1 RE CE hie s 1 hie hfe 1 RE 8:18

(i) 32 23; 98 23

There are practical applications suggested by this brief exposure to magnitude scaling. For example, if the input current to a network were greater than it should be, a factor Km 10 would reduce the current to 1/10 of the former value.

10

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which clearly is of the form Av s kv Thus, we may use (8.18) to write !1 and !2 1 1 1 CE RE 1 hie hfe 1 RE 2 RE CE hie (8.19) (8.20) 1 s 1 2 s 1

CHAP. 8]

1. (a) 200; (b) 24.5; (c) 112; (d) 13; (e) 9; ( f ) 33; (g) 4.5 2. (a) 121; (b) 23.47; (c) 7 23; (d) 18.5; (e) 3 22 2 3. (a) 24 ; (b) 24 ; (c) 156 4. (a) 40 ; (b) 9; (c) 140 5. (a) 15 ; (b) 15 ; (c) 24 6. (a) 5 ; (b) 72 ; (c) 175 7. (a) regular octagon; (b) regular hexagon; (c) equilateral triangle; (d) regular decagon; (e) square; ( f ) regular dodecagon (12 sides) 9. (a) 9; (b) 30; (c) 6 23; (d) 6; (e) 13 23; ( f ) 6; (g) 20 23; (h) 60 10. (a) 18 22; (b) 7 22; (c) 40; (d) 8 22; (e) 3.4; ( f ) 28; (g) 5 22; (h) 2 22

Typically, hfe ) 1 and hfe RE ) hie , so a reasonable approximation of !2 is !2 % 1 CE hie =hfe 8:21

Application of circuit laws to circuits which contain op amps and several storage elements produces, in general, several rst-order di erential equations which may be solved simultaneously or be reduced to a higher-order input-output equation. A convenient tool for developing the equations is the complex frequency s (and generalized impedance in the s-domain) as used throughout Sections 8.5 to 8.10. Again, we assume ideal op amps (see Section 7.16). The method is illustrated in the following examples.

5 11. (a) 30 23; (b) 14; (c) 27; (d) 18; (e) 8 23; ( f ) 4 23; (g) 48 23; (h) 42; (i) 6; ( j ) 10; (k) 2 23; 1

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