Engineering Circuit Analysis Solutions
Chapter 14
1. (a)
; (b
3.
(d)
; (c) 22.5; (d)
; (e)
; (b)
; (c)
5. (a)
(c)
; (b)
;
; (d)
7. (a
(b)
;
9. (a)
(d)
; (b)
11. (a)
;
;
; (c)
; (b)
; (c)
13. (a)
(b)
15.
17.
19.
21. (a)
; (b)
23. (a) ; (b) ; (c)
; (c)
; (d)
; (d)
25. (a) s>0; (b)s>0; (c) s>-0.5; (d) s>-1
27. (a)
29. (a)
;
; (b)
;(c)
; (b)
; (d) 5
; (c)
; (d)
31. (a) 0; (b) 1; (c) 1; (d) 1;
1
;
Engineering Circuit Analysis Solutions
33. (a) 2; (b) 1; (c)
; (d) 1
35. (a)
(c)
(b)
; (d)
37. (a)
(b)
39. (a)
;
; (c)
(b)
; (d)
;
–
(c)
(d)
(e)
41. (a)
(b)
(c)
43. (a)
(b)
(c)
(d)
45. (a)
(b)
(c
47.
)
49.
51.
53. (a) stable
s3 1
47 0
s2 13
35 0
s 44.3 0
1 35
(b)
s3
s2
s
1
1 1 0
13 35 0
-x 0
35
2
stable
Engineering Circuit Analysis Solutions
55. (a) 2; (b) 2; (c) 1; (d) 1
57. (a) -2; (b) 0; (c) 2; (d) 0
59. (a) 1, 0; (b)
, NaN; (c)
,0
61. (a) Resistor: 8 Ω; (b) Inductance: 2 H
63.
65. (a) 5 A; (b) 0 V
Chapter 15
3. (a)
(b)
5. (a)
; (b)
; (c) 2u(t)
7.
9. (b)
(c)
11. (b)
(c)
13. (a)
(b)
15.
17.
3
Engineering Circuit Analysis Solutions
19.
21.
23. (a)
(b)
(c)
(d)
25. (a)
(b)
27. Z=0.833 Ω
31.
(a)
(b)
(c)
(d)
Zero
0
0, -1
-4
2, -1
Pole
-12.5
-5, -3
-1, -7
0,-7,-1
33. (a) s=0. s=-0.2; (b) s=0, s=-4, s=-1, s=-3, s=-5; (c) s=2, s=-2;
(d) s=1, s=-1, s=6, s=-6
35 (a) for circuit a:
; for circuit b:
(b)
Zero
(a)
(b)
0,
Pole
-R/L
-R/L
37. Zeros: s=-0.3285, -5.3774; poles:
4
Engineering Circuit Analysis Solutions
39. (a) 0, -20, -3, -0.5; (b) -20, -3, -1; (c) -20, -3, -2; (d) -20, -3, -5, -15, -10
41. x(t)*y(t)=0 (t<1); x(t)*y(t)=t-1 (t>=1);
43.
f*g=
0
10t
20
10t-20
40
t<0
0<=t<2
2<=t<4
4<=t<6
t>6
45. (a) vin=vout; (b) vout=8u(t)
47.
(a)
49. (a)
(b)
(c)
(b)
51.
(a)
(b)
(d)
(c)
; (e)
5
=2,-2
Engineering Circuit Analysis Solutions
53.
55. (a)
(b)
57. (a) Cascade 2 stages for Fig. 15.43(b): R1=1 kΩ, C1=1 μF, Rf=1.41 kΩ;
(b) cascade 2 stages of Fig. 15.43(a), stage1: Cf1=1 μF, R1=333 Ω, Rf1=2 Ω;
stage2: Cf2=1 μF, R2=1 kΩ, Rf2=10 Ω
59. 3 stages, stage 1 (Fig. 15.43(b)) C1=1 μF, R1=20 Ω, Rf=3 kΩ;
stage 2&3 (Fig. 15.43(a)) Cf2=Cf3=1 μF, R2=R3=1 kΩ, Rf2=Rf3=13.3 Ω
61. C=1 μF, R=62.5 kΩ, R1=Rf=1 kΩ
63. C=1 μF, R=3.8 kΩ, R1=Rf=1 kΩ
Chapter 16
1. (a) Q0=100; ξ=0.005; (b) Q0=0.1, ξ=5; (c) q0=1000, ξ=5e-4; (d)Q0=1, ξ=0.5
3. 0.1<|Z|<12.3
7. (a) |Y(ω0)|=6e-5; (b) ω0=707 rad/s; (c) Q0=707
9.Q=
, ω0=4e6, Qmax=10368.6
11. (a) |Y|=0.3016, |Z|=3.3156; (b) |Y|=0.0551, |Z|=18.15; (c)|Y|=0.0349, |Z|=28.65;
(d) |Y|=1/32.5, |Z|=32.5
13. B~1kHz; (b) B~10MHz
15. |Z|=500 kΩ;
(b)
17 (a) Q0=1.11, |Z|=4.97 Ω; (b) Q0=0.894, ω=212.4, |Z|=4.95 Ω
19. (a)ω0=1.4e5; (b)Q0=14.1
6
Engineering Circuit Analysis Solutions
21. (a) Q=0.15, Rs=488.9 Ω, Cs=69 μF; (b) Q=12.5, Rs=3.2 Ω, Ls=200 mH
23.
when im(Z)=0, ω=ω0
25. (a) R=1 Ω, C=47 μF, L=2.2 μH; (b) R=500 kΩ, C=2 μF, L=166.7 kH; (c) R=25 Ω,
L=34.9 H, C=50 μF
27.
29. all elements are in parallel: -j1e6, 1250, 1.25j, 3.5j*Ix
31.
(a)
(b)
7
Engineering Circuit Analysis Solutions
33.
(a)
(b)
35
(a)
(a)
37.
(a)
(b)
39.
8
Engineering Circuit Analysis Solutions
41. (a) R=1 kΩ, C=2.2 μF;
(b)
43.
45. Fig. 16.41(b): R1=100 Ω, Rf=1.7 kΩ, C=1 uF, R2=1 kΩ
47. stage1 LPF: R1=100 Ω, Rf=216 Ω, C=1 μF, R2=909 Ω;
stage2 HPF: R1=100 Ω, Rf=216 Ω, C=1 μF, R2=10 kΩ
49. Fig. 16.41(b) R1=100 Ω, Rf=adjustable, C=1 μF, C=795 pF, Av=1+Rf/R1
51. (a) Fig. 16.48, RB=1 kΩ, RA=586 Ω, C1=C2=1 μF, R1=R2=187 Ω
(b) RA=416 Ω, RB=1 kΩ, C1=C2=1 nF, R1=R2=222 Ω
53. (a) RA=586 Ω, RB=1 kΩ, C1=C2=1 μF, R1=R2=1.12 kΩ
55. RA=3 kΩ, RB=1 kΩ, C1=C2=1 μF, R1=R2=256 Ω
57.
59. Lmax=270 μH, Lmin=89 μH
61. C=1 μF, R=800 Ω, R1=1 kΩ, Rf=260 Ω
63.
65. 3rd order BW LPF and 2nd order BW HPF
LPF (fig. 16.49) Ra=3 kΩ, Rb=1 kΩ, C=1 μF, R=159 Ω, Cf=1 μF, Rf=R1=159 Ω
HPF (fig. 16.48) RA=1 kΩ, RB=568 Ω, C=1 uF, R=1593 Ω
9
Engineering Circuit Analysis Solutions
Chapter 17
1. I1=1.757 A
3. (a)
470I1-470I2=V1
-470I1+12670I2-100000I3-2200I4=0
-10000I2+13200I3-2200I4=0
-2200I2-2200I3+9100I4=0
(b) ΔZ=1.13e14, Δ11=2.9e11
(c) Zin=389 Ω
5. Yin=3 s
7.
9. (a) V1/Rin+(V1-V2)/28=0, (v1-V2)/20+V1/Rx=0; (b) Rin=Rx
11.
13. (a)
; (b)
(c) P=10s
15. (a)
; (b) 9 μW
17.
19.
21. (a) 5.54 kΩ; (b) 22.16 W; (c) 14.62 W
23. (a) Zin=69.9j; (b) Zin=141j
25. Zin=1.86 MΩ
27. y11=0.0041, y12=-0.0031, y22=0.0037
29. y11=0.0041, y12=-0.0031, y22=0.0037
31. (a)Gv=1.2393; (b) Gi=6.741; (c)Gp=8.35; (d) Zin=-4.9 Ω;
10
Engineering Circuit Analysis Solutions
33.
35. (a)
; (b)
37.
39. Z11=-0.0049+0.0055j, Z22=4.94e3+2.88e3*j, Z12=48.5-30.9j, Z21=-470+530j
41.
,
43. (a)
; (b)
45. V1=1/6 V, V2=2/3 V, I1=1/6 A, I2=1/3 A,
47.
49.
51.
53. (a)
; (b)
55. (a)
; (b)
57.
59.
,
,
61.
63. (a)
,
,
,
, (b)
,
,
A, D: 1, B, C: m/rad,
11
Engineering Circuit Analysis Solutions
Chapter 18
1. (a) f0=1.43 Hz, ω0=9 rad/s, T=0.69 s; (b) f0=11.15 Hz, w0=70 rad/s, T=0.089 s;
(c) f0=0.64 Hz, ω0=4 rad/s, T= 1.57 s; (d) f0=0.64 Hz, w0=4 rad/s, T= 1.57s;
3. (a) 0; (b) 0; (c) 4; (d) 0
5. a0=-0.5, a1=a2=a3=0, b1=-1.27, b2=-0.64, b3=-0.42
7. a1=-15.79, a2=7.897, a3=0, b1=9.12, b2=-13.68, b3=12.16
9. y1(0.5)=0.891, y2(0.5)=1.3, y3(0.5)=0.94, g(0.5)=1
11.
13.
15. (a) odd; (b) even; (c) even; (d)not symmetry
17. a0=0, a1=0.436, a2=-0.409, a3=-0.184
19.
21.
12
Engineering Circuit Analysis Solutions
23.
25.
27. C0=0,
,
,
29. 9a) T=6 s; (b)
; (c) c0=-5/3, C1=1.38+3.98j,
C2=-0.69+-1.99j, C3=-1.06j, C-1=1.38-3.98j, C-2=-0.69+1.19j, C-3=1.06j
31. (a)
, (b) C4=-0.062, (c) C0=0.08; (d) |Cn_max|=0.08; (e)N=66
33. (b)
35. (a) 5/(jω+1); (b)
37.
39. 3.3 mJ
41. 1.78 J
43. (a)
; (b)
;
(c)
45. (a)
47. (a) 115.5sgn(t); (b)
; (b)
; (c)
49.
51.
53. (a)
; (b)
55. (a) 2.5 V; (b) 9 V; (c) 15 V
13
; (c)F=1/jω