Chapter 14
14.1 a) 2021.27 Hz
b) H(jco c ) = 0.7071 / - 4 5 ° ,
H(j02a> c ) = 0.981 / - 1 1 3 1 ° ,
H(j5w c ) = 0.196/-78.69°
c) v o ((0 c ) = 7.07cos(12,700f - 45°)V,
v o (02w c ) = 9.81 cos(2540r - 11.31°) V,
v 0 (5a) c ) = 1.96cos(63,500f - 78.69°) V
14.2 a) 31.42 ft
b) 3419.98 Hz
c) 33 ft, 5252.11 Hz
14.13 a) 5.305 kft
b) 333.86 Hz
14.14 a) 150 ft
b) 680ft
14.22 a) lOOkrad/s
b) 15.9 kHz
c) 8
d) 93.95 krad/s
e) 14.95 kHz
f) 106.45 krad/s
g) 16.94 kHz
h) 1.99 kHz
14.23 a) 5 kft, 50 mH
b) 3.52 kHz, 2.88 kHz
c) 636.62 Hz
14.35 a) 1 Mrad/s
b) 159.15 kHz
c) 15
d) 967.22 krad/s
e) 153.94 kHz
f) 1.03 Mrad/s
g) 164.55 krad/s
h) 10.61 kHz
14.36 a) 397.89ft, 3.17 mH
b) 4.42 kHz, 3.62 kHz
c) 800 Hz
14.46 a) 0.39H,0.10piF
b) | V W 1 = \V m ^\ = 0.707|Vpeak|,
I^TTOHJ = I ^ W l = 0.948|Kpcak|
c) [VUWHJ = 0.344|V pcak |
14.47 L = 0.225 H , C = 0.057/AF, 0.344|Vrpcak|
14.48 63.7 times as large as the DTMF tones
Chapter 15
15.6 a) R { = 67.16 ft, R 2 = 212.21ft
b)
+ •
»i
750 nF
67.16(1
•
212.21 ft
^ ^ _
^>
b - " ^
15.10 a) R x = 5.10 kft, R 2 = 25.55 kft b)
5.10kn 3^f
• VA | ( 1
T
-VW
25.55 kH
v ^ ^
15.15 a) 1 H , I F , 0.05 ft b) 2.5 H, 250 pF, 5 kft c) 250 pF
2.5 H
O V A
5kn
15.16 a) 1/0 F
(1/0*
b) - ,
S 2 + (1/(2)5 + 1
c) 10 kft, 6.4 H, 250 pF u) # 1L
e-wv-v-250 pF 6.4 H
10 kft:
s 2 + 1562.5.9 + 625 X 106
15.30 f cl = 38.52 Hz, f c2 = 1038.52 Hz,
R L = 30.65 ft, R H = 826.43 ft
15.31 R L = 21.18 kft, R H = 1.18 kft;
if Ri = 1 kft then R f = 6 kft
15.36 a) 3 b) -32.65 dB 15.38 a) First-order stage: 79.58 nF;
second-order stage: 151.15 nF, 39.79 nF
Trang 2b)
2V,
'77
79.58 nF
lkU
— V A —
1 + 2 Y — H=I 1 - 4«
- COS 110)()1 V
lkft
• — W W
+
I I
i k n lkft
39.79 nF ;±T
V V
) v in Y i,
— + - ^ - sina>0/ +
7T
2K
—— T^ r cos Hunt V
7 7 «=2A6 1 " « 2
~ cos (nojj)
15.39 a) First section: 3.05 kH, 20.77 kft;
second section: 7.35 k i l , 8.61 kil
b)
3.05 kO
+— I M I (
-10 nF -10 nF
: 7.35 kO
H H H f
-10 nF -10 nF
I
15.60 a) R = 5305 £l,aR = 10,478X1,
(1 - a)R = 133 ft, C = 15 nF,2C = 30 nF
b)
15 nF 15 nF
^ It
2 + 4 X 1 0 V
s 2 + IOOTT.? + 4 X l O V
15.61 C = 39.79 nF, |H(/w)L« = 20-01 dB,
|#07#A)I = 17.04 dB
15.62 Choose i?! = 100 k i l , then R 2 = 400 kft,
C, - 7.96 nF
Chapter 16
v 4K
16.1 a) y\ — sin nct)1 U t V
77 «=fe "
^ , 160 _ 320
16.2 + 20 sin a U
16.3 a) to (m = 31,415.93 rad/s,w„b = 157.08 krad/s b) /„a = 5000 H z , /o b = 25 kHz
c) a m = 0, a vb = 25 V d) %a = 0 for A: even;
«>ta = -—j- sin — for fc odd;
240
bk& = 0 for A: even; b k A = — - for k odd
irk
a kb = — - sin —— V for all k; b kb = 0 for all k irk 4
e) v a (t) =
80 £ ( 1 nir 3 \
— Y — sin —- cos «tt„f H— sin nwj V
""«=UAA * 2 " J
/ N _ 200 " (\ nir \ „
v b (t) = 25 + >j — sin —— cos nioj V
16.11 a) 27rrad/s b) yes c) no d) no 16.12 a) 62.5 Hz b) no c) yes d) yes e) yes
f) a v = 0; a k = 0 for all k;b k - 0 for k even;
0.16 kit
ov = -, -, sin —— for k odd
77½ 2 4
~ V ( « T T ) 2 + 4
16.22 a) 10 2 — — 2 cos (nco Q t - 6 n ) A,
«=1.3.5
d„ — tan" mr
b) 26.23 A
Trang 316.27 a) 41.998 cos(2000f - 0.60°) +
13.985 cos(6000f + 177.32°) +
5.984 cos( 14,0001 - 175.83°) V
b) The 5th harmonic at 10 krad/s is eliminated by
the bandreject filter whose center frequency is
10 krad/s
16.28 26.83 cos(500/ + 63.43°) + 16.64 cos( 1500/
-146.31°) + 11.14cos(2500r + 21.80°) V
16.34 a) 59.46 W
b) 60 W
c) - 0 9 0 4 1 %
16.35 1.85 W
16.36 a) 74.5356 V ( r m s )
b) 74.5306 V ( r m s )
16.39 a) 117.55 V ( r m s )
b) - 2 0 4 %
c) 69.2765 V ( r m s ) , - 0 0 0 8 1 %
V V
b)
|C
1
<
o
>
1
10 *
f 9
8
7
6
5
4
3
2
1
i
— i
-•
« i
<
i
—•—
i
!
- 3 - 2 - 1 0 1 2
d„(dcg)
135
90 f45
16.45 C„ = ^ C - / n ± 1 , ± 2 ,
6.46 a) 480 W
b) 68.58 V
c) - 2 0 2 %
.6.49 a)
\
20
18
16
14
12
10«
8
6
4
2
f)
(V)
— <
>
-i
i >
t >
i
—o—
1
- 7 - 6 - 5 - 4 - 3 - 2 - 1 ¢ 1 2 3 4 5 6 7
-«1-1
-90 -135
0 t (dcg)
135
90
45
L
16.50 a) A a (mA)
200
150
100
50
0
180 90.56 38-2 2603 19 1 15.4 12.73
T T f • j
0 u>„ 2<o (| 3o> (( 4o) (] 5a)„ 6a>„
0°
«0)„
0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8
140 122.48°
120
100
80
60
40
20
0
101.98° 9 7 26°
0 OJ 2(o„ 3o)„ 4o) 5o) 6&>„
Trang 4b)
I C, | (mA)
200
180
13.02
n c ^ 19-1 6.37 7.7 9.55 •
t f T T I
100
45.28 45.28
13.02 19.1 9-55 7.7 6.37
0 y.DO 7.7 6
1 T y y t
- 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6
150
- 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6
• • •
-90° - 9 0 ° • - 9 0 °
-97.26° -101.98°_ 12 2.48'
122^48° 101.98° 97.26°
90° • 90° 90°
1 150
Chapter 17
17.1 a) /
b) 0
c)
2A COT C O S ( W T / 2 ) — 2 sm(cor/2)
of
-20 - 1 5 - 1 0 10 15 20
17.2 a) co n A
4TT
sin(w,//4)
(co n t/4)
b) 79.58 X l ( T f t v 4
c)
, 2 ( « z - co 1 )
17.5 a) \ ^
« — co
b) -/48fl(o
; y ( a 2 + co 2 ) 4
+
a 2 + (co - co a ) 2 a 2 + (co + co 0 ) 2
—ja ja
a 2 + (co - co a ) 2 a 2 + (co + co 0 ) 2 e) e- JMt "
sin
17.19 a)
(co + COQ)T/2 sin
+
(&j - co () )r/2
2 (co + co 0 )(r/2) 2 (co - CO 0 )(T/2)
17.20 a) 6e~ 50( u(t) m A
b) Yes, check t h e initial conditions a n d final values 17.28 a) [ 1 2 5 e- / - 7 5 e " 5 /] « ( 0 + 5e 5 'u(-t) V
b) 5 V
c) 5 V
d) (12.5<T' -1.5e- 5t )u(t)V
e) Yes 17.30 l c o s ( 5 0 0 0 f + 90°) A
17.40 a) [ - 2 4 e ~ ' + 32e~ t/2 ]u(t) + 8e'u(-t)V
b)
•5 - 4 - 3 - 2 - 1 0
Trang 5c)
- 5 - 4 - 3 - 2 - 1 0 1 2
d) 900 J
e) 320 J
f) 95.95%
g) 99.75%
Chapter 18
18.2 y n = 168.75 mS; y l2 = -156.25 mS;
y 2l = -156.25 mS;y22 = 218.75 mS
18.3
18.8
18.13
18.14
18.29 18.30
18.34 18.40
Zn = 13ft;z1 2 = 12 H;
22i = 12ft;z2 2 = 16 ft
flU = - 4 X 10~4;a12 = - 2 0 ft;
a 21 = -0.5fxS;a 22 = -0.02
g u = 12.5 fiSlgn = 1*5;
g 2l = -250;g2 2 = 50Mft
a) y n =2QfiS;y u = 30nS;
y 2l = 5/LIS;>?22 = 20 nS
b) y n = 20MS;)/12 = 30nS;
y 21 = 5/xS;y 22 = 20 nS
12.5 a) 28V(rms) b) 11.20mW c) 2.88 /xW
4 2 0 M W 3.75 V
Trang 6Index
a-, b-, and c-phase current and voltage, 400,419
Acceptance ratings, 367
Active filter circuits, 558-603
bandpass filters, 566-570,585-588,594
bandreject filters, 570-573,585,588-591,594
bass volume control, 559,591-593
block diagrams, 567-568
Bode plots, 560-563
broadband filters, 567-573,594
Butterworth filters, 578-586,594-595
cascading identical filters, 574-577,594-595
first-order, 560-564
higher-order, 573-591,594
high-pass filters, 562-563,585,594
low-pass filters, 560-562,578-584,594
narrowband filters, 586-591,595
op amp filters, 560-586,594
prototype filters, 561-566,594
scaling, 564-566,594
Adjoint of a matrix, 715-716
Admittance (Y), 324,347
Ammeter, 66-67,76
Amplifier circuits, 98-99,105-106,118-119,144-173,
241-244,246,289-293
analysis of, 98-99
integrating, 241-244,246,289-293
mesh-current method for, 105-106
node-voltage method for, 98-99
operational (op amp), 144-173
responses and, 241-244,246,289-293
Thevenin equivalent in, 118-119
Amplitude modulation, 659
Amplitude plots, 742-747,751-754
Amplitude spectrum, 630-632,647-648
periodic functions described using, 630-632
transition from periodic to aperiodic, 647-648
Analog meters, 67,76
Aperiodic functions, Fourier transform, 644,646-648,672
Apparent power, 370,386
Attenuation, defined, 522
Average power (P), 363-367,373-375,380-382,386,
410-411,415-417,419,623-627,635
acceptance ratings, 367
calculations of, 363-367,373-375,386
Fourier series analysis for, 623-627,635
maximum power (Pm a x) transfer, 380-382
measurement of, 415—417
periodic functions, calculations with, 623-627,635
power factor (pf), 365,386 sinusoidal steady-state analysis for, 363-367,373-375,386 three-phase circuits, 445-446,452-454
two-wattmeter method, 415-417,419 wye (Y) connected loads, in, 410-411,419
B
Balanced three-phase circuits, 398-427 average power in, 410-411,415-417,419 circuit symbols for, 401^102,407
complex power in, 411,419 conditions for, 403
delta (A) connected loads,411—413 designing characteristics of, 398,419 electrical power, transmission and distribution of, 399, 418-419
instantaneous power in, 412,419 line current, 405
line voltage, 404-405 neutral terminal for, 401 phase current, 405 phase voltage, 405 power calculations in, 410-415 single-phase equivalent circuits and, 403-404,419 sinusoidal voltage phases for, 400-401,419 sources of three-phase voltage, 401-402 unspecified loads, 414
voltages (v), 400-405
wye (Y) connected loads, 410-411,413 wye-delta (Y-A) circuit, analysis of, 407-409 wye-wye (Y-Y) circuit, analysis of, 402-407 Bandpass filters, 525,536-545,551,566-570,585-588,594 active filter circuits, 566-570,585-588,594
bandwidth (/3), 537,539-540,551 broadband, 567-573,594
Butterworth, 585 cascading, 567-570 center (resonant) frequency (w„), 536-540,551 cutoff frequency (o»c) 538-540
frequency response plots, 525,537 narrowband, 586-588
operational amplifier (op amp), 566-570,585,594 passive filter circuits, 525,536-545,551
qualitative analysis, 537-538 quality factor (Q), 537,540,551,586-587 quantitative analysis, 538-544
relationship between frequency and time domains, 545
series RLC circuit as, 537-545 transfer function H(s) for, 544,551
781
Trang 7Bandreject filters, 525,545-549.551,570-573,585,
588-591,594
active filter circuits, 570-573,585,588-591,594
Butterworth filters, 585
cascading, 570-572
cutoff frequency (o) c ), 547-548
frequency response plots, 525,546
narrowband filters, 588-591
operational amplifier (op amp) filters, 570-573,585,594
passive filter circuits, 525,545-549,551
qualitative analysis, 546
quantitative analysis, 546-548
series RLC circuit as, 546-549
transfer function H(s) for, 549,551
Bandwidth (/3), 537,539-540,546-548,551
Bass volume control, 559,591-593
Black box, 58
Black box amplifier, 679,697
Block diagrams, 567-568
Bode plots, 560-563,741-757
amplitude, 742-747,751-754
complex poles and zeros, 749-751
correcting, 752-754
frequency response, 560-563
phase angle, 747-749,755-757
real, first order poles and zeros, 741-742
straight-line amplitude, 742-746,752-754
straight-line phase angle, 747-749
Branch, defined, 90-91
Broadband filters, 567-573,594
Butterworth filters, 578-586,594-595
bandpass, 585
bandreject, 585
design of circuits, 579-582
high-pass, 585,594-595
low-pass, 578-584,594-595
order of cascading, 582-584
transfer function H(s), 578-579
C
Capacitance (C), 174,182,203
circuit parameter of, 174,182,203
displacement current, 182
terminal equations for, 182-186,203
Capacitors, 174,182-189,203,319-320,469-470,498-499,506
current (/), 182-185,203
displacement current, 182
energy (iv), 184-186,203
frequency domain, 319-320
impulse function (/) in, 498-499
Laplace transform used for, 469-470,498-499,506
power 0),183-186,203
.v-domain, 469-470,506
series-parallel combinations, 188-189,203
switching operation, 498-499
terminal equations for, 182-186,203,469-470,506
voltage (v), 183-186,203 voltage to current (v-i) relationships, 183,319-320
Cascading active filters, 567-570,574-577,594-595 bandpass, 567-570
bandreject, 570-572 Butterworth, 582-584,594-595 identical lowpass, 574-577,594-595 order of, 574-575,582-584,594-595 Cascading connections, 289-293,297 Center frequency (a>„), 536-540,546-548,551 Characteristic determinant, 706
Circuit analysis, 10-11,30-33,37-45,47^18,71-73,76, 88-143,466-521,689-693
conceptual model, 10-11 delta to wye (A to Y) transformations, 71-73,76 dependant-source circuits, 42-45
ideal circuit components, 11
impulse function K8(t) in, 498-504,506
Kirchhoff s laws, 37-41,48,471 Laplace transform in, 466-506 maximum power transfer, 120-122,129 mesh-current method, 90,99-109,129 node-voltage method, 90,93-99,106-109,129 nonplanar circuits, 90-91
Norton equivalent, 115,129 Ohm's law, 30-33,47-48,470-471 physical prototype, 11
planar circuits, 90-91 .y-domain, 470-489,506 sensitivity, resistors, 89,125-128 simultaneous equations for, 91-93 source transformations, 109-113,129 superposition, 122-125,129,482-484 terminology for, 90-91
Thevenin equivalent, 113-119,129,479-480
transfer function H(s) in, 488-497,506
two-port circuits 689-693 Circuit theory, 6-7
Circuits, 2-87,212-305,398-427,488-489,522-603,
678-703 See also Amplifier circuits; Circuit analysis;
Equivalent circuits; Ideal basic circuit elements active filter, 558-603
balanced three-phase, 398-427 constant (dc) sources, 56 current (/),11-12,37-42 dependent sources, 26-27,29,42-45 electrical engineering and, 2-8 electrical resistance, 30-33 electrical safety of, 25,46-74 energy and, 14-17
first-order, 212-263 frequency-selective, 522-603 ideal basic elements, 12-14,24-55 International System of Units (SI) for, 8-10 Kirchhoff s laws, 37-^J-l
models of, 10-11,17-18,34-36 Ohm's law, 30-33
Trang 8open,35
parallel-connected (in parallel), 59-61,76
passive filter, 522-557
passive sign convention, 13
power (/;) and, 14—17
resistive, 56-87
responses of, 212-305
second-order, 264-305
series-connected (in series), 39,58,76
short 35
time invariant, 488-489
two-port, 678-703
variables of, 2-23
voltage (v), 11-12
Coefficient of coupling, 197,204
Common mode input, 156-157
Common mode rejection ratio (CMRR), 157-159,164
Complex numbers, 725-730
arithmetic operators, 727-728
graphical representation of, 726-727
integer power of, 729
notation, 725-726
roots of, 729-730
useful identities of, 728-729
Complex poles and zeros, 749-751
Complex power (5), 370-374,386,411,419
Component values, 763
Conductance (G), 31
Constant (dc) sources, 56
Controlled sources, 27
Convergence of Fourier integral, 648-650
Convolution, 489^195,506,659-660
Fourier transform of, 659-660
integral for transfer function and, 489-495,506
Cosine function, Fourier transform of, 654-655
Cramer's method,706
Critically damped responses, 269,277-278,283,286,297-298
Current (i), 11-13,26-29,37-41,47-48,66-69,147-149,
164,177-179,182-185,203,214-216,308-309,347,400,
405,419
a-, b-, and c-phase, 400,419
capacitors, 182-185,203
defined, 11-12
displacement, 182
electric charge and, 11-13
inductors, 177-179,203
input constraints, 147-148,164
Kirchhoff s law (KCL), 37-41,48
line, 405
measurement of, 66-69
operational amplifiers (op amps), 147-149,164
RC circuits, deriving expression for, 214-216
reference direction, 13
sinusoidal source, 308-309,347
sources, 26-29,47
terminal variables, 147
Current coil, 415
Current-divider circuits, 63,76 Current-division circuit analysis, 64-66,76 Current ratios, transformers, 340-342
Current to voltage (i-v) relationships, 177-179,182-183
Cutoff frequency (toc), 524-525,527-528,533,538-540, 547-548,550
bandpass filters, 538-540 bandreject filters, 547-548 bandwidth, relationship to, 539 center frequency, relationship to, 538-539 defined, 524-525,527,550
half-power frequency, 528 high-pass filters 533 low-pass filters, 527-529
D
Damped radian frequency ((o (i ), 274-275
Damping factor (coefficient), 275 d'Arsonval meter movement, 67-68 Decibel (dB), unit of, 739-740 Delta (A) interconnection, 71 Delta (A) connected loads, 411-413 Delta-to-wye (AtoY) equivalent circuits, 71-73,76 Delta-to-wye (A toY) transformations, 326-328 Dependent sources, 26-27,29,47,95-96,102-103 analysis of circuits with, 95-96,102-103 ideal circuit elements of, 26-27,47 interconnections of, 47
mesh-current method for, 102-103 node-voltage method for, 95-96 Derivatives of impulse functions, 435 Derived units, 9
Determinants, 706-709 Difference-amplifier circuit, 155-159,164 common mode input, 156-157
common mode rejection ratio (CMRR), 157-159,164 defined, 164
differential mode input, 156-157 Differential mode input, 156-157 Differentiation, operational transforms for, 438-439,658 Digital meters, 67,76
Direct approach, step response analysis, 281-282 Direct current (dc) sources, 56
Dirichlet's conditions, 607 Displacement current, 182 Dot convention, 190-192,195-196,204,341-342 ideal transformers, 341-342
mutual inductance (M), 190-192,195-196,204 Dual in-line package (DIP), 146
E
Effective value, see Root-mean-square (rms)
Electrical circuit, defined, 6 Electrical engineering, 2-8 circuit theory, 6-7
Trang 9Electrical engineering (Continued)
communication systems, 4
computer systems, 4
control systems, 4-5
overview of, 4-8
power systems, 5
problem solving, 3,7-8
role of, 2
signal-processing systems, 5-6
Electrical power, transmission and distribution of, 399,
418-419
Electrical safety and, 25,46-74
Energy (w), 14-17,179-181,184-186,197-200,203-204
capacitors, 184-186,203
inductors, 179-181,203
mutual inductance and storage of, 197-200,204
power and, 14-17
Equivalent circuits, 71-73,76,113-119,129,159-162,
329-332,479-480,731-738
delta to wye (A to Y), 71-73,76
frequency-domain, 329-332
ideal transformers for, 731,735-738
Laplace transform analysis of, 479-480
magnetically coupled coils and, 731-738
Norton, 115,129,329-330
operational amplifier (op amp), 159-162
7r-equivalent, 732-735
pi to tee (77 to T), 71-73
source transformations, 115-116,329-332
T-equivalent, 731-732
Thevenin, 113-119,129,329-332,479-480
transformation of, 71-73,76
Even-function symmetry, 611-612,634
Exponential form of the Fourier series, 627-629,635
F
Faraday's law, 193-194
Farads (F), unit of, 182
Feedback, op amps, 147-148,164
Feedback resistors, 291-293,297
Filters, 522-523,550 See also Frequency-selective circuits
Final-value theorem, Laplace transform, 455-457
First-order active filters, 560-564
First-order circuits, 212-263
defined, 212,214,246
flashing light, 213,245-246
general solutions for, 231-236,246
integrating amplifier, analysis of, 241-244,246
natural response of, 212,214-224,231-236,246
resistor-capacitor (RC), 212,214,220-224,229-236,
239,246
resistor-inductor (RL), 212,214-220,224-228,
236-238,246
sequential switching, 236-240,246
steady-state response of, 217
step response of, 212,224-236,246
unbounded response of, 240-241,246
Flashing light circuit, 213,245-246 Fourier series, 604-643
amplitude spectrum, 630-632 analysis, 607-608
application of, 619-623 average-power calculations, 623-627,635 coefficients, 607-616,634
Dirichlet's conditions, 607 exponential form of, 627-629,635 fundamental frequency, 607,634 harmonic frequency, 607,634 periodic functions and, 604-607,611-616,619-627, 630-632,634-635
phase spectrum, 630-632 root-mean-square (rms) value, 626-627,635 square wave input of sinusoids, 605,632-634 steady-state response, 619-627,635
symmetry and, 611-616,634 trigonometric form of, 617-618,634 waveforms, 604-606
Fourier transform, 644-677 amplitude spectrum transition, 647-648 aperiodic functions of, 644,646-648,672 circuit applications of, 661-663
convergence of Fourier integral, 648-650 cosine function, 654-655
defined, 646 derivation of, 646-648 elementary functions, 655 integral, 646-650
inverse, 647 Laplace transforms used to find, 650-653 mathematical properties of, 655-657 operational, 657-661
Parseval's theorem, 664-672 signum function, 653 sinusoidal steady-state response using, 663 telephone line frequency response, 645,672 time-domain functions of, 648-650,672 transient response using, 662
unit step function, 654 Frequency ( / ) , defined, 7 Frequency domain, 312-322,329-343,441,531,545,659-660 convolution in, 660
defined, 313 delta-to-wye (A to Y) transformations, 326-328 Fourier transform and, 659-660
impedance (Z), 320,322-332,336 Kirchhoff s laws, 321-322
Laplace transform and, 441 mesh-current method, 333-334 node-voltage method, 332-333 Norton equivalent circuit, 329-330 operational transforms of, 441,659-660 passive-filter circuits and, 531,545 phasors, 312-317,347
reactance, 320 sinusoidal steady-state analysis and, 312-322,329-343
Trang 10source transformations and, 326-332
Thevenin equivalent circuit, 329-332
time domain, relationship to, 531,545
transformers, 334-343
translation in, 441,659
voltage to current (v-i) relationships, 317-320
Frequency regions, 530
Frequency response, defined, 522
Frequency response plots, 524-525,560-563
Bode plots, 560-563
magnitude plot, 524-525
phase angle plot, 524-525
Frequency scaling (kf), 564,594
Frequency-selective circuits, 522-603
active filter circuits, 558-603
attenuation, 522
circuit symbols for, 524
filters, 522-523,550
passive filter circuits, 522-557
Functional Laplace transforms, 431,436^-37,459
Fundamental frequency, Fourier series, 607,634
G
Gain (A), 147,151
Graphical representation of complex numbers, 726-727
H
Half-power frequency, 528
Half-wave symmetry, 613-614,634
Harmonic frequency, 607,634
Heating appliances, 361,384-385
Henrys (H), unit of, 176
High-pass filters, 524-525,532-536,551,562-563,585,
594-595
active filter circuits, 562-563,585,594
Butterworth, 585,594-595
cutoff frequency (co c ), 533
frequency response plots, 524-525
operational amplifier (op amp), 562-563,585,594
passive filter circuits, 524-525,532-536,551
qualitative analysis, 532-533
quantitative analysis, 533-536
series RC circuits, 526-532
transfer function H(s) for, 536,551
Higher-order active filters, 573-591,594
Household distribution circuit, 307,346
Hybrid parameters, two-port circuits, 683
I
Ideal basic circuit elements, 12-14,24-55,174-211
active, 27
capacitors, 174,182-189,203
closed loop (path), 38,48
current (/), 26-29,37-42
dot convention, 190-192,195-196
electrical resistance, 30-33 electrical safety and, 25,46-74 inductors, 174,"l76-182,187-200,203 mutual inductance, 176,189-200,203-204 nodes, 37-38,48
passive sign convention, 13,176 passive, 27,176,203
polarity reference, 190-196 proximity switches, 175,200-202 reference direction, 13
resistors, 30-33,47-48 self-inductance, 176-182,193-194,196-197,203 series-connected (in series), 39
series-parallel combinations, 187-189,203 sources, 26-29,42-45,47
terminal equations for, 176-186,203
voltage (v), 26-29
Ideal transformers, 335,338-343,347,383-384,731-738 dot convention for, 341-342
equivalent circuits in, 735-738 frequency domain and, 334-343 impedance matching using, 343 limiting values of, 338-340 magnetically coupled coils and, 338,731-738 maximum power transfer with, 383-384 polarity of, 341-342
properties of, 338 sinusoidal steady-state analysis, 335,338-343,347 voltage and current ratios, 340-342
Identity matrix, 714-715 Ignition circuit, 265,294-296 Impedance (Z), 320,322-332,336,343,347,380-381 admittance ( Y), 324,347
combined in series and in parallel, 322-326 delta-to-wye (A to Y) transformations, 326-328 frequency domain source transformations, 326-332 matching using ideal transformers, 343
maximum power transfer with restricted, 380-381 Norton equivalent circuit, 329-330
reflected (Z,),336,347 susceptance, 324 Thevenin equivalent circuit, 329-332
voltage to current (v-i) relationships, 320
Improper rational function, 444,453^154,459 Impulse, defined, 433
Impulse function KS(t), 433-435,459,498-504,506
capacitor circuit analysis and, 498-499 circuit analysis using, 498-504,506 circuit symbols for, 498
defined, 433-434 derivatives of, 435 inductor circuit and, 499-501 Laplace transform and, 433-435,459,498-504,506 moment function (unit doublet), 435
sifting property, 434 sources, 501-504
strength (K) of, 433
switching operations for, 498-501,506