%PDF-1.1 %âãÏÓ 1 0 obj << /Producer (\376\377\000A\000c\000r\000o\000b\000a\000t\000 \000D\000i\000s\000t\000i\000l\000l\000e\000r\000 \0003\000.\0000\0001\000 \000f\000o\000r\000 \000W\000i\000n\000d\000o\000w\000s) /Creator (Microsoft Word 8.0) /ModDate (D:19990903190059) /Author (Burford J. Furman) /Title (Basic Electronics Solutions) /CreationDate (D:19990903190059) >> endobj 3 0 obj << /Length 7668 >> stream 1 1 1 rg BX /GS1 gs EX 1 0 612 792 re f BT /F3 1 Tf 14.04 0 0 14.04 229 737.278 Tm 0 0 0 rg 0.002 Tc -0.004 Tw [(Bas)6(ic E)6(l)-2(ec)10(tr)10(on)6(ic)10(s So)6(lu)6(t)6(i)-2(o)6(n)6(s)]TJ /F4 1 Tf 9 0 0 9 72.04 38.28 Tm 0 Tc 0 Tw (\323)Tj /F3 1 Tf 0.7867 0.0043 TD 0.005 Tc -0.002 Tw [(B)5(J)7( Fur)5(m)23(a)9(n)-12442(B)5(a)9(s)7(i)3(c)9( Ele)9(c)9(t)3(r)5(onic)9(s)7( Sol)16(u)-2(ti)16(ons)7(.)15(doc)-13098(Se)9(pte)9(m)23(be)9(r)5( 3, 19)12(99)]TJ 12 0 0 12 72.04 703.332 Tm 0 Tc (1.)Tj /F6 1 Tf 0.75 -0.011 TD 0 Tw ( )Tj /F3 1 Tf 0.75 0.011 TD (4R)Tj -1.5 -1.65 TD (2.)Tj /F6 1 Tf 0.75 -0.011 TD ( )Tj /F3 1 Tf 0.75 0.011 TD (102R)Tj -1.5 -1.65 TD (3.)Tj /F6 1 Tf 0.75 -0.011 TD ( )Tj /F3 1 Tf 0.75 0.011 TD 0.003 Tc (R/2)Tj -1.5 -2.33 TD 0 Tc (4.)Tj /F6 1 Tf 0.75 -0.011 TD ( )Tj ET 0 0 0 RG 1 J 1 j 0.48 w 10 M []0 d 1 i 92.08 638.64 m 143.08 638.64 l 155.92 638.64 m 167.92 638.64 l S BT /F3 1 Tf 12 0 0 12 169.84 635.64 Tm (R)Tj -1.16 -0.78 TD (11)Tj -0.04 1.41 TD (10)Tj -2.53 -1.41 TD 0.002 Tc (1R)Tj -0.87 0 TD 0 Tc ( )Tj -1.69 0 TD 0.001 Tc (10R)Tj -0.14 1.41 TD -0.001 Tc (\(10R\)\(1R\))Tj /F4 1 Tf 4.48 -0.63 TD 0 Tc (=)Tj -2.42 -0.78 TD (+)Tj /F3 1 Tf -3.78 -2.31 TD (5.)Tj /F6 1 Tf 0.75 0 TD ( )Tj ET 92.08 601.56 m 99.28 601.56 l S BT /F3 1 Tf 12 0 0 12 101.2 598.56 Tm (R)Tj -0.7 -0.78 TD (3)Tj 0 1.41 TD (2)Tj -1.73 -3.71 TD (6.)Tj /F6 1 Tf 0.75 0 TD ( )Tj ET 0.24 w 106.24 562.8 m 93.16 544.44 l 133.96 562.8 m 120.88 544.44 l 167.44 562.8 m 154.36 544.44 l S 0.48 w 92.08 564.6 m 176.92 564.6 l 189.88 564.6 m 199.84 564.6 l S BT /F3 1 Tf 12 0 0 12 192.04 552.24 Tm (2)Tj -0.11 1.41 TD (R)Tj -2.41 -2.06 TD 0.002 Tc (2R)Tj -0.54 0.77 TD 0 Tc (1)Tj -2.25 -0.77 TD 0.002 Tc (2R)Tj -0.54 0.77 TD 0 Tc (1)Tj -1.09 -0.25 TD ( )Tj -0.68 -0.52 TD (R)Tj -0.54 0.77 TD (1)Tj 3.11 1.29 TD (1)Tj /F4 1 Tf 4.07 -0.63 TD (=)Tj -2.93 -0.91 TD (+)Tj -2.79 0 TD (+)Tj /F3 1 Tf -3.3 -2.84 TD (7.)Tj /F6 1 Tf 0.75 0 TD ( )Tj ET 121.48 519.6 m 168.4 519.6 l S BT /F3 1 Tf 12 0 0 12 187.12 516.6 Tm (V)Tj -0.52 0 TD (6)Tj -2.62 -0.78 TD (10k)Tj -2.37 0 TD (10k )Tj 1.18 1.41 TD (10k)Tj -1.61 -0.63 TD (\))Tj -0.75 0 TD (V)Tj -1.01 0 TD (12)Tj -0.25 0 TD (\()Tj /F4 1 Tf 6.66 0 TD (=)Tj -2.49 -0.78 TD (+)Tj /F3 1 Tf -5.81 -1.62 TD (8.)Tj /F6 1 Tf 0.75 0 TD ( )Tj /F3 1 Tf 0.75 0 TD (Voltage divider)Tj -1.5 -1.65 TD (9.)Tj /F6 1 Tf 0.75 0 TD ( )Tj /F3 1 Tf 0.75 0 TD [(Short the voltag)10(e)4( sour)-7(ce, a)-6(nd cal)-12(culate the Th)-10(evenin r)-7(e)4(sistance. )-10(I)13(t)-2( turns out to simpl)-12(y)20( be th)-10(e)]TJ 0 -1.15 TD [(parallel combination of two 10 k r)-7(e)4(sistors, henc)-6(e the output impedanc)-6(e)4( is 5k.)]TJ -1.5 -1.65 TD (10.)Tj /F6 1 Tf 1.25 0 TD ( )Tj /F3 1 Tf 0.25 0 TD [(F)6(i)-2(nd the input impedance b)-20(y)20( )-10(first combining)10( the two 30k )-10(resistors in series. Th)-10(e resultin)-10(g)10( 60k)]TJ 0 -1.15 TD -0.001 Tc 0.001 Tw [(resistance is now in pa)-7(rallel with 10k from the lowe)-7(r le)-7(g)9( of th)-11(e pair of 10k )-10(resistors. The)]TJ T* 0 Tc 0 Tw [(resulting)10( 8.6k r)-7(e)4(sistance is in seri)-12(es with the upper 10k r)-7(e)4(sistor. Thus the input impedance is)]TJ T* (18.6k.)Tj -1.5 -1.65 TD (11.)Tj /F6 1 Tf 1.25 0 TD ( )Tj /F3 1 Tf 0.25 0 TD -0.001 Tc 0.001 Tw [(Use superposition to solve this problem. F)5(i)-3(rst, imag)9(i)-3(n)-11(e)3( that the -5V nod)-11(e is instead conn)-11(ected)]TJ 0 -1.83 TD 0 Tc 0 Tw [(to g)10(r)3(ound. Calcul)-12(ate the volta)-6(g)10(e)4(, )-10(V)]TJ 8.04 0 0 8.04 258.28 349.644 Tm (a)Tj 12 0 0 12 261.88 351.24 Tm (. V)Tj 8.04 0 0 8.04 276.52 349.644 Tm (a)Tj 12 0 0 12 280.12 351.24 Tm (=)Tj ET 313 354.24 m 373.96 354.24 l S BT 12 0 0 12 407.08 351.24 Tm (V)Tj -0.98 0 TD (33)Tj -0.25 0 TD (.)Tj -0.5 0 TD (3)Tj -2.11 -0.78 TD (2k)Tj -1.98 0 TD (2k )Tj -1.95 0 TD (2k)Tj 2.94 1.41 TD (2k)Tj -1.95 0 TD (2k)Tj -1.53 -0.63 TD (\))Tj -0.75 0 TD (V)Tj -0.5 0 TD (5)Tj -0.32 0 TD (\()Tj /F4 1 Tf 7.39 0 TD (=)Tj -2.09 -0.78 TD (+)Tj -1.98 0 TD (+)Tj 0.99 1.4 TD (+)Tj /F3 1 Tf 6.47 -0.62 TD -0.002 Tc 0.002 Tw [(. Now repl)-14(ace t)-4(h)-12(e -5V)]TJ -27.32 -1.9 TD -0.001 Tc 0.001 Tw [(node, and ima)-7(g)9(i)-3(ne the )-10(+5V node is conn)-11(ected to )-10(g)9(r)2(ound. Cal)-13(c)3(ulate V)]TJ 8.04 0 0 8.04 421.6 326.844 Tm 0 Tc 0 Tw (a)Tj 12 0 0 12 425.2 328.44 Tm 0.001 Tc -0.001 Tw [(, it is a)5(g)1(a)5(i)-1(n a)5( simple)]TJ -27.93 -1.84 TD 0 Tc 0 Tw [(voltag)10(e)4( divide)-6(r. V)]TJ 8.04 0 0 8.04 176.92 304.764 Tm (a)Tj 12 0 0 12 180.52 306.36 Tm (=)Tj ET 220.36 309.36 m 281.44 309.36 l S BT 12 0 0 12 322 306.36 Tm (V)Tj -1.03 0 TD (67)Tj -0.25 0 TD (.)Tj -0.5 0 TD (1)Tj -2.69 -0.78 TD (2k)Tj -1.97 0 TD (2k )Tj -1.96 0 TD (2k)Tj 1.97 1.41 TD (2k)Tj -2.5 -0.63 TD (\))Tj -0.75 0 TD (V)Tj -0.5 0 TD (5)Tj -0.9 0 TD (\()Tj /F4 1 Tf 8.75 0 TD (-)Tj -0.78 0 TD (=)Tj -2.1 -0.78 TD (+)Tj -1.98 0 TD (+)Tj -3.54 0.78 TD (-)Tj /F3 1 Tf 11.68 0 TD 0.001 Tc -0.001 Tw [(. The)5( fina)5(l solution is)]TJ -20.28 -1.9 TD 0 Tc 0 Tw (V)Tj 8.04 0 0 8.04 98.68 281.964 Tm (a)Tj 12 0 0 12 102.28 283.56 Tm -0.001 Tc (=3.33-1.67=1.67V)Tj -2.52 -1.65 TD 0 Tc (12.)Tj /F6 1 Tf 1.25 0 TD ( )Tj /F3 1 Tf 0.25 0 TD -0.001 Tc 0.001 Tw [(Short the voltag)9(e)3( sour)-8(ces to )-10(g)9(r)2(ound, )-10(and cal)-13(culate the )-10(equivalent resistan)-11(ce fr)-8(om node a to)]TJ 0 -1.15 TD 0 Tc 0 Tw [(g)10(r)3(ound. )-20(I)23(t)-2( tu)-10(rns out to be 2k in parallel with 4k, which is 1.5k. Thus, the Th)-10(evenin equival)-12(e)4(nt)]TJ T* [(circuit is a 1.67V sourc)-6(e)4( in series )-10(with at 1.5k resistor.)]TJ -1.5 -1.65 TD (13.)Tj /F6 1 Tf 1.25 0 TD ( )Tj /F3 1 Tf 0.25 0 TD [(Reduce the probl)-12(em into a simple voltag)10(e)4( divide)-6(r b)-20(y)20( collapsin)-10(g)10( the uppe)-6(r loop. The)]TJ 0 -1.14 TD [(uppermost resistors combine in series to 3k )-10(and then c)-6(a)4(n be combined in p)-10(a)4(rallel with the)]TJ 0 -1.84 TD -0.001 Tc 0.001 Tw [(remaining)9( 2k into an )-10(equivalent r)-8(e)3(sistance o)-11(f)2( )]TJ ET 311.08 183.6 m 318.04 183.6 l S BT 12 0 0 12 319.96 180.6 Tm 0 Tc 0 Tw (k)Tj -0.69 -0.78 TD (5)Tj 0 1.41 TD (6)Tj 1.36 -0.63 TD -0.001 Tc 0.001 Tw [(. This resistance now forms )-10(a simple)]TJ -19.83 -2.58 TD [(voltag)9(e)3( divide)-7(r with the 10k resistor, hen)-11(ce, V)]TJ 8.04 0 0 8.04 312.16 148.044 Tm 0 Tc 0 Tw (a)Tj 12 0 0 12 315.76 149.64 Tm (=)Tj ET 0.24 w 349.72 137.16 m 356.8 137.16 l S 0.48 w 348.76 152.64 m 394 152.64 l S BT 12 0 0 12 427.84 149.64 Tm (V)Tj -1.01 0 TD (46)Tj -0.25 0 TD (.)Tj -0.5 0 TD (4)Tj -1.64 -1.29 TD (k)Tj -1.02 0 TD (10)Tj -1.34 0 TD (k)Tj -0.7 -0.78 TD (5)Tj 0 1.41 TD (6)Tj 2.5 1.29 TD (\))Tj -0.55 0 TD (k)Tj -1.02 0 TD (10)Tj -0.24 0 TD (\()Tj -1.29 -0.63 TD (\))Tj -0.75 0 TD (V)Tj -0.5 0 TD (5)Tj -0.32 0 TD (\()Tj /F4 1 Tf 6.08 0 TD (=)Tj -2.5 -1.29 TD (+)Tj /F3 1 Tf 5.95 1.29 TD (.)Tj -30.55 -3.65 TD (14.)Tj /F6 1 Tf 1.25 0 TD ( )Tj /F3 1 Tf 0.25 0 TD -0.001 Tc 0.001 Tw [(The cap)-11(acitanc)-7(e of c)-7(a)3(pa)-7(citors in parallel add, so C)]TJ 8.04 0 0 8.04 331.48 104.244 Tm 0.007 Tc [(e)18(quiv)]TJ 12 0 0 12 349.36 105.84 Tm -0.001 Tc (=11C)Tj -23.11 -1.65 TD 0 Tc (15.)Tj /F6 1 Tf 1.25 0 TD 0 Tw ( )Tj /F3 1 Tf 0.25 0 TD (8C)Tj ET endstream endobj 4 0 obj << /ProcSet [/PDF /Text ] /Font << /F3 5 0 R /F4 6 0 R /F6 7 0 R >> /ExtGState << /GS1 8 0 R >> >> endobj 11 0 obj << /Length 8857 >> stream 1 1 1 rg BX /GS1 gs EX 1 0 612 792 re f BT /F3 1 Tf 14.04 0 0 14.04 229 737.278 Tm 0 0 0 rg 0.002 Tc -0.004 Tw [(Bas)6(ic E)6(l)-2(ec)10(tr)10(on)6(ic)10(s So)6(lu)6(t)6(i)-2(o)6(n)6(s)]TJ /F4 1 Tf 9 0 0 9 72.04 38.28 Tm 0 Tc 0 Tw (\323)Tj /F3 1 Tf 0.7867 0.0043 TD 0.005 Tc -0.002 Tw [(B)5(J)7( Fur)5(m)23(a)9(n)-12442(B)5(a)9(s)7(i)3(c)9( Ele)9(c)9(t)3(r)5(onic)9(s)7( Sol)16(u)-2(ti)16(ons)7(.)15(doc)-13098(Se)9(pte)9(m)23(be)9(r)5( 3, 19)12(99)]TJ 12 0 0 12 72.04 701.172 Tm 0 Tc (16.)Tj /F6 1 Tf 1.25 -0.011 TD 0 Tw ( )Tj ET 0 0 0 RG 1 J 1 j 0.24 w 10 M []0 d 1 i 153.16 702.24 m 139.84 683.76 l 180.04 702.24 m 166.72 683.76 l S 0.48 w 138.76 704.04 m 193.48 704.04 l 206.32 704.04 m 218.32 704.04 l S BT /F3 1 Tf 12 0 0 12 220 701.172 Tm (C)Tj -1.14 -0.78 TD (11)Tj -0.04 1.41 TD (10)Tj -2.73 -2.06 TD 0.001 Tc (10C)Tj -0.43 0.77 TD 0 Tc (1)Tj -1.1 -0.25 TD ( )Tj -0.62 -0.52 TD (C)Tj -0.52 0.77 TD (1)Tj 1.84 1.29 TD (1)Tj -5.95 -0.63 TD (Cequiv)Tj /F4 1 Tf 8.75 -0.011 TD (=)Tj -3.26 -0.91 TD (+)Tj -2.37 0.91 TD (=)Tj /F3 1 Tf -4.76 -3.059 TD (17.)Tj /F6 1 Tf 1.25 -0.011 TD ( )Tj /F3 1 Tf 0.25 0.011 TD -0.001 Tc 0.001 Tw [(I)12(ndu)-11(ctanc)-7(e)3(s of inductors in seri)-13(es add, so )-10(L)]TJ 8.04 0 0 8.04 297.88 662.692 Tm 0.007 Tc [(e)18(quiv)]TJ 12 0 0 12 315.76 664.332 Tm -0.001 Tc (=11L)Tj -20.31 -2.33 TD 0 Tc (18.)Tj /F6 1 Tf 1.25 -0.011 TD 0 Tw ( )Tj /F3 1 Tf 0.25 0.011 TD -0.001 Tc 0.001 Tw [(The re)-7(ciprocal induct)-13(a)3(nces o)-11(f)2( inductors in par)-8(a)3(llel add, so L)]TJ 8.04 0 0 8.04 378.28 634.732 Tm -0.011 Tc [(eq)-33(u)-18(i)-17(v)]TJ 12 0 0 12 396.28 636.372 Tm 0 Tc 0 Tw (=)Tj ET 405.16 639.24 m 417.04 639.24 l S BT 12 0 0 12 418.96 636.372 Tm (L)Tj -1.16 -0.78 TD (11)Tj -0.04 1.41 TD (10)Tj -27.71 -3.72 TD (19.)Tj /F6 1 Tf 1.25 -0.011 TD ( )Tj ET 116.2 602.16 m 167.44 602.16 l S BT /F3 1 Tf 12 0 0 12 201.04 599.292 Tm (V)Tj -1 0 TD (78)Tj -0.25 0 TD (.)Tj -0.5 0 TD (2)Tj -2.01 -0.78 TD (M)Tj -0.43 0 TD (1)Tj -1.35 0 TD (k)Tj -1.51 0 TD (800)Tj 2.75 1.41 TD (\))Tj -0.92 0 TD (M)Tj -0.43 0 TD (1)Tj -0.25 0 TD (\()Tj -1.64 -0.63 TD (\))Tj -0.75 0 TD (V)Tj -0.5 0 TD (5)Tj -0.32 0 TD (\()Tj /F4 1 Tf 6.58 -0.011 TD (=)Tj -2.3 -0.78 TD (+)Tj /F3 1 Tf 22.9 -2.529 TD (a)Tj ET 0.72 w 411.76 559.2 m 411.76 551.76 l 416.08 549.96 l 407.68 547.68 l 415.72 545.4 m 408.16 547.2 l 416.08 544.92 m 407.68 542.76 l 415.48 540.36 m 408.04 542.16 l 415.96 540 m 407.56 537.72 l 415.48 535.44 m 407.92 537.24 l 411.64 525.12 m 411.64 533.28 l 415.84 535.08 l 296.56 559.8 m 317.32 559.8 l 317.44 559.8 m 319.12 564.12 l 319.24 564.12 m 321.4 555.72 l 323.68 563.64 m 321.88 556.08 l 324.16 564.12 m 326.44 555.72 l 328.72 563.64 m 326.92 556.08 l 329.2 564 m 331.48 555.6 l 333.64 563.52 m 331.96 555.96 l 412.24 559.68 m 335.92 559.68 l 335.92 559.8 m 334.12 564 l S BT 9.96 0 0 9.96 320.8 545.306 Tm 0.006 Tc (800k)Tj ET 413.14 560.4 m 413.14 560.4 l 413.14 561.129 412.522 561.72 411.76 561.72 c 410.998 561.72 410.38 561.129 410.38 560.4 c 410.38 559.671 410.998 559.08 411.76 559.08 c 412.522 559.08 413.14 559.671 413.14 560.4 c b* BT 9.96 0 0 9.96 268.48 538.586 Tm 0.004 Tc -0.001 Tw (+5 V)Tj ET 296.92 559.44 m 296.92 498.48 l S BT 9.96 0 0 9.96 421.96 539.186 Tm 0.006 Tc (1M)Tj ET 1 1 1 rg 306.64 529.68 m 306.64 529.68 l 306.64 534.88 302.447 539.1 297.28 539.1 c 292.113 539.1 287.92 534.88 287.92 529.68 c 287.92 524.48 292.113 520.26 297.28 520.26 c 302.447 520.26 306.64 524.48 306.64 529.68 c b* 296.92 498.48 m 412.48 498.48 l 411.88 498.48 m 411.88 525.48 l S BT 12 0 0 12 411.04 586.452 Tm 0 0 0 rg 0 Tc 0 Tw (B)Tj ET 238.24 576 m 237.88 576 l 237.88 575.64 l 238.6 575.64 l 238.6 576.36 l 237.52 576.36 l 237.52 573.12 l 238.24 573.12 l 238.24 576 l f 237.52 568.08 0.72 2.88 re f* 237.52 563.04 0.72 2.88 re f* 237.52 558 0.72 2.88 re f* 237.52 552.96 0.72 2.88 re f* 237.52 547.92 0.72 2.88 re f* 237.52 542.88 0.72 2.88 re f* 237.52 537.84 0.72 2.88 re f* 237.52 532.8 0.72 2.88 re f* 237.52 527.76 0.72 2.88 re f* 237.52 522.72 0.72 2.88 re f* 237.52 517.68 0.72 2.88 re f* 237.52 512.64 0.72 2.88 re f* 237.52 507.6 0.72 2.88 re f* 237.52 502.56 0.72 2.88 re f* 237.52 497.52 0.72 2.88 re f* 237.52 492.48 0.72 2.88 re f* 238.24 490.32 m 237.52 490.32 l 237.52 489.72 l 240.52 489.72 l 240.52 490.44 l 237.88 490.44 l 237.88 490.08 l 238.24 490.08 l 238.24 490.32 l f 242.68 490.44 2.88 -0.72 re f* 247.72 490.44 2.88 -0.72 re f* 252.76 490.44 2.88 -0.72 re f* 257.8 490.44 2.88 -0.72 re f* 262.84 490.44 2.88 -0.72 re f* 267.88 490.44 2.88 -0.72 re f* 272.92 490.44 2.88 -0.72 re f* 277.96 490.44 2.88 -0.72 re f* 283 490.44 2.88 -0.72 re f* 288.04 490.44 2.88 -0.72 re f* 293.08 490.44 2.88 -0.72 re f* 298.12 490.44 2.88 -0.72 re f* 303.16 490.44 2.88 -0.72 re f* 308.2 490.44 2.88 -0.72 re f* 313.24 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