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TRANSCRIPT
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2005.6
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RC -------------------------------13
RC -------------------------------21
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1.
2.
3. !"#$%&
1.'( )*+,(-./012345#$6789:;< )(tu => )(ti ? @A0B3C45 t#$8!"DEFGHIJ45KLH#$MNOPH!QMRSTUVWFG?#$8XY'(Z245'( [./\]2Y^>\7=_`abcNde\7f= @A0BcNde\7gh9TFGab8@AcN\7ghicNjklamb8XY'(Z2cN'( nop45'(8[pcN'(8-qrstuv7
2.\] wxVWyz|~.8)*deVW8A-./\]2Y^>\7=!S!!\7 :YVW! )(tf ./\]2 ⋅⋅⋅⋅⋅⋅++++= ttttE
tf 1111 7sin7
15sin
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1sin
4)( ωωωω
π :1-1(a)g1 b8!S!\7l./YVW!8:1-1(b)g1 8 ¡¢yz|£
(a) (b) 1-1
3.¤¥\ B¦§¨©8RC.¨ª¤\«¬¥\«8®!"#¯ °¤\« :1-2g1
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1-2 RC wxo.
dt
duRCuuuu c
cRc +=+=1 ± RC=τ ²G48 cuu ≈1 8dt
duRCuu R
12 ≈= ³´ )(2 tu ´µ )(1 tu ¶·¸¤\¹º8g/»Z2¤\« ±´µ )(1 tu 2¼"VW½¾48 )(2 tu !":1-3g1 ¿´!"./À8´<ÁÂÃÄÅÆ8ÇÃÄMROP¡¢45Èτ ±¼"½¾ÉRÊτ EFËÊ`8Ìτ ÊG48g"ͽ¾ÎÏÍÐ
1-3 RC Ñ¥\« :1-4g1
1-4 RC wxo.
dtuRC
uuuu RRcR ∫+=+= 11 ± RC=τ ²F48 Ruu ≈1 8 ∫≈= dtu
RCuu c 12
1 ³´ )(2 tu ´µ )(1 tu ¶·¸¥\¹º8g/»Z2¥\« ±´µ )(1 tu 2¼"VW½¾48´ )(2 tu !":1-5(a)g1 ¿´!"./À8´<ÁÂÒÓÅÆ8ÇÒÓMROP¡¢45Èτ ±¼"½¾ÉRÊτ EFËÊ
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`8Ìτ EÊG48g"½¾ÒÓÔÎÏÕÖ8X4´´µ!"ÎÏm· ±¼"½¾ÉRÊτ EG8Ìτ ÊF48g"½¾×ÔÎÏØÙ8X4´2YÚÛ! :1-5(b)g1
(a) τ (b) τ 1-5 RC
4. @A./\2Ü";YpbcNdeVWÝÞpabcNdeVWÝwxo.8×ßàá2bcNdeVW8p!D=mâãs#$ àßà 2deVW8XYäåæB\]f©ªçè é5.ê ÜB4ëê8ìȨíî8³YïðîñY6Y7 íîBìò맨Èóô :¨Yõcde!ïðîñYcNÊödeDE8 Y÷Díî8øZíD! :1-6g1 ¿1-6©./À8åíî÷Dqùú"û=õcde!pütYý õcde!Z2íî öcde!Z2þ!8ÇcNZ2þ!cN íD!m·8[./íc!Hím!=½¾íî!?
1-6
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∫∫ −=−=tt
zs dhtxdthxty00
)()()()()( ττττττ l.2
)()()( thtxty zs ∗= ã8쥥\åæap ª8!./"Ë#$R %»84ë¥\Bº\©Ë&sóô§¨ 1.! °' 1-7g18wxyz|~8() *+!) 1V <i,E¡ 4V8cN 1f ¡ 10Hz8mâ¡ 0 ѨMatlab-!"8!.7!"DE=VW /0 ); =1V =3V =5V =7V =9V cN; =1f =3f =5f =7f =9f !; =RmV =T !!!!"#$%&'()*+,&'(-"#$%&'()*+,&'(-"#$%&'()*+,&'(-"#$%&'()*+,&'(-....
1-7
2.bcN °' 1-8g18!() ѨMatlab-!"8!.7!"DEHVW=mâ /0 ; =RmV =T =ϕ
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1-8
3.abcN °' 1-9g18!() ѨMatlab12!"8!.7!"3FDE=VW /0 ; =RmV =T
1-9
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(a) (b) 1-11 ѨMatlab´!"#$ !.7ͽ¾!"ÃÄÔÉR /9#:EFG8¨1!«´!"#$8!.7ͽ¾!"ÃÄÔÉR8;0x<µ02-2 §=>© 2-2 C=10mF
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1.wxg@,x8ABY´CúYVW!"
2.DE45!=?ã½¾©´F¹º
3.GHIJ
1.KL4ë'(
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3.KLHOP8Matlab12
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1.VWcQ'(
2.cRÉRMN
3.ST!"#$ cQ%&
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1.VWcQ wxyz\.8)*YdeVW8A-./\]2Y^>\7=_`abcNde\78BYde\7gh9TUab 2sV^8VW¸01YVW©qriXYcN\7=cN\7gh9TFG8¨KR!÷DFGm §ú8'cNöõZ[\]^_8ÎË&sVW÷DcQÝ:`ZcN\7ml¨m §ú\]^_8ÎË&sVWmâcQ :;YVW¼"½¾ )(tf 8Ç!": 2-1g1
2-1 ! Ç©; A2¼"½¾DE8τ 2¼"½¾ÉR8T 2¼"½¾VW )(tf BYVWO0a2 =0
)(A
tf é é2222
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t
<<−<<−
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ττ
ττ Çyz|~2 += ∑∞=1
11
1 cos2
2sin21)(
n
tnn
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Atf ω
τωτωτ
Ç©b n!÷D2Tn
Tn
T
Acn πτ
πττ sin2= ± τ5=T 48./ËÇ÷DcQ: 2-2g1
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2-2 ¿ 2-2./À8VW÷DcQci/Ãd'ä bY8cQpaeJúf8BYúg0Yde\78³cQcihi( bÞ8cQBQú-jB!cN 1ω cNÒ8³cQci!( b48QúöR8l³!÷Dkp3C!lömnoGݱ!nplö48!\7÷DqÎnprG8³cQcist( ¿÷DcQ
Tn
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2-3 b8±T Ea#89#τ E48!cNT
πω 21 = a#8g/Qú5w¬zxlaJ9# p83Cτ oG8÷D2!cN
τπ2 H
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2.VWcRÉR ¿oÒv8VW(!\7pnp` g¡!\7Ï`8_à!"Ï~¶!" p8A`!\78aJB ª©²F8̦ÒlpaA %2!÷Dcist(8³j7@Au\y©Bõc\7©8g/!öY\78¦ÒåæiTA8¿./a X8B¦ ª©8AÊõYu\!\7Î#s Y8¿cN~&A3ö\7cN5XYcNjk8Z2i,hicR8qZcRÉR8¬ZcÉ B¨©8 qùú2cQ8ÈÈZ¿~&cQqùúbYäcNf5cRª2cRÉR YcQ8lÈ/¿cN~&cQ÷Dqùú3FE10
1 cNf5cR,2cRÉR aË8±½¾τ EoG48cRÉRτπ
ω2=B lFs8cRÉROgqr!lls : 2-3©g1
3.dȨcQ °de!cQ de! ttf Ω= sin)( 8: 2-4(a)g1Ý Ç÷DcQ: 2-4(b)g1
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(a) (b) 2-4 Ñde÷DíîcQ deíî ( ) ttmAtf 0coscos1)( ωΩ+= 8: 2-5(a)g1 Ç© A2÷DE8 1≤m 2÷Díîº8
Ω2íî¬åíîdeqùúcN8 0ω 2þ!cN8 Ω>>0ω ÝÇ÷DcQ: 2-5(b)g18¿÷DcQ©./À8åíîde )(tf Bcë©qr 0ω þ!cN\7H( Ω−0ω )Ãc\7=( Ω+0ω )Òc\7 2-4(b)m98RvíîcQ¿ÊõcNΩ&ÊöcN 0ωÒ
(a) (b) 2-5 /÷½¾cQ de÷Díîm·8¨Yõc½¾ïðîYöcde!8./Ë&: 2-6(a)g1÷½¾8Ç÷DcQ: 2-6(b)g1
(a) (b) 2-6
1.VW½¾cQ °' 5-7(a)g18' 2-7 (b)(86Matlab-®`2´!
(a) (b) !"#$
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2-7 29#Matlab-(8; 2-7 (b)©ã«cNFrequency92 2Hz8h79Duty
cycle92 20%Iτ Ea#8Ça# VWcQxRHcQDR#$ 2sW9Ê8.;cQ3FR2 90Hz
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2-9 !"#$
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(a) (b) !"#$
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2-10 /¥~¦\Analysis§¨8©ª¦yz\Fourier Analysis”«¬8' 5-11(à8¦®¯Simulate”'°8cQ\ !"# !"# !"# !"#$$$$
2-11 %&'()!"#$
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2.0Matlab´cQ
1.KLVWcQ\
2.KLVWcQ'(ScRÉRMN
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RC
1. RCDc'(.78s] Dc'(%&
2.ºn±¯´
3.º\º²³
1.ºcN'( eJ LTI ºcN'(øZcN&§'(8pºBdeô&§3cN#$#$µ¶8øZº )(ωH Yûú(º8: 3-1g1
)(ωH)(ωX )(ωY
3-1 LTI*+,
Ǻ )(ωH ,2
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)()(
ωωω
X
YH = © )(ωX 2º·#¯8 )(ωY 2ºBûô&§·#¯ º )(ωH 8u¸sºOB¹i'(8¡¢ºº»¼SfºF«8½un¹8p¾Eº'(YTA )(ωH pωU8./012
)()()( ωϕωω jeHH =
(Gain) -. (Phase) / -. 3-2 0123 -.
Ç©;² )(ωH 3ω#$ÅÆZ2ºDc'(Ý¿5 )(ωϕ 3ω#$ÅÆZ2ºmc'(
cN'(aÀ.¨0a018[.¨3cN f (¬ω )#$Cú¾E8: 3-2g1 ±cN'(CúÁ¨ ¾E48øZ2!'8: 6-3g1
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(Gain) -. (Phase) / -. 3-3 0123 4" -.
2.RCõìÂ!Dc'(
RCõìÂ!: 6-4g1
Ǻ2
)()(
)(
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=+
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+=
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3-4 0 RC12356
± 0=ω 48 1)( =ωH 8 0)( =ωϕ ݱτ
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1)( =ωH 8 o45)( −=ωϕ ݱ ∞→ω 48 0)( →ωH 8o90)( −→ωϕ
Dc'(0Ã8 bFG´µ8cNÏö8´ÄoÏFÝcNÏõ8´ÄoÏG¬./Å2nÄo lÎpv8 Æ28õc9ÊPÇì8öc aPÇì8%»XZ2õìÂ!« ¿Dc'(Cú[./À8±Dc'(ÃÄ&3FE2
1 ±Á¨!'01Dc'(483FEÃÄ 3dB8g §cN2RCc
1=ω (¬ cf )8È[Z cω (¬ cf )Z2ÉÊcN ZcN¿ 0 & cω (¬ cf )jkZ2ìcRÉ ωΒ (¬ fB ) ì48:`cN\7ÄoDRab8JË_cN\7m DRã#$8X±¯Z
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2DR±¯Ý:`cN\7macNd98JË_cN\7m â(ã#$8X±¯Z2mⱯ ¿ 3-5a©./À8cN2 50Hz= 150HzÜde\7pB RCõìÂ!«cRÉRO8cN2 300Hzde\7pYB RCõìÂ!«cRÉR½ ±X4àì 3-5ag1õìÂ!«à8./À´!"ås±¯ : 3-5bg18©1v 2´µ8 2v 2´
a RC b RC 3-5 ¿º5RÀ8 3-42YY̺8ÌciYÍäRC
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3-9 RC
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Ò4Ó<«(;' 3-12( XÁ¨ÔÅE Ç© Input A offset voltage
(VAOFF)01«´µ A Ó<8E8 Input B offset voltage (VBOFF)01«´µ BÓ<8E8 Input C offset voltage (VCOFF)01«´µ CÓ<8EÝ Input A gain (KA)01«´µ A ÓlÕ8 Input B gain (KB)01«´µ BÓlÕ8 Input C gain (KC)01«´µ CÓlÕÝ Output gain (KOUT)01«´ÓlÕ8 Output offset voltage (VOOFF)01«´Ó<8E ÒE(0Ã8Æ«´µÓ=´Óa ÖF=^>\7
3-12 23*4567%89
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3-14 < =67%89
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3-16 $%!>7%89?@# 3-17H 3-18 ©g1 Integrator stage initial conditions (VINT)01¥\«ÌEÝDenormalized corner frequency (W)01ußÅà$5cNÝ Numerator 3rd order coefficient (A3)01º\á`£ 3£º8Numerator 2nd order coefficient (A2)01º\á`£ 2£º8 Numerator 1st order coefficient (A1)01º\á`£ 1£º8 Numerator constant (A0)01º\á`£È£Ý Denominator 3rd order coefficient (B3)01º\â`£ 3£º8 Denominator 2nd order coefficient (B2)01º\â`£ 2£º8 Denominator 1st
order coefficient (B1)01º\â`£ 1£º8 Denominator constant (B0)01º\â`£È£ HBÒE(48§±wxcI9#º\áH\â`£º8ÇÁ¨ºÔÅE
3-17 $%!>7%89A 3-18 $%!>7%89B ÑTUHOP 1© Ñ8!;º<µ0 4-3 §=>©
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1.ãAHOP 1© °Dc'(Cú8ÉÊcNä
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A1
0 = U 023 == BB Q11 =B Q
RCB
10 = j
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RC
1. RC
2. !
3."#$%&
1.' () LTI '*+',-./012345678,94523':;<:;=>*+? )(ωH @ABCD8EFG 3-1HI
)(ωH)(ωX )(ωY
3-1 LTI #
J? )(ωH KLM
)(
)()(
ωωω
X
YH = NO )(ωX M4523PQR:S )(ωY M/CD8TU6V,23PQR:S ? )(ωH WXY/Z[\]^@_`abcdefgU$hi45j-klABmn )(ωH -ωo?pqrIM
)()()( ωϕωω jeHH =
(Gain) q (Phase) r 3-2
JOs% )(ωH 9ω:;tu+Mvwx )(ωϕ 9ω:;tu+My
'zp|?rNrI~p|9' f (ω ):;EklFG 3-2HI 'E|kl*+MGFG 6-3HI
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(Gain) q (Phase) r 3-3 ?%
2.RC
RCFG 6-4HI
J?M
)()(
)(
1
1
1
1
)(
)()( 1
2
21
2 ωϕωωωωω
ωω ∠=−∠+
=+
== − HRCtg
RC
RC
RCj
RCV
VH
NO2
2
)(
1
1
)(
RC
RCH
+=
ωω +M RCtg ωωϕ 1)( −−= +My'EFG 3-2HI
3-4 RC*+
0=ω 1)( =ωH 0)( =ωϕ vτ
ω 11 ==RC
2
1)( =ωH o45)( −=ωϕ v ∞→ω 0)( →ωH o90)( −→ωϕ
r@23'V23v'V23pqM-<23 <23z ¡¢B+Mg £E~pq¤V6¥¦§¨2
1 ©ª|GrI«§¨6¥ 3dB¬H,'MRCc
1=ω ( cf )®¯ cω ( cf )+M°±'¯'£ 0 ¦ cω ( cf )²³+M´µ ωΒ ( fB ) 23 F¶·'"¸z¹º»·'"y¸¼½:;¢¾+
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M¸vF¶·'"y¿z$'e0¹º»·'"yÀÁ¼½:;¢¾+MyÀ £G 3-5ªa¬Opq¤V'M 50Hz 150HzÃB01"-/ RCg´µ¸Y23<'M 300Hz01"-AB/ RCg´µ¸h23¢ÄB23ÅÆÇÈe23 G 3-5ªa¬HIgÇpq¤VV23ÉÊVËFG 3-5ªb¬HIGO1v M23 2v MV23
a RC b RC 3-5 £x¸¤G 3-4MABAÌÍÎ[ABÏÐRC
p1−= CÐFG 3-6HI£JC Ñ Ï Ð " Ò p q ¤ V M A B 7 K J ' F G
4-2HI
ωj
pσ
0
pj +ω
6-6 S |G 3-7%&ÓGpqÔ¦ÕlAÌ%&|G 3-8?%&ÓGpqÔ¦ÕlAÌ%&
RCs
RCsH
1
1)(
+=
)(1 sV )(2 sV
3-7 !"# 3-8 $%!"#
1.RC
Ö×G 3-9(ØÙÚÁv|ÛÜÝ'EÙ°±' cf
Þß:à RÜÝ'E:;Ùáa¶âr 4-1,ãäO
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3-9 RC
& 4-1
)(ΩR )(Hzf c )(HzB f
10
100
1000
å×G 3-10(ØÙÚÁ|IgÜÝÉËæ
3-10 '()*+
2.|çèiU%&AÌg Ö×G 3-11(ØÙéêG 3-9ÚÁ
3-11 , -./0!"1
çèiUÚÁ∗×6ëìíîï
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ðÄñòÆ gÚÁs×G 3-12ÚÁ¢Q|ó¨JO Input A offset voltage
(VAOFF)rIÆ g A ñòôõ¨ Input B offset voltage (VBOFF)rIÆ g Bñòôõ¨ Input C offset voltage (VCOFF)rIÆ g Cñòôõ¨v Input A gain (KA)rIÆ g A ñö÷ Input B gain (KB)rIÆ g Bñö÷ Input C gain (KC)rIÆ g Cñö÷v Output gain (KOUT)rIÆ gVñö÷ Output offset voltage (VOOFF)rIÆ gVñòôõ¨ÕlÚÁrÆ g·BñÂVñz23ø½ùÂúû"
3-12 23*4567%89
üý"gÚÁs×G 3-13ÚÁJO gain (K)rIý"gVö÷v Input offset
voltage (VIOFF)rIý"gñòôõ¨v Output voltage lower limit (VL)rIý"gVò6þ¨ Output voltage upper limit (VU)rIý"gVòÕþ¨v upper and lower limit smoothing
range (VS)rIý"gÕÑ6þ¨²³v Output initial conditions (VOIC)rIý"gVTUè/ÕlÚÁ,éêÎ!ß:ý"gVö÷J\|ó¨
3-13 :;7%89 gÚÁs×G 3-14ÚÁJLpÕl
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3-14 < =67%89
ÞmoY 1OìíÞÙáâr 4-2,ãäO
& 4-2
)(ΩR )(Hzf c )(HzB f )/( VVA )( VVK
10
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1000
3.|?%&AÌg Ö×G 3-15(ØÙéêG 3-9ÚÁ?v
3-15 , $%!"
?%ÚÁ×6ëìíîï /G 3-16HIÓO 3ªModels¬ªEdit¬××G 3-17ÑG3-18ÚÁ¢Q|ó?%
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3-16 $%!>7%89?@# G 3-17ÑG 3-18 OHI Integrator stage initial conditions (VINT)rIý"g̨vDenormalized corner frequency (W)rIWt;x'v Numerator 3rd order coefficient (A3)rI?"N 3Numerator 2nd order coefficient (A2)rI?"N 2 Numerator 1st order coefficient (A1)rI?"N 1 Numerator constant (A0)rI?"Nv Denominator 3rd order coefficient (B3)rI?" N 3 Denominator 2nd order coefficient (B2)rI?" N 2 Denominator 1st
order coefficient (B1)rI?" N 1 Denominator constant (B0)rI?" Nè/ÕlÚÁ,éêÎ!ß:?"Ñ" NJ\|ó¨
3-17 $%!>7%89A 3-18 $%!>7%89B ÞmoY 1OìíÞÙá?âr 4-3,ãäO
& 4-3
)(ΩR )(Hzf c )(HzB f 1A 0A 1B 0B
10
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1.!"#VY 1OìíÖEV°±'Ð
2.$VEÑ°±'Ñ´µ¸$j
1.%& RC'ÐÑ°±'Ñ´µ¸'()
2.%&%&c?'()
3.%&YOH*|ÛgÂ+,gU*|
∗ -./07%89CDEF
GH:;*+ 6-4IJKL
)()()(
212 tvtvdt
tdvRC −= M N?O -./0:;PEQRS ∫= dttvAtv io )()( T
dt
tdv
Atvi
)(1)( 0= UN?O< =6PEQRS )()( tKvtv io = UGH !"# 6-7VWKL
)()()(1
212 tKvtvdt
tdv
A+= X YZ!" [\LRS]^X_`a b;]^McQdeZ !"f:;gh
RCA
1= Q< =6ghi 1−=K j
∗∗ $%7%89CDEF
GH:;*+ 6-4IJKLk $%i
RCs
RCsH1
1
)(+
= l N $%m)nJ2 ioi
012
23
3
012
23
3)(BsBsBsB
AsAsAsAsH
++++++
= p YZ!" $%p_`a $%lcQdeZ!" $%Xf% 0123 === AAA QRC
A1
0 = U 023 == BB Q11 =B Q
RCB
10 = j
∗
∗