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Ng33̙f@8\ g4BdBd@:A 0ppp@ <4ddl$ 0\.g4:d:d@:A 0p@ pp<4BdBdl$ 0\.D ʚ;ʚ;<4ddddlT# 0Xj0___PPT10 *___PPT9 z? %O =Dependent Sources ReviewOUndergraduate Students: Amy Parker & Stephen Lopez Advisor: Dr. David Binkley(P3Dependent SourcesHDependent SourcesDependent Source Example 1SDependent SourcesVDependent SourcesWDependent Source Example 2\  ` 3ffffƍ` 3f3fff̙3ff̙` ______` 3f33>?" dZ@$3?lKd@  l@ P`lA n?" dd@   @@``PP   @ ` `p>> {  (    Tf3??#" `@pFF  "0 t  0f3#" `t  0f3#" `"  <̋G0*"  @   B0 ?"@  T Click to edit Master title style! !$  0  "@  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S3   ` ??"    }E 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVEDFF&dF  "p 0t"   0G3#" `r B T3??"`f  C 0Abottom logo"HB  s *޽h ? 3f3fff̙3ff̙y___PPT10Y+D=' = @B + Capsules  P  B(     6f3#" `p  @ "  <LG0*"pp  @   < "4    W#Click to edit Master subtitle style$ $vF     "  z"  B 6G3#" ` R r   Z3??#" `L  3   `) ??"   }E 2002 University of North Carolina at Charlotte, ALL RIGHTS RESERVEDFF&    `P ??"NnR  T Click to edit Master title style! !f  C 0Abottom logo"\  C &Acrown2"RB  s *޽h ? 3f3fff̙3ff̙y___PPT10Y+D=' = @B + 0,(  , , 0Pw P   w X*  , 0Lw    w Z*  , 6lw _P  w X*  , 6w _  w Z* H , 0޽h ? 3380___PPT10.jipl @#(  x  c $ NnR  x  c $h 0p      TD' ?? 0   g)University of North Carolina at Charlotte"*(2*f3H  0޽h ? 3f3fff̙3ff̙y___PPT10Y+D=' = @B + ?  p#(   "  fAp 3? ??v4 8 3$D 0x  c $0a'@  ' c  Tb' ??@ ,$ 0 sDependent sources generate voltages or currents proportional to other voltages or currents appearing in a circuit. t 2t  Zg' ??,$ 0 D For example,  2 "  Zk' ?? # ,$  0 d,One type of dependent source is shown above.- 2-   Z@p' ??f,$ 0 XVs: 2 1   Zu' ?? X ,$ 0 sRin: 2 $   Z{' ??x,$  0 fEVin, 2    T' ?? ,$ 0 RDependent current sources appear in most three and four terminal semiconductor devices, such as BJT s and MOSFET s.t 2t,`  Z' ?? ,$ 0 ?+ - 072ffd  Z' ?? ) ,$ 0 <Notice, this voltage source is controlled by the voltage Vin,= 2: 92   ` ?? ,$D  0+  Ttm' ??  ,$  0 s-(A Voltage Controlled Voltage Source - VCVS) *.(2,   Tp' ??P ,$  0 eVin,(2   T' ?? ,$  0 G+* 2  T' ?? m ,$ 0 H -* 2O  T0' ?? ` ,$ 0 AE designates the voltage gain. The VCVS is denoted as E in Spice.:B(2 ?F H  0޽h ? 3f3fff̙3ff̙**___PPT10p*+`DD'' = @B D&' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(Dq' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*"D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*"D' =-g6B fade*<3<*"D ' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*D_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(++0+' ++0+' ++0+' ++0+ ' ++0+ ' ++0+ ' ++0+' ++0+' ++0+' ++0+' ++0+' ++0+' ++0+' ++0+' +@?  .,%(  ,b ,,  A<sP ,$D 0x , c $*@  ' t , T' ??j@ p,$ 0 There are three other types of dependent sources that appear in circuit analysis. The next one to be discussed is a current source.  2 , Z' ??p,$ 0 @Observe,  2   , TD' ??,$ 0 :Both of these dependent sources are voltage controlled. Let s take a look at an example of the voltage controlled current source. 2a  , Z' ?? Sk ,$ 0 9This current source is also controlled by the voltage Vin,: 27 6* !, ZT' ??  ,$  0 l4 The second type of dependent source, shown above...5 25B ", # lD3fjJ?? ,$@  0# #, Z' ??c ( ,$  0 eRin, 2 C $, ZH' ??,$  0 GmVinJ 2   %, Z(' ??3!S,$ 0 JVs, 2 2 &,  ` ??,$D  0) ', TT' ??  ,$  0 q-(A Voltage Controlled Current Source - VCCS) (.(2,  (, Tq ??c p ,$ 0 eVin,(2  ), Tq ?? u ,$ 0 G+* 2 *, T q ??S : ,$ 0 I -* 2 +, Tq ?? ` ,$ 0 BGm designates a transconductance gain and is shown as G in Spice pC(2  &F    -, Ttq ??@: ZContinued& *  2 f3H , 0޽h ? 3f3fff̙3ff̙S*K*___PPT10+*+XD7'' = @B D&' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(Dd' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*,,%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*,,D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*,,D' =-g6B fade*<3<*,,Dr ' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%,%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(,%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*),%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<**,%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*",%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$,%(D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*!,%(D' =-6B'blinds(horizontal)*<3<*!,D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*',%(D' =-6B'blinds(horizontal)*<3<*',D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*+,%(D' =-6B'blinds(horizontal)*<3<*+,D_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*&,%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*&,D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*&,DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(++0+,q ++0+,q ++0+ ,q ++0+ ,q ++0+!,q ++0+#,q ++0+$,q ++0+%,q ++0+',q ++0+(,q ++0+),q ++0+*,q ++0++,q +ƀ  |%t%' %( 0   %0 # 0e0eAw  ?A@ A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?P  H  $@ 0 q 0 # 0e0eAr  ?A@ A5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?^  H  $D 0 6  Tl@q ?? P  ,$ 0 ~HNext, determine the easiest method of analysis and write your equations.I 2Ix  c $Cq@  q k  TDFq ?? @ r,$$ 0 qNotice, this current source is voltage controlled. Dependent sources can be either current or voltage controlled.&r 2qB   `D??z0 ,$D 0  TWhere, 2  Tq ??P p,$# 0 Req = R1R2/(R1+R2) 2     2   ` ??  ,$D  0#   ZPq ??@ ` ,$ 0 eRin, 2  ! Zܦq ??,$ 0 JVs, 2  " T\q ?? p* ,$ 0 eVin,(2  # Tlq ??u~,$ 0 G+* 2 $ Tq ?? ,$ 0 I -* 2 ' T|q ?? P 0@ ,$  0 gReq = R1//R2 (1)8 2 H  0޽h ? 3f3fff̙3ff̙ZZ___PPT10Z+\XDT' = @B DT' = @BA?%,( < +O%,( < +D&' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =%( D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =%( D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =%( Dc' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(|D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(Dg' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*Du' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<* %(D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D+' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*%D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*%D' =-g6B fade*<3<*%D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%( DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D#' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(++0+q ++0+q ++0+q ++0+q ++0+q ++0+q ++0+q ++0+q ++0+q ++0+q ++0+ q ++0+ q ++0+ q ++0+ q ++0+q ++0+q ++0+q ++0+q ++0+q ++0+q ++0+q ++0+ q ++0+!q ++0+"q ++0+#q ++0+$q ++0+'q +?<  @F(  @b @  A<1 ,$D 0x @ c $ds@  s M @ Ts ??@ ,$ 0 ]The next type of dependent source to be discussed is the current controlled voltage source. ^ 2^ @ Z s ??@d,$ 0 @Observe,  2 l @ Ts ??@,$ 0 |This dependent source is the first of two current controlled sources. The last type is similar but offers a current output. } 2}\ @ Z s ??  ,$ 0 4This voltage source is controlled by the current Iin,5 22 1 @ Zs ??  ,$  0 ^& The current controlled voltage source' 2'+ @ Ts ??  ,$  0 s/(The Current Controlled Voltage Source - CCVS) (0(2.  @ T"s ??  ,$  0 KH designates the transresistance gain. The CCVS is denoted by H in Spice. ^L(2  =F  , @ T*s ??@: ZContinued& *  2 f3 @ Z,/s ???p,$ 0 XVs: 2 1 @ Z(5s ??( ,$ 0 sRin: 2 $ @ Z,:s ??P-p,$  0 fHIin, 2  @ Zt>s ???@p,$ 0 ?+ - 072ff2 @  ` ??P@,$D  0 @ T@Cs ?? ,$ 0 KIin,(2 B @ ZD?? p p ,$@   0H @ 0޽h ? 3f3fff̙3ff̙1)))___PPT10 )+cDM&' = @B D&' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(Dz' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*@D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*@D' =-g6B fade*<3<*@D ' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-o6Bwipe(up)*<3<*@D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-6B'blinds(horizontal)*<3<*@D_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*@D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*@DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(++0+@s ++0+@s ++0+@s ++0+@s ++0+@s ++0+@s ++0+@s ++0+@s ++0+@s ++0+@s ++0+@s ++0+@s +;  VND(  Db D  A<1 ,$D 0x D c $,ns@  s = D Tos ??@,$ 0 MThe Last of the dependent sources is the current controlled current source. N 2N D Zts ??@d,$ 0 @Observe,  2 r D THxs ??@`,$ 0 Let s take a look at a current controlled current source example.B 2B\ D ZD}s ??  ,$ 0 4This current source is controlled by the current Iin,5 22 1& D Zs ??  ,$  0 h0 The last current controlled dependent source...1 21+  D THs ??  ,$  0 s/(The Current Controlled Current Source - CCVS) (0(2. t  D T s ?? ` ,$  0 BF designates the current gain. The CCCS is denoted as F in Spice ^C(2  3F    D TԒs ??@: ZContinued& *  2 f3  D ZLs ???p,$ 0 XVs: 2 1  D Zs ??X ,$ 0 sRin: 2 $ D Zs ??P-p,$  0 fFIin, 2 2 D  ` ??P@,$D  0 D Ts ??P ,$ 0 KIin,(2 B D ZD??  ,$@  0B D # lD3fjJ??P,$@  0H D 0޽h ? 3f3fff̙3ff̙((___PPT10(+qTD@&' = @B D%' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(Dm' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*DD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*DD' =-g6B fade*<3<*DD{ ' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* D%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-o6Bwipe(up)*<3<*DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* D%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-6B'blinds(horizontal)*<3<*DD' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* D%(D' =-6B'blinds(horizontal)*<3<* DD' =%(D' =%(DT' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<* D%(D' =-6B'blinds(horizontal)*<3<* DD_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*DD' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*DDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(+h+0+Ds ++0+Ds ++0+Ds ++0+Ds ++0+Ds ++0+ Ds ++0+ Ds ++0+ Ds ++0+ Ds ++0+Ds ++0+Ds +w  "" HH"(  H6 H Ts ?? P  ,$ 0 ~HNext, determine the easiest method of analysis and write your equations.I 2I H0 # 0e0eAr  ?@ 5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?^P H  $@ 0 s H0 # 0e0eAw  ?@ 5%8c8c     ?1d0u0@Ty2 NP'p<'p@A)BCD|E?P  H  $D 0 sx H c $s@  s B H  `D??z0 ,$D 0 H Ts ??p p ,$ 0 cReq* 2   H Ts ?? P  ,$ 0 RHere we see R1 and R2 can be combined and simplified to form a new resistance Req.tS 2   :   H Tls ??j@p,$ 0 JGiven: The circuit pictured below with Iin appearing in a separate circuitHK 2#  '!<  H TWhere, 2 H T#w ??P p,$" 0 Req = R1R2/(R1+R2) 2     2 H  ` ??  ,$D  0# H Z0/w ??  * ,$ 0 eRin, 2  H Z`4w ??,$ 0 JVs, 2  H T09w ?? p* ,$ 0 eIin,(2  H T=w ?? P 0@ ,$ 0 gReq = R1//R2 (1)8 2 B H ZD??@@@` ,$@  0H H 0޽h ? 3f3fff̙3ff̙SS___PPT10S+KDnN' = @B D)N' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* H%(Dv' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*HD' =-g6B fade*<3<*HD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bwipe(up)*<3<*HDc' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<* H%(D' =-o6Bwipe(up)*<3<* HD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* H%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* H%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(Dg' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* H%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*HD' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*HD' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<* H%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*H%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*H%(D' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*H%(D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*HD' =-g6B fade*<3<*HD' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*HD' =-g6B fade*<3<*HD' =%( DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*HD' =-g6B fade*<3<*HD' =%( D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*H%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*H%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<* H%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*H%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D#' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(+@+0+Hw ++0+Hw ++0+ Hw ++0+ Hw ++0+ Hw ++0+ Hw ++0+ Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw ++0+Hw +Hfx\%h]$;MwwwwRo)uoB{w{oߛ̛߷{2;۽[oC/iV謿6g6[? 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