!"##$%&'()&*"#+$,"&-$&-."&/0&12"+343$(&5'6&4788#","(-&9$2&$8&',8&3(87-&$:4"-&;$#-'<"&=>?@A&'()&3(87-&63'4&+722"(-&=0BAC&/.34&#'6&*3##&*'#D&-.2$7<.&)"-'3#")&+'#+7#'E$(4%&@10FG&43,7#'E$(4%&'()&2"'#H*$2#)&,"'472","(-4&-.'-&<2"'-#I&."#8&-$&2"3(9$2+"&-."&+$(+"8-4&"4-'6#34.")&3(&-."&$8&',8&>?@&'()&0B&#"+-72"C&&

J&

/."&)"-'3#")&+'#+7#'E$(&8$2E$(&$9&-.34&#'6&+'(&6"&)$("&6I&.'()%&67-&+'#+7#'E$(&-$$#4&47+.&'4&K'-.FLM&$2&GN+"#&+'(&."#8&<2"'-#IC&&

/."&43,7#'E$(&"N"2+34"4&+'(&6"&8"29$2,")&3(&'(I&@10FG&43,7#'-$2%&43(+"&/"N'4&0(4-27,"(-4&82$;3)"4&<"("23+&@10FG&,$)"#4&$9&-."&$8&',84&74")&3(&-.34&#'6C&!$*";"2%&-."&43,7#'E$(4&'2"&,$4-&+$(;"(3"(-#I&)$("&3(&/0OLH/0%&*.3+.&34&'&92""&@10FG&43,7#'-$2&';'3#'6#"&92$,&-."&/"N'4&0(4-27,"(-4&*"643-"C&/0OL&43,7#'E$(&4+.",'E+4&'2"&",6"))")&3(&-."&82"4"(-'E$(C&&&

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

S&

0(&"N8"23,"(-&J%&*"Y##&)"-"2,3("&-."&":"+-4&$9&>?@&'()&0B&3(&'&+32+73-&*."2"&-."&3(87-&2"434-'(+"%&Z0O%&34&"Q7'#&-$&[&$.,4C&

\&

P324-%&+'#+7#'-"&-."&"N8"+-")&-$-'#&$7-87-&;$#-'<"&)7"&-$&>?@&'()&0B&9$2&-."&+32+73-&4.$*(&."2"%&743(<&-."&-"+.(3Q7"4&'()&"Q7'E$(4&<3;"(&3(&-."&>?@&'()&0B&#"+-72"C&/'D"&($-"&$9&-."&]7,8"2&8$43E$(4&3(&-."&-'6#"C&^K1J\&'()&^K1J_&'2"&$8"(%&'()&^K1JV&34&+#$4")C&^K1JV&4.$2-4&-."&($(H3(;"2E(<&3(87-&$9&TV&-$&<2$7()%&+'743(<&Z0O&-$&6"&[&$.,4C&&F'#+7#'-"&-."&$7-87-&;$#-'<"&-*3+"&`&a24-&*3-.&-."&?1LSJJ&4"#"+-")&9$2&TV&'()&Tb%&-."(&*3-.&-."&?1LJccC&/."&)3:"2"(-&8'2',"-"24&$9&-."4"&$8&',84&*3##&<3;"&I$7&)3:"2"(-&2"47#-4C!&

_&

0(&$2)"2&-$&8"29$2,&-."&+'#+7#'E$(4%&I$7&("")&-$&D($*&-."&-I83+'#&'()&,'N3,7,&;'#7"4&$9&>?@&'()&0B&9$2&"'+.&$8&',8C&/.$4"&;'#7"4&'2"&<3;"(&."2"C&&&G(-"2&I$72&'(4*"24&3(&-."&-'6#"&'-&-."&6$d$,&$9&-."&4#3)"C&/."&4$#7E$(4&'2"&'#2"')I&82$;3)")&-$&'##$*&I$7&-$&+."+D&I$72&*$2DC&

V&

?("&3,8$2-'(-&8$3(-&-$&($-"&34&-.'-&0B&'()&>?@&+'(&6"&8$43E;"&$2&("<'E;"C&/.34&,"'(4&-.'-&-."2"&'2"&)3:"2"(-&8$44363#3E"4&9$2&-."&$7-87-&;$#-'<"&)7"&-$&>?@&'()&0B&*.3+.&,74-&'##&6"&+$(43)"2")C&&P324-%&+'#+7#'-"&ZeGf%&-."&"Q73;'#"(-&3(87-&2"434-'(+"%&-."(&,7#E8#I&ZeGf&6I&0B&-$&)"-"2,3("&-."&3(87-&;$#-'<"&)7"&-$&0BC&O"N-%&74"&-."&"Q7'E$(&>$7-&g&hJ%&<'3(&$9&-."&a24-&4-'<"%&E,"4&hS%&<'3(&$9&-."&4"+$()&4-'<"%&E,"4&-."&47,&$9&>?@&'()&>0B&-$&+'#+7#'-"&-."&-$-'#&$7-87-C&L<'3(%&-."2"&'2"&9$72&8$44363#3E"4C&13+D&-."&#'2<"4-&;'#7"C&&Z"8"'-&-."&4',"&4-"84%&743(<&-."&,'N3,7,&;'#7"4&3(4-"')&$9&-."&-I83+'#&;'#7"4C&/."&8#$-&$(&-."&6$d$,&4.$*4&-."&h'7443'(&)34-2367E$(&$9&8$4436#"&$7-87-&;'#7"4C&

b&

Z"8"'-&-."&4',"&82$+")72"&9$2&-."&?1LJccC&/."&)3:"2"(-&48"+3a+'E$(4&$9&-."&?1LJcc&*3##&<3;"&'&)3:"2"(-&$7-87-&;$#-'<"&2"47#-&3(&6$-.&-."&-I83+'#&'()&,'N3,7,&+'4"C&

i&

/."&("N-&4-"8&34&-$&27(&'&@10FG&43,7#'E$(&'('#I434&9$2&-."&-$-'#&MF&$7-87-&;$#-'<"C&/."&("+"44'2I&/0OLH/0&43,7#'E$(&4+.",'E+4&'2"&",6"))")&3(&-.34&4#3)"&4"-&`&43,8#I&)$76#"H+#3+D&-."&3+$(4&-$&$8"(&-.",C&G(472"&-.'-&-."&]7,8"24&'2"&4"-&+$22"+-#IC&0(&-."&?1LSJJ&+32+73-%&^K1J\&'()&^K1J_&'2"&$8"(%&'()&^K1JV&34&+#$4")C&0(&-."&?1LJcc&+32+73-%&^K1j&'()&^K1J[&'2"&$8"(%&'()&^K1JJ&34&+#$4")C&&/$&43,7#'-"&-."&$7-87-&;$#-'<"%&+#3+D&L('#I434&!&MF&L('#I434&!&F'#+7#'-"&($)'#&;$#-'<"4C&

c&

P$2&-."&?1LSJJ%&I$7&4.$7#)&<"-&'&2"47#-&$9&'2$7()&J\\CSc,>C&P$2&-."&?1LJcc%&I$7&4.$7#)&<"-&'&2"47#-&$9&'6$7-&HJ[Ci\,>C&

j&

K'D"&472"&-$&)34'6#"&-."&MF&8$*"2&4788#I&6"9$2"&4"k(<&78&-."&-"4-&1FBl&0(&-."&>32-7'#B"(+.&4$m*'2"%&+#3+D&-."&8$*"2&67d$(&3(&-."&MF&1$*"2&@788#I&'2"'&-$&-72(&$:&-."&8$*"2C&F."+D&-."&92$(-&8'("#&$9&-."&>32-7'#B"(+.&7(3-&-$&,'D"&472"&-."&5GM4&'2"&?PPl&L#4$&,'D"&472"&-.'-&-."&P7(+E$(&h"("2'-$2&34&?PPC&

J[&

/$&82"8'2"&-."&-"4-&6$'2)&9$2&-."&,"'472","(-%&3(4-'##&-."&]7,8"24&'()&)";3+"4&$(&+32+73-&\&'()&+32+73-&_&'4&4.$*(&."2"C&&&?(&+32+73-&\%&3(4-'##&^K1j%&^K1JJ%&'()&^K1JS%&'4&*"##&'4&-."&?1LJcc&3(&4$+D"-4&T\&'()&T_C&?(&+32+73-&_%&3(4-'##&^K1J\%&^K1JV%&'()&^K1Jb%&'4&*"##&'4&-."&?1LSJJ&3(&4$+D"-4&TV&'()&TbC&

JJ&

/.34&4#3)"&4.$*4&-."&97##&4+.",'E+&9$2&F32+73-&\&$(&-."&/0&12"+343$(&5'64&-"4-&6$'2)C&n$7&*3##&74"&-.34&+32+73-&-$&,"'472"&-."&":"+-4&$9&>?@&'()&0B&$(&-."&?1LJccC&&

JS&

/.34&4#3)"&4.$*4&-."&97##&4+.",'E+&9$2&F32+73-&_&$(&-."&/0&12"+343$(&5'64&-"4-&6$'2)C&n$7&*3##&74"&-.34&+32+73-&-$&,"'472"&-."&":"+-4&$9&>?@&'()&0B&$(&-."&?1LSJJC&&

J\&

P$2&-."&-"4-&6$'2)&-$&97(+E$(&82$8"2#I%&3-&34&3,8$2-'(-&-.'-&I$7&$(#I&3(4-'##&]7,8"24&'()&)";3+"4&3(&+32+73-4&\&'()&_C&M$&($-&3(4-'##&'(I&]7,8"24&$2&)";3+"4&3(&'(I&$-."2&+32+73-4&$(&-."&1FBl&Z",$;"&'(I&]7,8"24&$2&)";3+"4&92$,&-."&7(74")&+32+73-4&'()&4-$2"&-.",&3(&-."&4-$2'<"&'2"'&'-&-."&6$d$,&$9&-."&-"4-&6$'2)C&

J_&

/.34&4#3)"&<3;"4&-."&+$(("+E$(&)3'<2',&6"-*""(&-."&/0&12"+343$(&5'64&-"4-&6$'2)&'()&-."&O'E$('#&0(4-27,"(-4&>32-7'#B"(+.C&F$(("+-&-."&82$;3)")&8$*"2&+'6#"&-$&-."&MF&8$*"2&4788#I&$9&-."&>32-7'#&B"(+.&'()&8$*"2&+$(("+-$2&^_&$(&-."&-"4-&6$'2)C&F$(("+-&>$7-J&$(&-."&-"4-&6$'2)&-$&>32-7'#B"(+.&$4+3##$4+$8"&+.'(("#&J%&'()&>$7-S&$(&-."&-"4-&6$'2)&-$&>32-7'#&B"(+.&$4+3##$4+$8"&+.'(("#&S%&743(<&BOF&+'6#"4C&

JV&

O"N-&'88#I&8$*"2&-$&-."&O'E$('#&0(4-27,"(-4&>32-7'#B"(+.&'()&+$(("+-&3-&-$&I$72&+$,87-"2&*3-.&'&T@B&+'6#"C&/."&.'2)*'2"&4.$7#)&6"&)"-"+-")&'4&'&;32-7'#&FM&)23;"%&'()&I$7&+'(&27(&-."&>32-7'#B"(+.&4$m*'2"&)32"+-#I&92$,&-."&)23;"C&?(+"&-."&4$m*'2"&$8"(4%&+$(a<72"&-."&4$m*'2"&'4&9$##$*4o&&@"-&-."&E,"&4+'#"&-$&J[[,4&8"2&)3;343$(%&*3-.&-."&'+Q7343E$(&,$)"&4"-&-$&pL7-$Cq&G('6#"&+.'(("#4&J&'()&S&$(&-."&$4+3##$4+$8"%&'()&4"-&-.",&-$&JN%&MFH+$78#")&,$)"C&L)]74-&-."&;"2E+'#&4+'#"&'4&("")")&92$,&J[,>r)3;&-$&J>r)3;C&@"-&-."&sSV>&8$*"2&4788#I&-$&sJS>%&[CV[[LC&@"-&-."&HSV>&8$*"2&4788#I&-$&HJS>%&[CV[[LC&12"44&-."&8$*"2&67d$(&-$&-72(&$(&-."&8$*"2&4788#I&2'3#4C&&G('6#"&p,"'(q&,"'472","(-4&$(&6$-.&+.'(("#4&3(&$2)"2&-$&2"')&-."&$7-87-&;$#-'<"&$9&"'+.&+32+73-C&

Jb&

n$7&,74-&'#4$&4"-&-."&,$)"&$9&-."&>32-7'#&B"(+.&$4+3##$4+$8"C&F#3+D&-."&67d$(&4.$*(&$(&-."&92$(-&8'("#%&-."(&4"-&L+Q7343E$(&-$&p@',8#"q&'()&1"2434-"(+"&-$&pM34'6#")Cq&

Ji&

/."&"N8"+-")&$7-87-&;$#-'<"&2"47#-4&92$,&-."&,"'472","(-&'2"&4.$*(&."2"C&/."&?1LSJJ&.'4&'&,"'472")&$7-87-&;$#-'<"&$9&i_Ci,>%&'()&-."&?1LJcc&.'4&'&,"'472")&$7-87-&;$#-'<"&$9&_Cb[,>C&&n$7&,'I&.';"&)3:"2"(-&2"47#-4&3(&I$72&"N8"23,"(-C&&!$*&)3)&-."&,"'472")&'()&43,7#'-")&2"47#-4&+$,8'2"&-$&-."&-I83+'#&.'()&+'#+7#'-")&2"47#-4t&/'D"&'&,$,"(-&-$&#$$D&$;"2&-."&82";3$74&2"47#-4&'()&)2'*&I$72&$*(&+$(+#743$(4C&&&

Jc&

P$2&-."&("N-&8'2-&$9&-."&#'6%&*"Y##&2"8"'-&-."&4',"&82$+")72"&'4&"N8"23,"(-&J%&67-&-.34&E,"&*3-.&VD! of input resistance. This will emphasize the effects of input bias current, IB.&

Jj&

L4&4.$*(&3(&-."&4+.",'E+%&]7,8"2&^K1JV&4.$2E(<&-."&8$43E;"&3(87-&$9&TV&-$&<2$7()&34&($*&2",$;")C&^7,8"2&^K1J_&34&($*&3(4-'##")&3(&$2)"2&-$&+$(("+-&-."&8$43E;"&3(87-&$9&TV&-$&'&VD! resistor. The IB of U5 will now flow through this resistor, developing a DC voltage due to Ohm’s law and increasing the amount of offset voltage. As before, calculate the total output voltage due to VOS and IB for this circuit, using both the OPA211 and OPA188.&

S[&

/."&)'-'&4.""-&8'2',"-"24&9$2&6$-.&)";3+"4&'2"&82$;3)")&'<'3(&9$2&2"9"2"(+"C&G(-"2&I$72&+'#+7#'-")&2"47#-4&3(&-."&#$*"2&-'6#"C&/."&'(4*"24&.';"&6""(&82$;3)")&4$&-.'-&I$7&+'(&+."+D&I$72&*$2DC&

SJ&

U3-.&Z0O&g&VD%&-."&+'#+7#'E$(4&+.'(<"&4#3<.-#I&43(+"&-."&;$#-'<"&+'74")&6I&0B&34&($*&':"+-")&6I&Ze0OC&T4"&-."&("*&"Q7'E$(&>0B&g&0BuZeGf&s&0BuZe0OC&?-."2*34"%&-."&4-"84&'2"&-."&4',"&'4&3(&"N8"23,"(-&JC&Z"8"'-&-."&+'#+7#'E$(4&9$2&-."&,'N3,7,&;'#7"4C&

SS&

Z"8"'-&6$-.&4"-4&$9&+'#+7#'E$(4&9$2&-."&?1LJcc%&'<'3(&743(<&-I83+'#&'()&,'N3,7,&;'#7"4C&L4&6"9$2"%&-."&)3:"2"(-&"#"+-23+'#&+.'2'+-"234E+4&$9&-."&?1LJcc&*3##&2"47#-&3(&)3:"2"(-&$7-87-&;$#-'<"&+'#+7#'E$(4C&

S\&

Z"H27(&-."&43,7#'-")&MF&($)'#&;$#-'<"&'('#I434%&,'D3(<&472"&-$&74"&-."&82$8"2&]7,8"2&4"k(<4C&&0(&-."&?1LSJJ&+32+73-%&^K1J\&'()&^K1JV&'2"&$8"(%&'()&^K1J_&34&+#$4")C&0(&-."&?1LJcc&+32+73-%&^K1j&'()&^K1JJ&'2"&$8"(%&'()&^K1J[&34&+#$4")C&

S_&

/."&]7,8"2&4"k(<4&$(&-."&-"4-&6$'2)&,74-&6"&,$)3a")&6"9$2"&2"H27((3(<&-."&6"(+.&,"'472","(-C&Z",$;"&]7,8"24&^K1JJ&'()&^K1JV%&'()&3(4-'##&]7,8"24&^K1J[&'()&^K1J_C&L##&$-."2&]7,8"24&'()&)";3+"4&2",'3(&-."&4',"&92$,&-."&82";3$74&"N8"23,"(-C&

SV&

0(&"N8"23,"(-&S%&-."&?1LJcc&.'4&'&,"'472")&$7-87-&;$#-'<"&$9&\C_j,>%&'()&-."&?1LSJJ&.'4&'&,"'472")&$7-87-&;$#-'<"&$9&\iV,>C&&n$7&,'I&.';"&)3:"2"(-&2"47#-4&3(&I$72&"N8"23,"(-C&&!$*&)3)&-."&,"'472")&'()&43,7#'-")&2"47#-4&+$,8'2"&-$&-."&.'()&+'#+7#'-")&2"47#-4t!0(&-.34&"N',8#"%&-."&?1LSJJ&$7-87-&*'4&<2"'-"2&-.'(&-."&+'#+7#'-")&'()&43,7#'-")&-I83+'#&;'#7"4%&67-&#"44&-.'(&-."&+'#+7#'-")&,'N3,7,&;'#7"C&/."&?1LJcc&$7-87-&*'4&#"44&-.'(&-."&+'#+7#'-")&'()&43,7#'-")&-I83+'#&;'#7"4C&&&

Sb&

5"-Y4&($*&+$,8'2"&-."&2"47#-4&$9&6$-.&"N8"23,"(-4C&!$*&)3)&-."&+.'(<"&3(&3(87-&2"434-'(+"&':"+-&-."&$7-87-&;$#-'<"&,"'472","(-t&&0(&-."&?1LSJJ%&3(+2"'43(<&-."&3(87-&2"434-'(+"&+'74")&'&)2','E+&3(+2"'4"&3(&$7-87-&;$#-'<"C&!$*";"2%&-."&?1LJcc&)3)&($-&4""&47+.&'&#'2<"&3(+2"'4"C&/.34&34&6"+'74"&-."&?1LSJJ&.'4&'&,7+.&#'2<"2&3(87-&63'4&+722"(-&=0BA%&-.'(&-."&?1LJccC&

Si&

/.'-&+$(+#7)"4&-.34&#'6&`&-.'(D&I$7&9$2&I$72&E,"l&

Sc&