§ 3-4 Analog addition and subtraction
The addition circuit
2
2
3
3
1
1,0
RRRa
???? ??????
2
2
3
3
1
1
RRR
an o d eat
aaa ?????? ?????
:
Let R1=R3 and
R2/R1= k,we have
)(1,312 ??? ????kif
The result we have found for two
inputs may be extended to any
number of inputs.
)( 4
4
2
3
3
2
1
1
2
2 ?????? ???? R
R
R
R
R
R
v o l t ag eou t pu t
v o l t ag e si n pu t
???
???
2
31,
?
??
)RRRR( 3
3
2
1
1
2
2 ??? ???
)( 312 ??? ??? k
kRa n d
kR
h a v ewe
30
20
3
1
?
?
?
23
3
2
1
2 ??
R
Ra n d
R
R
kRl e t 60,2 ?
)RRRR( 3
3
2
1
1
2
2 ??? ???
312 23 ??? ???
As a example,if it is required to design a circuit
to realize
The differential amplifier circuit
By superposition:
3
1
21
1
22212 )1( ?????
ba
by
RR
R
R
R
R
R
???????
If Ra=R1,Rb=R2.
)( 13
1
2
2 ??? ?? R
R
12
1
133
1
2 ??
?
???
b
a
b
a R
Ror
R
RR
R
1
1
2
3
1
2
1
1
??
R
R
R
R
R
R
b
a
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
kRRRh a vewekRl et ba 1030 12 ????
)(
RR,w h e n
132
12
??? ???
?
If we require that
132 32 ??? ??
The circuit may be analyzed by superposition.