Non-inverting Op Amplifier
• Place a feedback resistor R f
from op amp output to neg input
• The R i
between setpoint and ground
• Allows current to flow from output to input
• Voltage divider R f
/R s
sets voltage at input
• This circuit gives positive gain
• Called Non-inverting op amp
• Note: text uses V g
for V in
• Also shows a R g
on input which is not needed

Non-inverting Op Amplifier Gain
• Key point: Infinite op amp input resistance means no input current
• Thus voltage across the op amp input V sp
must be zero
I in
= 0 thus V sp
= 0
• Hence voltage at summing point sp must equal input voltage
V s
= V in
• Since no input current to the op amp neg input
I s
=
V in
R s
I s
= I f
• Thus voltage across the feedback resistor becomes
V = I R = I = V in
R f f f s
R f
V o
= V s
+ = V in
R i f
+
V f
• The voltage amplification (or gain) is:
A v
=
V
V o in
=
R i
+
R i
R
R i
R
R s f f

Example Non-inverting Op Amplifier
• For an non-inverting op amp with
R s
= 1 K Ω and R f
= 9 K Ω
V
CC
= +15 V V
EE
= -15
• What is the output for a 0.5 V input
• The voltage gain is:
A v
=
V
V o in
=
R i
+
R i
R f =
1000 + 9000
1000
= 10
• Thus the output is:
V o
= V in
R i
+ R f = V in
A v
= 0 .
5 × 10 = 5 V
R i
• NOTE: must keep output less than power voltages - input limited
• In real circuits use resistors in Kilo-ohm range
• Thus reduce effects of smaller resistance eg contacts

Summing Inverting Op Amplifier (EC 6.4)
• Using inverting op amps to combine many signals
• Have each input resistance connected to SP
• But only one feedback resistor
• Each signal can have different amplification
• Again the SP is a virtual ground
V sp
= 0 I sp
= 0
• Current from each input V sj
is
I sj
=
V
R si sj
• By KCl the total input current is
I s − total
= j
N
= 1
I sj
= j
N
= 1
V sj
R j
• True because summing point a virtual ground
• Note each input does not affected the other inputs

Summing Inverting Op Amp Gain
• Then by KCL the feedback current = input current
I f
= −
V
R f f
= I s − total
= j
N
∑
= 1
I sj
= j
N
∑
= 1
V sj
R j
• Then in terms of output voltage
V o
= V f
= j
N
∑
= 1
− V sj
R f = j
N
∑
= 1
− V sj
A
R j
• Note: V o
must not exceed V
EE
or V
CC
• The amplification (or gain) per channel is:
A vj
= −
R
R f sj
• Simple control systems use this summing input vj

Example of Summing Op Amp
• Create an op amp circuit that will generate the sum equation
V o
= − V
1
− 2 V
2
• To begin set R f
to the largest multiplication factor
• Ie: times some common R for the design
• Here: largest gain A max
is for V
• Now choose the minimum resistance: ie common R = 1 K Ω
R f
= A max
R min
2
which is 2
= 2 × 1000 = 2 K Ω

Example of Summing Op Amp Con’d
• For the input resistances
• Set the R sj
equal to common R f
times the multiplyer for that input
R j
=
R
A f j
• Thus for the example
R
1
=
R f
A
1
=
2000
1
= 2 K Ω
R
2
=
R f
A
2
=
2000
2
= 1 K Ω