Post on 21-Dec-2015
Operational Amplifier
Ideal OP Amp
1. iin=0, no current flow into op amp.
2. V+=V-
• Typically one end of op amp is connected to ground, therefore, V+=V-= 0V, virtual ground. Often V+ is connected to ground to avoid stability problem.
Circuit model
Two golden rules to perform calculations on op amps with negative feedback:
Applications: building block for analog systems
• Amplifiers• Adders and Substractors• Integrators & Differentiators• Clock generators• Filters• Digital-to-analog converters
Using op-amps
No flexibility
Let’s build a circuit……noninverting amplifier
When A is very large
Suppose A=106, R1=9R, R2=R
Gain: • determined by resistance ratio• insensitive to A, temperature, fab variation
Why did this happen? Negative feedback
e.g. vIN=5V
Suppose I perturb the circuit (e.g. force v0 momentarily to 12V somehowStable point is when v+v-
Key: negative feedback portion of output fed to –ve input.
e.g. Car antilock brakes small corrections
How to control a high-strung device
• Antilock brakes
More op amp insights:
• Observe, under negative feedback,
• We also know • i+ 0• i- 0
Yield an easier analysis method (under negative feedback)
Insightful analysis method: under negative feedback
Voltage follower
has minimum effects on previous and next circuit.
Why is this circuit useful?
Inverting Amplifier
0 inFs iii
F
out
S
S
Fs
R
v
R
v
ii
00
SS
Fout v
R
Rv
S
F
S
out
R
R
v
vGain
Feedback resistor, always to negative input
Summing Amplifier: Add Circuit
FN iiii .....21
F
out
SN
SN
S
S
S
S
R
v
R
v
R
v
R
v ...
2
2
1
1
SN
SN
FS
S
FS
S
Fout v
R
Rv
R
Rv
R
Rv ...2
21
1
SNSSS
Fout vvv
R
Rv ...21
If RS1=RS2=…=RSN=RS
Non-innverting Amplifier
S
in
vvv
i
vv
0 since
F
out
S
Fs
R
vv
R
v
ii
0
SS
F
S
Fout
vR
R
vR
Rv
1
1 _
S
F
S
out
R
R
v
vGain
Feedback resistor, always to negative input
Differential Amplifier: Substractor
221
2 vRR
Rv
vv
21
1
21 0
R
vv
R
vv
ii
out
121
2 vvR
Rvout
Very useful if both signals are corrupted with noise: Electrocardiogram (EKG)