operational amplifiers (op-amps). operational amplifier (op-amp) not a discrete device (resistor,...
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Operational Amplifiers (Op-Amps)
Operational Amplifier (Op-Amp)• Not a discrete device
(resistor, cap, ind, diode, transistor etc.)
• IC !• 2-input terminals
– Inverting and non-inverting– Output terminal– Two supply terminals
• Inexpensive – yet very useful in instrumentation applications
• We will only consider ideal op-amps !
-
+
Inverting Input
Non-inverting Input
Output
PowerSupplies
Operational Amplifiers (Op-Amps)
Ideal Op-Amps
1. Infinite open-loop voltage gain2. Infinite input impedance3. Zero output impedance4. Infinite bandwidth5. Zero input voltage offset
5 characteristics
A Simple Model for the Op-Amp• Very High Gain amplifier
with a high input and low output resistance !
• AOL: “Open-Loop” Gain (105- 107)
• RIN: input resistance (Mohms)
• ROUT: Output Resistance (10s of ohms)
v-
v+
-
+
-+
AOL(v+-v-)
RIN
ROUT
IIN
Ideal Op-Amps
1. Input currents = 02. Difference in input voltages = 0
“Golden Rules”
Input Current (IN) is zero !V+=V-
Ideal Op-Amps
1. Calculate the input voltage2. Write node equation at op-amp
input to find the output voltage
Analysis Procedure
Inverting Amplifier
Find the voltage gain Vo/Vi.
1. Calculate the input voltage2. Write node equation at op-amp
input to find the output voltage
Vb = 0Va = 0
Since Ia = 0, I1 = If
1
f
i
o
R
R
V
V
Non-Inverting Amplifier
Find the voltage gain Vo/Vi.
1. Calculate the input voltage2. Write node equation at op-amp
input to find the output voltage
Vb = Vi
Va = Vi
Since Ia = 0, I1 = If
1
f1
i
o
R
RR
V
V
Integrator
R
VI in
C t
0
CC d)(IC
1)t(V
t
0
in d)(VRC
1
By KVL, Vout = –VC
t
0
inout d)(VRC
1V
Differentiator
dt
dVC
dt
dVCI inC
C RIV Cout
dt
dVRCV in
out
Two-Stage Amplifier
Gain = Vo1/Vi Gain = Vo2/Vo1
Total Gain = (Vo1/Vi) (Vo2/Vo1) = Vo2/Vi
Example
Example
Work this Example!_________