Operational Amplifier

1. Operational Amplifiers
Dr. Varun Kumar
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2. Outlines
1 Introduction to Operational Amplifier
2 Types of Operational Amplifier
3 Differential Amplifier
Differential mode
Common mode
Common mode rejection ratio (CMRR)
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3. Introduction to Operational Amplifier
⇒ An operational amplifier is an integrated circuit that can amplify weak
electric signals.
⇒ An operational amplifier has two input pins and one output pin.
⇒ Its basic role is to amplify and output the voltage difference between
the two input pins.
Characteristics of ideal Op-Amp
⇒ Input resistance Ri → ∞
⇒ Output resistance R0 = 0
⇒ Voltage gain Av = −∞
⇒ Bandwidth = ∞
⇒ Characteristics do not drift with temperature.
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4. Continued–
Op-amp symbol and its type
Types of op-amp
1 Non-inverting amplifier
2 Inverting amplifier
3 Differential amplifier
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5. Continued–
(a) Basic operational amplifier
(b) Low frequency equivalent circuit of operational amplifier (V2 − V1 = Vi )
⇒ The open circuit voltage gain is Av and gain under load is AV
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6. Virtual ground
(a) Inverting op-amp with aided voltage shunt feedback.
(b) Virtual ground in the op-amp.
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7. Output voltage of op-amp in feedback network
⇒ Output voltage in case of inverting amplifier (Rf =feedback
resistance) and (R1 = Source resistance)
Vo = −
Rf
R1
Vi
⇒ Output voltage in case of non-inverting amplifier
Vo =
1 +
Rf
R1
Vi
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8. Differential amplifier
In ideal differential amplifier, output voltage
vo = Ad (v1 − v2) (1)
Two modes of operation in diff-amp, i.e common mode and differential
mode
vc =
v1 + v2
2
and vd = v1 − v2 (2)
Note: If v0
1 = 50µV and v0
2 = −50µV , v0
d = 100µV . On the other side if
v1” = 1050µV and v2” = 950µV , vd ” = 100µV . In both cases output Vo
will not be same for differential amplifier.
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9. Continued–
Common Mode Rejection Ratio (CMRR):
Let A1 is the voltage gain, if individual voltage v1 is applied and A2 for v2.
Output voltage
vo = A1v1 + A2v2 (3)
v1 = vc +
vd
2
and v2 = vc −
vd
2
(4)
or
vo = Acvc + Ad vd (5)
where
Ac ≡ A1 + A2 and Ad ≡
A1 − A2
2
(6)
Ad → Voltage gain for differential signal
Ac → Voltage gain for common mode signal
CMRR ≡ ρ ≡

12. Ad
Ac

15. (7)
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16. Continued–
From (5) and (7), the output voltage can be expressed as
vo = Ad vd
1 +
1
ρ
vc
vd
(8)
Note: For ideal differential amplifier, CMRR→ ∞
Q Consider a situation, If v0
1 = 50µV and v0
2 = −50µV is one set of
input and v1” = 1050µV and v2” = 950µV is the another set of
input. If CMRR for a given op-amp is 100. Calculate
Percentage difference in output voltage for two signals.
Repeat the above problem for ρ = 10000.
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