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Operational Amplifiers
Dr. Varun Kumar
Dr. Varun Kumar (IIIT Surat) Unit-4 1 / 10
Outlines
1 Introduction to Operational Amplifier
2 Types of Operational Amplifier
3 Differential Amplifier
Differential mode
Common mode
Common mode rejection ratio (CMRR)
Dr. Varun Kumar (IIIT Surat) Unit-4 2 / 10
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.
Dr. Varun Kumar (IIIT Surat) Unit-4 3 / 10
Continued–
Op-amp symbol and its type
Types of op-amp
1 Non-inverting amplifier
2 Inverting amplifier
3 Differential amplifier
Dr. Varun Kumar (IIIT Surat) Unit-4 4 / 10
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
Dr. Varun Kumar (IIIT Surat) Unit-4 5 / 10
Virtual ground
(a) Inverting op-amp with aided voltage shunt feedback.
(b) Virtual ground in the op-amp.
Dr. Varun Kumar (IIIT Surat) Unit-4 6 / 10
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
Dr. Varun Kumar (IIIT Surat) Unit-4 7 / 10
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.
Dr. Varun Kumar (IIIT Surat) Unit-4 8 / 10
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 ≡

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Operational Amplifier

  • 1. Operational Amplifiers Dr. Varun Kumar Dr. Varun Kumar (IIIT Surat) Unit-4 1 / 10
  • 2. Outlines 1 Introduction to Operational Amplifier 2 Types of Operational Amplifier 3 Differential Amplifier Differential mode Common mode Common mode rejection ratio (CMRR) Dr. Varun Kumar (IIIT Surat) Unit-4 2 / 10
  • 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. Dr. Varun Kumar (IIIT Surat) Unit-4 3 / 10
  • 4. Continued– Op-amp symbol and its type Types of op-amp 1 Non-inverting amplifier 2 Inverting amplifier 3 Differential amplifier Dr. Varun Kumar (IIIT Surat) Unit-4 4 / 10
  • 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 Dr. Varun Kumar (IIIT Surat) Unit-4 5 / 10
  • 6. Virtual ground (a) Inverting op-amp with aided voltage shunt feedback. (b) Virtual ground in the op-amp. Dr. Varun Kumar (IIIT Surat) Unit-4 6 / 10
  • 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 Dr. Varun Kumar (IIIT Surat) Unit-4 7 / 10
  • 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. Dr. Varun Kumar (IIIT Surat) Unit-4 8 / 10
  • 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 ≡
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  • 12. Ad Ac
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  • 15. (7) Dr. Varun Kumar (IIIT Surat) Unit-4 9 / 10
  • 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. Dr. Varun Kumar (IIIT Surat) Unit-4 10 / 10