1. Operational Amplifiers
Dr. Holbert
Lecture 8
Operational Amplifiers
Dr. Holbert
February 11, 2008
Lect8
EEE 202
EEE 202

2. Op Amps Op Amp is short for operational amplifier
Amplifiers provide gains in voltage or current
Op amps can convert current to voltage
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EEE 202

3. Applications of Op Amps
Op amps can be configured in many different ways using resistors and other components
Most configurations use feedback
Op amps can provide a buffer between two circuits
Op amps can be used to implement integrators and differentiators
Lowpass and bandpass filters
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4. The Op Amp Symbol High Supply Non-inverting input + Output –
Ground
Low Supply
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5. The Op Amp Model
An operational amplifier is modeled as a voltage-controlled voltage source. + –
Inverting input
Non-inverting input
Rin v+ v–
A(v+ – v– ) vo
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6. Typical vs. Ideal Op Amps
Typical Op Amp:
The input resistance (impedance) Rin is very large (practically infinite).
The voltage gain A is very large (practically infinite).
Ideal Op Amp:
The input resistance is infinite.
The gain is infinite.
The op amp is in a negative feedback configuration.
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7. Consequences of the Ideal
Infinite input resistance means the current into the inverting (–) input is zero:
i– = 0
Infinite gain means the difference between v+ and v– is zero:
v+ – v– = 0
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8. The Basic Inverting Amplifier– + – + +
Vin
Vout –
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9. Solving the Amplifier Circuit
Apply KCL at the inverting (–) input:
i1 + i2 + i– =0 – R1 R2 i1 i– i2
Vin
Vout V–
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10. Solve for Vout
From KCL
Thus, the amplifier gain is
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11. Recap The ideal op-amp model leads to the following conditions:
i– = 0 = i+
v+ = v–
These conditions are used, along with KCL and other analysis techniques (e.g., nodal), to solve for the output voltage in terms of the input(s)
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12. Where is the Feedback? R2 R1 – + – + +
Vin
Vout –
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13. Review
To solve an op-amp circuit, we usually apply KCL at one or both of the inputs
We then invoke the consequences of the ideal model
The op amp will provide whatever output voltage is necessary to make both input voltages equal
We solve for the op-amp output voltage
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14. The Non-Inverting Amplifier+ + – + –
vin
vout R2 R1 –
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15. KCL at the Inverting Input+ –
vin
vout R1 R2 i– i1 i2
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16. Solve for vout
Hence, the non-inverting amplifier has a gained output (> unity) relative to the resistance ratio
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17. A Mixer Circuit R1 Rf + – R2 v1 – + – + + v2
vout –
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18. KCL at the Inverting Input– + v2
vout R2 Rf R1 v1 i1 i2 if i–
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19. Solve for vout
So, the mixer circuit output is a (negative) combination of the input voltages
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20. Class Examples
Drill Problem P4-1
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