1. Op Amps
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2. Introduction Op Amp is short for operational amplifier.
An operational amplifier is modeled as a voltage controlled voltage source.
An operational amplifier has a very high input impedance and a very high gain.
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3. Use of Op Amps
Op amps can be configured in many different ways using resistors and other components.
Most configurations use feedback.
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4. Applications of Op Amps
Amplifiers provide gains in voltage or current.
Op amps can convert current to voltage.
Op amps can provide a buffer between two circuits.
Op amps can be used to implement integrators and differentiators.
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5. More Applications
Lowpass and bandpass filters.
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6. The Op Amp Symbol High Supply Non-inverting input + Output -
Ground
Low Supply
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7. The Op Amp Model v+ Non-inverting input + vo Rin + - v-
A(v+ -v- )
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8. Typical Op Amp
The input resistance Rin is very large (practically infinite).
The voltage gain A is very large (practically infinite).
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9. “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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10. The Basic Inverting Amplifier- +
Vin
Vout R1 R2
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11. 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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12. Solving the Amplifier Circuit
Apply KCL at the inverting input:
i1 + i2 + i-=0 R2 i2 R1 - i1 i-
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13. KCL
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14. Solve for vout
Amplifier gain:
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15. Recap The ideal op amp model leads to the following conditions: i- = 0
v+ = v-
These conditions are used, along with KCL and other analysis techniques, to solve for the output voltage in terms of the input(s).
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16. Where is the Feedback? - +
Vin
Vout R1 R2
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17. 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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18. The Non-Inverting Amplifier+ -
vin
vout R1 R2
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19. KCL at the Inverting Input+ + - + i-
vin -
vout i1 i2 R2 R1 -
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20. KCL
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21. Solve for Vout
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22. A Mixer Circuit - + v2
vout R2 Rf R1 v1
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23. KCL at the Inverting InputRf i1 if + R2 v1 i2 - - i- v2 + - + +
vout -
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24. KCL
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25. KCL
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26. Solve for Vout
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