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**Operational Amplifier**

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Ideal OP Amp Circuit model Two golden rules to perform calculations on op amps with negative feedback: iin=0, no current flow into op amp. V+=V- Typically one end of op amp is connected to ground, therefore, V+=V-= 0V, virtual ground. Often V+ is connected to ground to avoid stability problem.

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**Applications: building block for analog systems**

Amplifiers Adders and Substractors Integrators & Differentiators Clock generators Filters Digital-to-analog converters

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Using op-amps No flexibility

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**Let’s build a circuit……noninverting amplifier**

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**When A is very large Suppose A=106, R1=9R, R2=R Gain:**

determined by resistance ratio insensitive to A, temperature, fab variation

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**Why did this happen? Negative feedback**

e.g. vIN=5V Suppose I perturb the circuit (e.g. force v0 momentarily to 12V somehow Stable point is when v+v- Key: negative feedback portion of output fed to –ve input. e.g. Car antilock brakes small corrections

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**How to control a high-strung device**

Antilock brakes

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**More op amp insights: Observe, under negative feedback, We also know**

Yield an easier analysis method (under negative feedback)

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**Insightful analysis method: under negative feedback**

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**Voltage follower Why is this circuit useful?**

has minimum effects on previous and next circuit.

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Inverting Amplifier Feedback resistor, always to negative input

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**Summing Amplifier: Add Circuit**

If RS1=RS2=…=RSN=RS

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**Non-innverting Amplifier**

Feedback resistor, always to negative input

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**Differential Amplifier: Substractor**

Very useful if both signals are corrupted with noise: Electrocardiogram (EKG)

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