Operational amplifiers

• Inverting input (−): Input that causes the output to swing negatively.
• Non-inverting input (+): Input that causes the output to swing positively.
• Output terminal: Delivers the amplified voltage.
• Power supply terminals: $+V_s$ and $-V_s$

Basic operating equation (open-loop configuration):

• If $V_+ > V_- \Rightarrow V_0$ is positive
• If $V_+ < V_- \Rightarrow V_0$ is negative
• If $V_+ = V_- \Rightarrow V_0 = 0$

When $V_0$ approaches $+V_s$ or $-V_s$, the amplifier enters saturation. The minimum differential input to cause saturation:

Example: If $A_0 = 10^5$ and $V_s = 15 \text{V}$, then:

Negative Feedback

1. Output is fed back to the inverting input via resistors.
2. Stabilizes gain and improves bandwidth.
3. Used in linear amplifier applications.

Positive Feedback

1. Output fed back to the non-inverting input.
2. Used in oscillators and comparators.
3. Causes instability; not used for amplification.

Inverting Amplifier

Gain:

• Negative sign means output is 180° out of phase.
• Uses virtual ground at inverting input.

Non-Inverting Amplifier

Gain:

• Output is in phase with input.
• High input impedance; useful for buffering.

Other Configurations

1. Voltage Follower: Gain = 1, used for impedance matching.
2. Summing Amplifier: Combines multiple inputs into one output.
3. Differential Amplifier: Amplifies the difference between two inputs.
4. Integrator: Outputs integral of input signal.
5. Differentiator: Outputs derivative of input signal.

• Gain decreases with frequency due to internal compensation.
• Slew Rate: Maximum rate of change of output voltage.

Example:

• Linear region: Output proportional to input difference.
• Saturation: Output stuck at $+V_s$ or $-V_s$.