Op-Amps are crucial components in circuits designed to filter, oscillate, or generate specific waveforms.

6.1 Active Filters

Active filters use active components like Op-Amps along with passive elements (resistors, capacitors) to shape the frequency response of a circuit.

• Active Low-Pass Filter: Allows low-frequency components to pass while rejecting high-frequency components.
• Active High-Pass Filter: Allows high-frequency components to pass while rejecting low-frequency components.
• Active Band-Pass Filter: Allows a specific band of frequencies to pass, typically created by cascading a high-pass and a low-pass filter.
• Active Band-Stop Filter: Rejects a specific band of frequencies, typically created by summing the outputs of parallel low-pass and high-pass filters.

6.2 Sinusoidal Oscillators

An oscillator converts DC energy into a periodic AC output signal. Sinusoidal oscillators operate based on the Barkhausen criteria:

1. The loop gain (A_{v}\beta) must be greater than or equal to unity.
2. The total phase shift around the loop must be 0° or 360°.

• RC Phase Shift Oscillator: Uses an inverting amplifier (180° phase shift) and a feedback network of three cascaded RC sections (providing the remaining 180° shift).
  • Frequency of Oscillation: f=\frac{1}{2\Pi RC\sqrt[]{6}}
  • Gain Condition: \frac{R_f}{R_1}\geq29
• Wien Bridge Oscillator: Uses a non-inverting amplifier (0° phase shift) and a feedback network that provides 0° phase shift at the oscillation frequency.
  • Frequency of Oscillation: f=\frac{1}{2\Pi RC}
  • Gain Condition: 1+\frac{R_f}{R_1}\geq3 (or R_f \geq 2R_1)

6.3 Waveform Generators

• Square Wave Generator: An Op-Amp circuit using both positive and negative feedback that causes the output to repeatedly switch between positive (+V_{sat}) and negative (-V_{sat}) saturation as a capacitor charges and discharges.
• Triangular Wave Generator: Created by cascading a square wave generator with an integrator. The integrator converts the square wave output into a triangular wave.