Overview
This lecture introduces ideal operational amplifier (op-amp) assumptions, demonstrates nodal analysis for an inverting op-amp circuit, and explains output voltage limitations due to power supply saturation.
Op-Amp Basics and Difference Amplifier
- An op-amp's output voltage ( V_{out} = A \cdot V_D ), where ( V_D ) is the voltage difference between positive and negative terminals.
- This configuration is called a difference amplifier because it amplifies the differential input.
- Op-amps require a power supply, typically ±12V in common circuits.
Practical Limitations and Output Saturation
- Op-amp gain ( (A) ) can be 100,000 or more, but output cannot exceed supplied voltages, e.g., ±12V.
- Maximum input difference ( V_D ) is limited by ( V_{out(max)} = A \cdot V_D ); for ±12V and ( A = 100,000 ), ( |V_D| \leq 120 ) microvolts.
- Ideal assumption: output can reach ±12V, but real op-amps seldom reach supply rails due to internal losses.
Ideal Op-Amp Assumptions
- Input resistance is infinite (no current flows into either input terminal).
- Voltage at the positive terminal equals voltage at the negative terminal (( V_+ = V_- )).
- Op-amp can supply unlimited output current (idealized for ease of analysis).
Inverting Op-Amp Circuit Analysis
- Circuit analyzed with resistors ( R_1 ) and ( R_2 ), goal: find ( V_{out} ) in terms of ( V_{in} ).
- By nodal analysis: ( V_{out} = -\frac{R_2}{R_1} V_{in} ).
- The gain is (-\frac{R_2}{R_1}); negative sign indicates the output is inverted.
Worked Example & Output Saturation
- For ( R_1 = 1k\Omega ), ( R_2 = 5k\Omega ), gain = -5.
- For several ( V_{in} ) values:
- ( V_{in} = -1V \rightarrow V_{out} = 5V )
- ( V_{in} = 1V \rightarrow V_{out} = -5V )
- ( V_{in} = 2V \rightarrow V_{out} = -10V )
- ( V_{in} = 3V \rightarrow V_{out} = -15V ) (exceeds -12V, so output saturates at -12V)
- Op-amp output "rails" at supply limits (±12V), and cannot exceed them, a condition called saturation.
- The allowable ( V_{in} ) range to avoid saturation: between (-2.4V) and (+2.4V) for this example.
Key Terms & Definitions
- Op-amp (Operational Amplifier) — An electronic device that amplifies the difference between its two input terminals.
- Difference Amplifier — Amplifies the voltage difference between two inputs.
- Gain — The ratio by which an op-amp circuit multiplies the input voltage.
- Saturation (Railing) — When output voltage reaches the limits set by the power supply.
- Inverting Op-Amp — A configuration where the output is inverted and scaled by the gain.
Action Items / Next Steps
- Start a separate sheet to record different op-amp configurations and corresponding formulas.
- Review and memorize the ideal op-amp assumptions.
- Prepare to analyze other op-amp configurations in upcoming lessons.