Operational Amplifier Golden Rule Checker
Overview: The Ideal Op-Amp Golden Rules
In operational amplifier circuit analysis, negative feedback networks are analyzed rapidly by applying the two ideal op-amp assumptions (often called the Golden Rules):
Infinite Open-Loop Gain (A_{ol} \to \infty): When an op-amp operates in its linear region with negative feedback, the voltage difference between the non-inverting and inverting input terminals is driven to zero (a virtual short): \mathbf{V_+ = V_-}
Infinite Input Impedance (R_{in} \to \infty): Because the input stage draws negligible current, the current entering both the non-inverting and inverting terminals is zero: \mathbf{I_+ = I_- = 0\text{ A}}
Part 1: Interactive Nodal & KCL Schematic Analyzer
Select an amplifier topology below and adjust the input voltages and resistor values. Observe how the virtual short (V_+ = V_-) dictates the branch currents and closed-loop output voltage V_{out} in real time.
Summary of Standard Closed-Loop Topologies
Before testing AC waveform clipping and completing the design challenges in Part 2, review how Kirchhoff’s Current Law (KCL) at the inverting node (V_-) yields the closed-loop gain for each standard configuration:
| Topology | Node Voltage (V_+ = V_-) | Ideal Closed-Loop Output (V_{out}) | Input Impedance (Z_{in}) |
|---|---|---|---|
| Non-Inverting | V_- = V_{in} | V_{out} = V_{in}\left(1 + \dfrac{R_f}{R_{in}}\right) | \infty (Extremely High) |
| Inverting | V_- = 0\text{ V} (Virtual Ground) | V_{out} = -\left(\dfrac{R_f}{R_{in}}\right)V_{in} | R_{in} |
| Summing Mixer | V_- = 0\text{ V} (Virtual Ground) | V_{out} = -R_f\left(\dfrac{V_1}{R_1} + \dfrac{V_2}{R_2}\right) | R_1, R_2 per channel |
| Difference (Matched) | V_- = V_2\left(\dfrac{R_4}{R_3 + R_4}\right) | V_{out} = \dfrac{R_f}{R_1}\left(V_2 - V_1\right) | R_1 (Inverting) |
| Unity Buffer | V_- = V_{in} | V_{out} = V_{in} (A_v = 1) | \infty (Impedance Isolator) |
Part 2: AC Waveform Clipping & Design Verification Lab
Real operational amplifiers cannot output voltages beyond their DC power supply rails (+V_{CC} and -V_{EE}). Whenever the ideal mathematical output exceeds these limits, the output stage saturates and clips the waveform.
Use the virtual oscilloscope below to inspect sinusoidal, triangular, and square wave amplification, complete the 5 progressive design challenges, and export your verified circuit directly to LTspice (.cir) or LaTeX (circuitikz).