This circuit demonstrates the distinctly non-linear, exponential behavior of a light-emitting diode (#LED1) by plotting its current-voltage ($I$-$V$) curve directly on an XY-mode oscilloscope.
### Circuit Operation
- **Excitation:** AC source #Vin provides a $100\text{ Hz}$ sinusoidal voltage swinging between $-4\text{ V}$ and $+4\text{ V}$.
- **Current Limiting:** Resistor #R1 ($100\ \Omega$) limits the forward peak current to protect #LED1 from overcurrent damage.
- **Diode Action:**
- **Reverse Bias ($v_{\text{anod}} < 0\text{ V}$):** The LED remains non-conductive, blocking current flow entirely ($i \approx 0\text{ A}$).
- **Sub-threshold ($0\text{ V} < v_{\text{anod}} < 1.8\text{ V}$):** Negligible current flows because the applied potential is below the bandgap turn-on threshold.
- **Forward Conduction ($v_{\text{anod}} \ge 2.0\text{ V}$):** Once the forward voltage overcomes the knee threshold ($\approx 2\text{ V}$), carrier recombination begins, the LED illuminates, and current increases exponentially:
$$I_D = I_S \left( e^{\frac{V_D}{n V_T}} - 1 \right)$$
