@Muse - In a monostable (one-shot) configuration, the 555 timer generates a single output pulse of a fixed duration whenever it receives a falling edge at the trigger input.
### How It Works
1. **Quiescent State:**
- Before triggering, the trigger input #trig is held high ($9\text{ V}$, above $\frac{1}{3}V_{CC} = 3\text{ V}$).
- The output #out remains low ($0\text{ V}$), and the internal discharge transistor is turned on, clamping the timing node #tc to ground across capacitor #C1.
2. **Triggering:**
- When the signal source #Vtrig pulls #trig below $\frac{1}{3}V_{CC}$ ($3\text{ V}$), the internal comparator sets the 555's flip-flop.
- The output #out drives high to nearly $V_{CC}$ ($9\text{ V}$), and the internal discharge transistor turns off.
3. **Timing Interval:**
- With the discharge clamp released, timing capacitor #C1 charges through timing resistor #R1 toward $V_{CC}$:
$$v_{C1}(t) = V_{CC}\left(1 - e^{-t / (R_1 C_1)}\right)$$
- The threshold input monitors #tc. Once $v_{C1}$ reaches $\frac{2}{3}V_{CC}$ ($6\text{ V}$), the upper comparator resets the flip-flop.
4. **Reset and Discharge:**
- Output #out goes low, turning on the internal discharge transistor, which rapidly discharges #C1 back to $0\text{ V}$.
- The circuit remains idle until the next negative trigger edge.
### Pulse Duration
The pulse width $T$ is determined by #R1 and #C1:
$$T = \ln(3) \cdot R_1 C_1 \approx 1.1 \cdot R_1 C_1$$
With $R_1 = 10\text{ k}\Omega$ and $C_1 = 1\ \mu\text{F}$:
$$T \approx 1.1 \times 10^4\,\Omega \times 10^{-6}\text{ F} \approx 11\text{ ms}$$
