QB_PH_SEC8_020: Digital Electronics

In a 555 timer configured as an astable multivibrator with timing resistors $R_A, R_B$ and timing capacitor $C$, the duty cycle of the output pulse waveform is given by

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Capacitor Charge Phase ($T_{\text{high}}$)**: The timing capacitor $C$ charges from $\frac{1}{3}V_{\text{CC}}$ to $\frac{2}{3}V_{\text{CC}}$ through series resistors $R_A + R_B$: $T_{\text{high}} = (R_A + R_B) C \ln(2) \approx 0.693 (R_A + R_B) C$ 2. **Capacitor Discharge Phase ($T_{\text{low}}$)**: The internal discharge transistor turns ON, discharging $C$ from $\frac{2}{3}V_{\text{CC}}$ down to $\frac{1}{3}V_{\text{CC}}$ through resistor $R_B$ alone: $T_{\text{low}} = R_B C \ln(2) \approx 0.693 R_B C$ 3. **Total Time Period**: $T = T_{\text{high}} + T_{\text{low}} = 0.693 (R_A + 2 R_B) C$ 4. **Duty Cycle Calculation**: $\text{Duty Cycle} = \frac{T_{\text{high}}}{T} = \frac{0.693(R_A + R_B)C}{0.693(R_A + 2R_B)C} = \frac{R_A + R_B}{R_A + 2 R_B}$ 5. **Conclusion**: Option (A) is correct.