Lecture on Designing Astable Multivibrators using 555 Timer IC

Introduction

• Astable Multivibrator: A circuit whose both states are unstable and the output continuously changes between the two states.
• Applications: Commonly used in the design of relaxation oscillators.
• Objective: Learn how to design an astable multivibrator using the 555 timer IC.

Circuit Overview

• Unused Pins: Reset pin connected to supply voltage; Control pin connected to ground via capacitor C1.
• Important Connections: Threshold and trigger pins connected together.
• Initial Conditions: On startup, the capacitor is fully uncharged (voltage at pin 2 and 6 = 0V).

Working Principle

1. Initial State:

   • Voltage at pin 2 and 6 = 0V.
   • Voltage divider nodes = 2/3 Vcc and 1/3 Vcc.
   • Second comparator output = logic 1; First comparator output = logic 0.
   • Flip-flop output (Q) = logic 1; 555 timer output = logic high.

2. Charging Phase:

   • Capacitor C1 charges through resistors R1 and R2.
   • Voltage at pins 2 and 6 increases.
   • When voltage > 1/3 Vcc: Second comparator output = logic low.
   • When voltage > 2/3 Vcc: First comparator output = logic high; Flip-flop resets to logic 0.
   • Transition: Output changes from logic high to low.

3. Discharging Phase:

   • Capacitor discharges through transistor.
   • Voltage at pins 2 and 6 decreases.
   • When voltage < 2/3 Vcc: First comparator output = logic low.
   • When voltage < 1/3 Vcc: Second comparator output = logic high; Flip-flop sets to logic 1.
   • Transition: Output changes from logic low to high.

Timing Diagram

• Charging: Capacitor charges toward Vcc, output = logic high.
• Discharging: Capacitor discharges toward 0V, output = logic low.
• T1: Time for output to be high (capacitor charging from 1/3 Vcc to 2/3 Vcc).
• T2: Time for output to be low (capacitor discharging from 2/3 Vcc to 1/3 Vcc).
• Mathematical Representation:
  • T1 = 0.693 * (R1 + R2)
  • T2 = 0.693 * R2

Duty Cycle

• Definition: Ratio of T1 to the total time period (T1 + T2).
• Formula: Duty cycle = (R1 + R2) / (R1 + 2R2).
• Duty cycle > 50% as T1 > T2 (charging through R1 + R2; discharging through R2).

50% Duty Cycle Design

• R1 = 0: Achievable but risks damaging the internal transistor.
• Alternative: Use a diode between pin 7 and 2.
  • Charging: Through R1 and diode (resistance less than R2).
  • Discharging: Through R2 (diode OFF).
• Ideal Diode: Forward resistance = 0; T1 = 0.693 * R1, T2 = 0.693 * R2.

Practical Design Example

• Desired Frequency (F): 10 kHz, Duty Cycle: 50%.
• T = 0.1 ms: Total time period.
• C = 0.1 uF: Assumed capacitor value.
• Calculations:
  • T = 0.693 * (R1 + R2) * C
  • R1 + R2 = (0.1 ms) / (0.693 * 0.1 uF)
  • R1 = R2 = 720 Ohm (using potentiometers for tuning).

Derivation of Expressions

1. T1 Calculation:
   • Vf + (Vin - Vf) * e^(-T/R'C)
   • Initial Voltage = Vcc/3; Final Voltage = Vcc.
   • T1 = 0.693 * (R1 + R2) * C
2. T2 Calculation:
   • Vc = 0 + (2/3 Vcc) * e^(-T2/R2C)
   • Initial Voltage = 2/3 Vcc; Final Voltage = 0V.
   • T2 = 0.693 * R2 * C

Conclusion

• Summary: Designing an astable multivibrator using a 555 timer IC involves understanding the charging and discharging cycles of the capacitor and configuring the circuit to achieve the desired frequency and duty cycle.
• Contact: Questions or suggestions can be left in the comments.
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