7.07 Multivibrator Waveforms, 555 Timer & Timing Derivations
aliases:
- BJT Astable Frequency Derivation
- BJT Monostable Pulse Width
- 555 Timer Architecture
- 555 Astable & Monostable Timing Equations
- 50% Duty Cycle Extension
tags:
- digital-electronics
- ece-2103
- term-2-1
- study-order/7.07
type: uni-note
course: “ECE 2103 - Digital Electronics and Logic Circuits”
chapter_map: “07 Chapter Map - Multivibrators, Memory & Converters”
term: 2-1
teacher: Foysal Sir
status: enhanced
Related Concepts: 7.01 Multivibrator Topologies (Astable, Monostable, Bistable & 555 Timer) | 7.03 Digital-to-Analog Converters (DAC Topologies & Analysis) | 7.02 Semiconductor & Magnetic Memory Systems
7.07 Multivibrator Waveforms, 555 Timer & Timing Derivations
Overview: Complete mathematical derivations for BJT astable/monostable relaxation oscillators and IC 555 timer configurations.
1. BJT Astable Multivibrator Frequency Derivation [PYQ: 2015, 2017, 2021]
Base voltage vb2(t) rises exponentially during charging:
vb2(t) = VCC - 2 VCC e^-t / (RB C)
Setting vb2(t1) = 0 V:
t1 = RB C ln(2) ≈ 0.693 RB C
Total Period T = t1 + t2 = 1.386 RB C ⇒ f = 1 / (1.386 RB C) ≈ 0.72 / (RB C)
2. IC 555 Timer Astable Mode [PYQ: 2015, 2018, 2020, 2024]
- thigh = 0.693 (RA + RB) C
- tlow = 0.693 RB C
- f = 1.44 / ((RA + 2RB) C)
- Duty Cycle D = (RA + RB) / (RA + 2RB) x 100%
50% Duty Cycle Steering Diode
Connect a diode in parallel with RB (anode to Pin 7, cathode to Pin 6). Charging bypasses RB directly through RA, yielding thigh = 0.693 RA C. Setting RA = RB gives D = 50%.