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This section explores the fundamentals of the 555 Timer in astable mode, particularly focusing on rectangular waves and duty cycle calculations. It discusses the relationship between pulse width (PW) and cycle time (T) to determine duty cycle, along with practical applications involving a capacitor in an RC circuit. The content includes activities that require calculating the time constants for charging and discharging, as well as building a simulation in Multisim. Gain insights into frequency, pulse width, and duty cycle calculations critical for timer applications.
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Rectangular Waves- Reminder: Duty Cycle – ratio of pulse width to cycle time where PW= the pulse width of the circuit input T= the cycle time of the circuit input 2
Rectangular Wave If you repeatedly switch between the battery and the short you are effectively applying a rectangular time pulse to the RC circuit. b) If SW = PW, what is the duty cycle? a) If SW = .5 PW, what is the duty cycle?
Rectangular Wave Response The voltage across the capacitor will behave as below in response to such a wave:
In-Class Activity • For the circuit above, what value of C will allow the capacitor to “fully” charge and “fully” discharge if the square wave has a period of 2ms? • What is the time constant for this circuit?
In-Class Activity • Determine the charging time constant and the discharging time constant in the circuit below:
The 555 Compares the voltage at pin 6 to 2/3 Vcc The 555 Compares the voltage at pin 2 to 1/3 Vcc
Typical Wiring for a 555(astable mode) Notice that the boxed area is just an RC circuit
Current Flow During Capacitor Charging The capacitor charges via RA and RB until vc = 2/3 Vcc
Capacitor Voltage and Output Voltage Vcc 0 Red arrows indicate voltages during charging phases
Current Flow During Capacitor Discharging The capacitor discharges through just RB until vc = 1/3 Vcc
Capacitor Voltage and Output Voltage Vcc 0V Blue arrows indicate voltages during discharging phases
Timing During the charging phase, the capacitor voltage can be written as: During the discharging phase, the capacitor voltage can be written as:
In-Class Activity • How long does it take to:a) charge up from 1/3 Vcc to 2/3 Vcc? • Hint: Calculate time to reach each voltage first then subtract • b) discharge from 2/3 Vcc to 1/3 Vcc
555 Timing • Pulse width – capacitor charging time:PW = (RA + RB)C ln(2) sec • Space width – capacitor discharging time:SW = RB C ln(2) sec • Period = Pulse width + Space widthT = PW + SW = (RA + 2RB)C ln(2) sec • Frequency – 1/Periodf = 1/(RA + 2RB)C ln(2) = 1.443/(RA + 2RB)C Hz
555 Duty Cycle • Duty Cycle = 100 PW/T %or
In-Class Activity • In Multisim, build this 555 circuit, use RA = RB = 1kΩ and C = 1µF. • 555 can be found in Place-Mixed-Timer-LM555CM • What are the following: T, PW, SW, duty cycle, f? • Show them in hand calculations and record what you see on Multisim oscilloscope