Transcript Rectangular Wave

Section 24.4
The 555 Timer
• Rectangular Waves
- Reminder: Duty Cycle – ratio of pulse width
to cycle time
PW
duty cycle (%) 
X 100
T
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.
a) If SW = .5 PW,
what is the duty cycle?
b) If SW = 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:
555 Integrated Circuit Timer
Inside the 555 is a voltage divider
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:

vc (t )  Vcc 1  e
 t /( RA  RB )C

During the discharging phase, the
capacitor voltage can be written as:

vc (t )  Vcc e
 t / RBC

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 width
T = PW + SW = (RA + 2RB)C ln(2) sec
• Frequency – 1/Period
f = 1/(RA + 2RB)C ln(2) = 1.443/(RA + 2RB)C Hz
555 Duty Cycle
• Duty Cycle = 100 PW/T %
or
RA  RB C ln( 2)
DutyCycle  100
%
RA  2RB C ln( 2)
RA  RB 
 100
%
RA  2RB 
In-Class Activity
• In Multisim, build this 555
circuit, use RA = RB = 1kΩ
and C = 1µF.
• 555 can be found in PlaceMixed-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