1. Astable
AIM:
To understand what an astable does and use the equations to calculate period and frequency for a 555 based astable
PRIOR KNOWLEDGE:
Units for resistance and capacitance and the relationship between period and frequency

2. Introduction
An ASTABLE circuit is digital – the output is either ON or OFF
The ASTABLE oscillates between being ON and being OFF. If the output is OFF then after some time the output will come ON. If the output is ON then after some time the output will go OFF.
The ON time is called the MARK
The OFF time is called the SPACE
The total time for one complete cycle is called the PERIOD (T)
The MARK and SPACE depend on the values of the Resistors and Capacitors
Remember:
T = 1 / f
T = period
f = frequency

3. 555 Astable Circuit
Good: The 555 astable is easy to build and provides enough current to drive LEDs, small bulbs and motors
Bad: The MARK is always longer than the SPACE and so a true square wave can not be achieved
Ra, Rb and C are the timing components that determines the MARK, SPACE and PERIOD
Pin 4 must be held HIGH to make the 555 oscillate
The output can provide 100mA of current to drive LEDs and buzzers

4. The MARK is always longer than the SPACE so the ratio is never 1:1
555 Astable Equations
The ON time (MARK) is determined by the values of Ra, Rb and C and is given by the equation:
𝑇 𝑂𝑁 =0.7 × 𝑅 𝑎 + 𝑅 𝑏 ×𝐶
The OFF time (SPACE) is determined by the values of Rb and C and is given by the equation:
𝑇 𝑂𝐹𝐹 =0.7 × 𝑅 𝑏 ×𝐶
The Mark Space ratio (Mark:Space) is given by:
𝑇 𝑂𝑁 𝑇 𝑂𝐹𝐹 = 𝑅 𝑎 + 𝑅 𝑏 𝑅 𝑏
Ra and Rb
are also called R1 and R2
If Ra is much smaller than Rb then the mark:space ratio is almost 1:1 and the output is almost a square wave
The MARK is always longer than the SPACE so the ratio is never 1:1

5. 555 Astable Equations The PERIOD (T) is the total time for one cycle:
PERIOD = MARK + SPACE 𝑇 𝑝𝑒𝑟𝑖𝑜𝑑 = 𝑇 𝑂𝑁 + 𝑇 𝑂𝐹𝐹
The Astable period is given by the equation:
𝑇=0.7 × 𝑅 𝑎 + 2𝑅 𝑏 ×𝐶
Alternatively the frequency is given by:
𝑓= 𝑅 𝑎 + 2𝑅 𝑏 ×𝐶
Add the equations for TON and TOFF
Where does this come from?
In the equation for T, the constant is ≅ 0.7
and
1/0.693 ≅1.44
Frequency (f) is given by:
f = 1 / T

6. The minimum resistor value is 1kΩ
Example 1
An Astable is built with the following component values:
𝑅 𝑎 =1𝑘Ω 𝑅 𝑏 =47𝑘Ω and C=220𝜇𝐹
What is the period, frequency and mark:space ratio?
Remember to use standard units for R and C
𝑇=0.7× ×47000 ×220× 10 −6 =14.6𝑠
𝑓= 1 𝑇 therefore 𝑓= =0.07𝐻𝑧
Mark:Space ratio is 𝑇 𝑂𝑁 𝑇 𝑂𝐹𝐹 = 𝑅 𝑎 + 𝑅 𝑏 𝑅 𝑏 = =1.02:1
Mark and Space are almost the same ( 𝑇 𝑂𝑁 =7.4𝑠 and 𝑇 𝑂𝐹𝐹 =7.2𝑠) so the Astable is almost a square wave repeating every 15 seconds
The minimum resistor value is 1kΩ

7. Example 2
Design an Astable with a period of 10ms and a mark:space ratio close to 1:1 to give a reasonable square wave.
Use the equation for period 𝑇=0.7 × 𝑅 𝑎 + 2𝑅 𝑏 ×𝐶
Convert period to standard units 10ms = 0.01s
Choose a small value for Ra 𝑅 𝑎 =1𝑘Ω
Choose a sensible value for C 𝐶=0.1𝜇𝐹 or 𝐶=100𝑛𝐹
Calculate the value of Rb 𝑅 𝑏 =71𝑘Ω
Ra is much smaller than Rb and so the mark:space ratio will be approximately 1:1 as required.
What is the frequency?
71kΩ is not a standard E24 series value so either use 68k or add resistors in series
100Hz

8. Example 3 Design an Astable with a frequency of 4kHz
Use the equation for period 𝑇=0.7 × 𝑅 𝑎 + 2𝑅 𝑏 ×𝐶
Convert frequency to period 𝑇= = 𝑠
Choose a small value for Ra 𝑅 𝑎 =1𝑘Ω
Choose a sensible value for C 𝐶=10𝑛𝐹
Calculate the value of Rb 𝑅 𝑏 =17𝑘Ω
The small value of Ra means that the output will be almost a square wave. If in doubt, just use Ra = 1kΩ.
Note: with these values, frequency = 4080Hz. It would be better to use Rb = 16kΩ and Ra = 3k6Ω (both E24) giving f = 4010Hz

9. Example 4
Design an Astable with a frequency of 4kHz and a mark:space ratio of 2:1 (ON for twice as long as OFF)
Use the equation for period 𝑇=0.7 × 𝑅 𝑎 + 2𝑅 𝑏 ×𝐶
Convert frequency to period 𝑇= = 𝑠
Choose a sensible value for C 𝐶=10𝑛𝐹
Calculate the value of (Ra + 2Rb) 𝑅 𝑎 +2 𝑅 𝑏 =36𝑘Ω (i)
Use the mark:space equation 𝑇 𝑂𝑁 𝑇 𝑂𝐹𝐹 = 𝑅 𝑎 + 𝑅 𝑏 𝑅 𝑏 = 2 1
Rearranging gives 𝑅 𝑎 + 𝑅 𝑏 =2 𝑅 𝑏 and so 𝑅 𝑎 = 𝑅 𝑏 (ii)
Looking at (i) and (ii) gives 𝑅 𝑎 = 𝑅 𝑏 =12𝑘Ω

10. Summary
The 555 Astable is easy to build and can provide enough current to drive LEDs and other outputs
The mark:space ratio cannot be 1:1 so the output is never a square wave
𝑇 𝑂𝑁 =0.7 × 𝑅 𝑎 + 𝑅 𝑏 ×𝐶
𝑇 𝑂𝐹𝐹 =0.7 × 𝑅 𝑏 ×𝐶
𝑇 𝑂𝑁 𝑇 𝑂𝐹𝐹 = 𝑅 𝑎 + 𝑅 𝑏 𝑅 𝑏
𝑇=0.7 × 𝑅 𝑎 + 2𝑅 𝑏 ×𝐶
𝑓= 𝑅 𝑎 + 2𝑅 𝑏 ×𝐶
The output is almost a square wave if Ra << Rb

11. Questions Describe the output of the 555 Astable in words
What could you use an astable for?
How can you make the astable output stay OFF?
What is meant by the mark:space ratio?
Which component(s) control the frequency?
What is the smallest value allowed for the timing resistors?
If Ra = 47kΩ, Rb = 120kΩ and C = 33nF what is:
Period?
Frequency?
Mark:Space ratio?

12. Answers The output goes ON and OFF repeatedly
A flashing light (low frequency) or buzzer (high frequency)
Make Pin 4 = LOW by connecting it to 0V or Logic 0
The ON time divided by the OFF time
Ra, Rb and C
1kΩ
0.0067s or 6.7ms
150Hz (actually 151Hz but only need 2 s.f.)
1.4:1 (On for 1.4 times longer than OFF)