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 www.pfnicholls.com

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

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

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

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= 1.44 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 0.693 ≅ 0.7 and 1/0.693 ≅1.44 Frequency (f) is given by: f = 1 / T

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× 1000+2×47000 ×220× 10 −6 =14.6𝑠 𝑓= 1 𝑇 therefore 𝑓= 1 14.6 =0.07𝐻𝑧 Mark:Space ratio is 𝑇 𝑂𝑁 𝑇 𝑂𝐹𝐹 = 𝑅 𝑎 + 𝑅 𝑏 𝑅 𝑏 = 1000+47000 47000 =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

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

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= 1 4000 =0.00025𝑠 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

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= 1 4000 =0.00025𝑠 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

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= 1.44 𝑅 𝑎 + 2𝑅 𝑏 ×𝐶 The output is almost a square wave if Ra << Rb

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?

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)