Tutorial 11 - Astables

Monostable circuits  give out a single pulse.  These are not on the syllabus, but if you want to find out more about them, please click here.

Astable circuits do not have a stable state.  They are constantly changing from 0 to 1 and back.  They emit a train of pulses which are high (1) or low (0).  These pulses can be square waves, or can be configured to be rectangular.

A common device to produce these pulses is the 555-timer.  You are NOT expected to describe the 555 timer circuit, but it's worth being able to recognise the circuit.

555-timer in Astable Mode

The 555 timer can be wired up to produce a train of pulses by ensuring that the circuit is astable, which means that it is not in a stable state. We can make astable circuits from other components, but the 555 timer gives a train of digital pulses. The diagram shows the circuit. The output of the circuit is a square wave, as shown. We need to consider some definitions:

• The mark time [t(H)] is the time at which the output is a 1.

tH= 0.7(RA + RB)C

• The space time [t(L)] is the time at which the output is a 0.

tL = 0.7 RBC

• The mark to space ratio = mark time ÷ space time.

Ratio = tH ÷ tL

• The astable period T is the time taken for one complete cycle, the mark and the space times added together.

T = mark + space = tL + tH

• The frequency = 1 ÷ period. The time tH will be longer than tL, unless R1 is very small compared to R2. If this is the case, then tH will be approximately equal to tL, but not quite equal. We can say to a first approximation that the mark to space ratio is 1. This will result in a square wave output.

The duty cycle = mark time ÷ period.

 Worked Example What is the frequency of the square wave output from the circuit? Use the formula Answer From the diagram we can see that: R1 = 4700 W R2 = 2200 W C = 2.0 × 10-6 F   We need to substitute these values into the formula:                         f = ____1.4_____ = __________________ 1.4____________                             (R1 + 2R2)C          [4700 W + (2 × 2200 W)] × 2.0 × 10-6 F                                               = ____ 1.4_______ = 77 Hz                          9100 × 2.0  × 10-6

 An astable 555 timer has the following external component values: R1 = 100 kilohms; R2 = 47 kilohms; C1 = 10 microfarads. What is the mark and space? Question 2 An astable has a 2.2 F capacitor, R1 value of 10 k, and R2 value 20 k. (a) Calculate the astable frequency. (b) Work out the mark time, the space time, and the mark to space ratio. (c) Is output a square wave?

This is a 555-timer in astable mode.  It is NOT a tidy looking circuit: But it does give out a good rectangular wave: The mark time is longer than the space time.

NAND gate Astable

We can make an astable circuit the output of which oscillates at a frequency determined by the value of the time constant of a capacitor and a resistor. If you look carefully at the arrangements of the NAND gates, it does not take a genius to see that the two NAND gates are wired as NOT gates, so this set up is also called a NOT gate astable.  Let’s have a look at how the circuit works:

• Suppose the output of Y is high.

• This means that the input to Y is low.

• The capacitor will charge up.

•  A current flows through the resistor R which means there will be a voltage across it.

• This raises the input to Y to high and it will trigger to the output being low.

• Since X is connected to the feedback loop, its output will be low.

• The low output of X will cause the capacitor to discharge.

• This makes the input to Y low, hence the output to go to high.

• And so on…

We can summarise this in the timing diagram: We can show that the mark time is given by the relationship:

tH =1.1 RC

Similarly the space time is given by:

tL »1.1 RC

Therefore the period:

T = tH + tL = 2.2 RC

So the frequency:

f = 1/T = 1/2.2 RC

 A NAND gate astable has a capacitor of capacitance 20 mF with a resistor of resistance 150 kW.  What is the period of the astable?