Review Article
Design and Implementation of the Astable Multivibrator
Edward Ong Yong Seng, Nanyang Technological University, VALENS, Singapore.
Received Date: August 01, 2019; Published Date: August 05, 2019
Abstract
This progress report covers the design and implementation of the Astable Multivibrator. An Astable Multivibrator consists of two amplifying stages connected in a positive feedback loop by two capacitiveresistive coupling networks. The amplifying elements may be junction or fieldeffect transistors, vacuum tubes, operational amplifiers, or other types of amplifier.
transistors, vacuum tubes, operational amplifiers, or other types of amplifier. The circuit is usually designed in a symmetric form as a crosscoupled pair. Two output terminals can be defined at the active devices, which will have complementary states; one will have high voltage while the other has low voltage, (except during the brief transitions from one state to the other).
Circuitry testing and troubleshooting were carried out in the Astable Multivibrator in both designs. The latter wasn’t implemented due to the big difference between the mark/space ratio of 1:100.
Introduction
The circuit has two astable (unstable) states that change alternatively with maximum transition rate because of the “accelerating” positive feedback. It is implemented by the coupling capacitors that instantly transfer voltage changes because the voltage across a capacitor cannot suddenly change. In each state, one transistor is switched on and the other is switched off. Accordingly, one fully charged capacitor discharges (reverse charges) slowly thus converting the time into an exponentially changing voltage. At the same time, the other empty capacitor quickly charges thus restoring its charge (the first capacitor acts as a timesetting capacitor and the second prepares to play this role in the next state). The circuit operation is based on the fact that the forwardbiased baseemitter junction of the switchedon bipolar transistor can provide a path for the capacitor restoration (Figure 1).
State 1 (Q1 is switched on, Q2 is switched off)
In the beginning, the capacitor C_{1} is fully charged (in the previous State 2) to the power supply voltage V with the polarity shown in Figure 1. Q1 is on and connects the lefthand positive plate of C_{1} to ground. As its righthand negative plate is connected to Q2 base, a maximum negative voltage (V) is applied to Q2 base that keeps Q2 firmly off. C_{1} begins discharging (reverse charging) via the highvalue base resistor R_{2}, so that the voltage of its righthand plate (and at the base of Q2) is rising from below ground (V) toward +V. As Q2 baseemitter junction is reversebiased, it does not conduct, so all the current from R_{2} goes into C_{1}. Simultaneously, C_{2} that is fully discharged and even slightly charged to 0.6 V (in the previous State 2) quickly charges via the lowvalue collector resistor R_{4} and Q1 forwardbiased baseemitter junction (because R_{4} is less than R_{2}, C_{2} charges faster than C_{1}). Thus, C_{2} restores its charge and prepares for the next State C_{2} when it will act as a timesetting capacitor. Q1 is firmly saturated in the beginning by the “forcing” C_{2} charging current added to R^{3} current. In the end, only R^{3} provides the needed input base current. The resistance R^{3} is chosen small enough to keep Q1 (not deeply) saturated after C_{2} is fully charged.
When the voltage of C_{1} righthand plate (Q2 base voltage) turns positive and reaches 0.6 V, Q2 baseemitter junction begins diverting a part of R_{2} charging current. Q2 begins conducting and this starts the avalanchelike positive feedback process as follows. Q2 collector voltage begins falling; this change transfers through the fully charged C_{2} to Q1 base and Q1 begins cutting off. Its collector voltage begins rising; this change transfers back through the almost empty C_{1} to Q2 base and makes Q2 conduct more thus sustaining the initial input impact on Q2 base. Thus, the initial input change circulates along the feedback loop and grows in an avalanchelike manner until finally Q1 switches off and Q2 switches on. The forwardbiased Q2 baseemitter junction fixes the voltage of C_{1} righthand plate at 0.6 V and does not allow it to continue rising toward +V.
State 2 (Q1 is switched off, Q2 is switched on)
Now, the capacitor C_{2} is fully charged (in the previous State 1) to the power supply voltage V with the polarity shown in Figure 1. Q2 is on and connects the righthand positive plate of C_{2} to ground. As its lefthand negative plate is connected to Q1 base, a maximum negative voltage (V) is applied to Q1 base that keeps Q1 firmly off. C_{2} begins discharging (reverse charging) via the highvalue base resistor R_{3}, so that the voltage of its lefthand plate (and at the base of Q1) is rising from below ground (V) toward +V. Simultaneously, C_{1} that is fully discharged and even slightly charged to 0.6 V (in the previous State 1) quickly charges via the lowvalue collector resistor R^{2} and Q2 forwardbiased baseemitter junction (because R^{2} is less than R^{3}, C_{1} charges faster than C_{2}). Thus, C_{1} restores its charge and prepares for the next State 1 when it will act again as a timesetting capacitor...and so on... (the next explanations are a mirror copy of the second part of State 1).
MultiVibrator Frequency
The duration of state 1 (low output) will be related to the time constant R_{2}C_{1} as it depends on the charging of C_{1}, and the duration of state 2 (high output) will be related to the time constant R^{3}C_{2} as it depends on the charging of C_{2}. Because they do not need to be the same, an asymmetric duty cycle is easily achieved.
The voltage on a capacitor with nonzero initial charge is:
Looking at C_{2}, just before Q2 turns on, the left terminal of C_{2} is at the baseemitter voltage of Q1 (V_{BE}_Q1) and the right terminal is at V_{CC} (“V_{CC}” is used here instead of “+V” to ease notation). The voltage across C_{2} is V_{CC} minus V_{BE}_Q1. The moment after Q2 turns on, the right terminal of C_{2} is now at 0 V which drives the left terminal of C_{2} to 0 V minus (V_{CC}  V_{BE}_Q1) or V_{BE}_Q1  V_{CC}. From this instant in time, the left terminal of C_{2} must be charged back up to V_{BE}_Q1. How long this take is half our multivibrator switching time (the other half comes from C_{1}). In the charging capacitor equation, substituting:
For this circuit to work, V_{CC}>>V_{BE}_Q1 (for example: V_{CC}=5 V, V_{BE}_ Q1=0.6 V), therefore the equation can be simplified to:
The period of each half of the multivibrator is therefore given by t = ln (2) RC.
The total period of oscillation is given by:
where...
• f is frequency in hertz.
• R_{2} and R^{3} are resistor values in ohms.
• C_{1} and C_{2} are capacitor values in farads.
• T is the period (In this case, the sum of two period durations).
For the special case where
• t_{1} = t_{2} (50% duty cycle)
• R_{2} = R^{3}
• C_{1} = C_{2}
Output Pulse Shape
The output voltage has a shape that approximates a square waveform. It is considered below for the transistor Q1.
During State 1, Q2 baseemitter junction is reversebiased and capacitor C_{1} is “unhooked” from ground. The output voltage of the switchedon transistor Q1 changes rapidly from high to low since this lowresistive output is loaded by a high impedance load (the series connected capacitor C_{1} and the highresistive base resistor R_{2}).
During State 2, Q2 baseemitter junction is forwardbiased and capacitor C_{1} is “hooked” to ground. The output voltage of the switchedoff transistor Q1 changes exponentially from low to high since this relatively high resistive output is loaded by a low impedance load (capacitor C_{1}). This is the output voltage of R^{2}C_{1}integrating circuit.
To approach the needed square waveform, the collector resistors have to be low in resistance. The base resistors have to be low enough to make the transistors saturate in the end of the restoration (RB < β.RC).
Initial PowerUp
When the circuit is first powered up, neither transistor will be switched on. However, this means that at this stage they will both have high base voltages and therefore a tendency to switch on, and inevitable slight asymmetries will mean that one of the transistors is first to switch on. This will quickly put the circuit into one of the above states, and oscillation will ensue. In practice, oscillation always occurs for practical values of R and C.
However, if the circuit is temporarily held with both bases high, for longer than it takes for both capacitors to charge fully, then the circuit will remain in this stable state, with both bases at 0.6 V, both collectors at 0 V, and both capacitors charged backwards to −0.6 V. This can occur at startup without external intervention, if R and C are both very small.
Improvement to the Astable Multivibrator
(Figure 2) This design of the Astable Multivibrator has been tested but not implemented due to the big difference between the mark and space ratio of 1:100. The waveforms are generated as shown (Figure 3).
Improvement to the Astable Multivibrator
(Figure 4) The Astable Multivibrator has additional resistors of 15Kohm, 150Kohm, 150Kohm to the respective Base node of the BC846 transistors and the waveform results are as shown (Figure 5).
Acknowledgement
None.
Conflict of Interest
No conflict of interest.

Edward Ong Yong Seng. Design and Implementation of the Astable Multivibrator. Glob J Eng Sci. 3(1): 2019. GJES.MS.ID.000554.

Accelerating, Astable, Circuit, Voltage, Multivibrator frequency, Time period, Frequency, Resistor, capacitor, Pulse shape

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