Multivibrator

A multivibrator is an electronic circuit used to implement a variety of simple two-state systems such as oscillators, timers and flip-flops. It is characterized by two amplifying devices (transistors, electron tubes or other devices) cross-coupled by resistors or capacitors. The name "multivibrator" was initially applied to the free-running oscillator version of the circuit because its output waveform was rich in harmonics. ^[1] There are three types of multivibrator circuits depending on the circuit operation:

• astable, in which the circuit is not stable in either state —it continually switches from one state to the other. It does not require an input such as a clock pulse.
• monostable, in which one of the states is stable, but the other state is unstable (transient). A trigger causes the circuit to enter the unstable state. After entering the unstable state, the circuit will return to the stable state after a set time. Such a circuit is useful for creating a timing period of fixed duration in response to some external event. This circuit is also known as a one shot.
• bistable, in which the circuit is stable in either state. The circuit can be flipped from one state to the other by an external event or trigger.

Multivibrators find applications in a variety of systems where square waves or timed intervals are required. For example, before the advent of low-cost integrated circuits, chains of multivibrators found use as frequency dividers. A free-running multivibrator with a frequency of one-half to one-tenth of the reference frequency would accurately lock to the reference frequency. This technique was used in early electronic organs, to keep notes of different octaves accurately in tune. Other applications included early television systems, where the various line and frame frequencies were kept synchronized by pulses included in the video signal.

History

The classic multivibrator circuit (also called a plate-coupled multivibrator) is first described by H. Abraham and E. Bloch in Publication 27 of the French Ministère de la Guerre, and in Annales de Physique 12, 252 (1919). It is a predecessor of Eccles-Jordan trigger^[2] derived from this circuit a year later.

Astable multivibrator

An astable multivibrator is a regenerative circuit consisting of two amplifying stages connected in a positive feedback loop by two capacitive-resistive coupling networks. The amplifying elements may be junction or field-effect transistors, vacuum tubes, operational amplifiers, or other types of amplifier. The example diagram shows bipolar junction transistors.

The circuit is usually drawn in a symmetric form as a cross-coupled 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).

Operation

Figure 1: Basic BJT astable multivibrator

The circuit has two stable 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 time-setting capacitor and the second prepares to play this role in the next state). The circuit operation is based on the fact that the forward-biased base-emitter junction of the switched-on bipolar transistor can provide a path for the capacitor restoration.

State 1 (Q1 is switched on, Q2 is switched off):
In the beginning, the capacitor C1 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 left-hand positive plate of C1 to ground. As its right-hand negative plate is connected to Q2 base, a maximum negative voltage (-V) is applied to Q2 base that keeps Q2 firmly off. C1 begins discharging (reverse charging) via the high-resistive base resistor R2, so that the voltage of its right-hand plate (and at the base of Q2) is rising from below ground (-V) toward +V. As Q2 base-emitter junction is backward-biased, it does not impact on the exponential process (R2-C1 integrating network is unloaded). Simultaneously, C2 that is fully discharged and even slightly charged to 0.6 V (in the previous State 2) quickly charges via the low-resistive collector resistor R4 and Q1 forward-biased base-emitter junction (because R4 is less than R2, C2 charges faster than C1). Thus C2 restores its charge and prepares for the next State 2 when it will act as a time-setting capacitor. Q1 is firmly saturated in the beginning by the "forcing" C2 charging current added to R3 current; in the end, only R3 provides the needed input base current. The resistance R3 is chosen small enough to keep Q1 (not deeply) saturated after C2 is fully charged.

When the voltage of C1 right-hand plate (Q2 base voltage) becomes positive and reaches 0.6 V, Q2 base-emitter junction begins diverting a part of R2 charging current. Q2 begins conducting and this starts the avalanche-like positive feedback process as follows. Q2 collector voltage begins falling; this change transfers through the fully charged C2 to Q1 base and Q1 begins cutting off. Its collector voltage begins rising; this change transfers back through the almost empty C1 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 avalanche-like manner until finally Q1 switches off and Q2 switches on. The forward-biased Q2 base-emitter junction fixes the voltage of C1 right-hand 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 C2 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 right-hand positive plate of C2 to ground. As its left-hand negative plate is connected to Q1 base, a maximum negative voltage (-V) is applied to Q1 base that keeps Q1 firmly off. C2 begins discharging (reverse charging) via the high-resistive base resistor R3, so that the voltage of its left-hand plate (and at the base of Q1) is rising from below ground (-V) toward +V. Simultaneously, C1 that is fully discharged and even slightly charged to 0.6 V (in the previous State 1) quickly charges via the low-resistive collector resistor R1 and Q2 forward-biased base-emitter junction (because R1 is less than R3, C1 charges faster than C2). Thus C1 restores its charge and prepares for the next State 1 when it will act again as a time-setting capacitor...and so on... (the next explanations are a mirror copy of the second part of Step 1).

Multivibrator period (frequency)

Derivation

The duration of state 1 (low output) will be related to the time constant R₂C₁ as it depends on the charging of C1, and the duration of state 2 (high output) will be related to the time constant R₃C₂ as it depends on the charging of C2. Because they do not need to be the same, an asymmetric duty cycle is easily achieved. The extended content below contains a derivation of the multivibrator period (frequency); click the show button to see the content.

The voltage on a capacitor with non-zero initial charge is:

$V_\text{cap}(t) = \left((V_\text{capinit} - V_\text{charging}) \times e^{-t/(RC)}\right) + V_\text{charging}$

Looking at C2, just before Q2 turns on the left terminal of C2 is at the base-emitter 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 C2 is V_CC minus V_{BE_Q1} . The moment after Q2 turns on, the right terminal of C2 is now at 0 V which drives the left terminal of C2 to 0 V minus (V_CC - V_{BE_Q1}) or V_{BE_Q1} - V_CC. From this instant in time, the left terminal of C2 must be charged back up to V_{BE_Q1}. How long this takes is half our multivibrator switching time (the other half comes from C1). In the charging capacitor equation above, substituting:

V_{BE_Q1} for V_cap(t)

(V_{BE_Q1} - V_CC) for V_capinit

V_CC for V_charging

results in:

$V_{\text{BE}\_\text{Q1}} = \left(((V_{\text{BE}\_\text{Q1}} - V_\text{CC}) - V_\text{CC}) \times e^{-t/(RC)}\right) + V_\text{CC}$

Solving for t results in:

$t=-RC \times \ln\left(\frac{V_{\text{BE}\_\text{Q1}} - V_\text{CC}}{V_{\text{BE}\_\text{Q1}} - 2 V_\text{CC}}\right)$

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:

$t = -RC \times \ln\left(\frac{-V_\text{CC}}{-2 V_\text{CC}}\right)$

or

$t = -RC \times \ln\left(\frac{1}{2}\right)$

or

$t = RC \times \ln(2)$

The period of each half of the multivibrator is therefore given by t = ln(2)RC.

Summary

The total period of oscillation is given by:

T = t₁ + t₂ = ln(2)R₂ C₁ + ln(2)R₃ C₂

$f = \frac{1}{T} = \frac{1}{\ln(2) \cdot (R_2 C_1 + R_3 C_2)} \approx \frac{1}{0.693 \cdot (R_2 C_1 + R_3 C_2)}$

where...

• f is frequency in hertz.
• R₂ and R₃ are resistor values in ohms.
• C₁ and C₂ are capacitor values in farads.
• T is the period (In this case, the sum of two period durations).

For the special case where

• t₁ = t₂ (50% duty cycle)
• R₂ = R₃
• C₁ = C₂

$f = \frac{1}{T} = \frac{1}{\ln(2) \cdot 2RC} \approx \frac{0.721}{RC}$ ^[3]

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 base-emitter junction is backward-biased and the capacitor C1 is "unhooked" from ground. The output voltage of the switched-on transistor Q1 changes rapidly from high to low since this low-resistive output is loaded by a high impedance load (the series connected capacitor C1 and the high-resistive base resistor R2).

During State 2, Q2 base-emitter junction is forward-biased and the capacitor C1 is "hooked" to ground. The output voltage of the switched-off transistor Q1 changes exponentially from low to high since this relatively high resistive output is loaded by a low impedance load (the capacitance C1). This is the output voltage of R₁C₁ integrating circuit.

To approach the needed square waveform, the collector resistors have to be low resistance. The base resistors have to be low enough to make the transistors saturate in the end of the restoration (R_B < β.R_C).

Initial power-up

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.

Frequency divider

An astable multivibrator can be synchronized to an external chain of pulses. A single pair of active devices can be used to divide a reference by a large ratio, however, the stability of the technique is poor owing to the variability of the power supply and the circuit elements; a division ratio of 10, for example, is easy to obtain but not dependable. Chains of bistable flip-flops provide more predictable division, at the cost of more active elements. ^[3]

Protective components

While not fundamental to circuit operation, diodes connected in series with the base or emitter of the transistors are required to prevent the base-emitter junction being driven into reverse breakdown when the supply voltage is in excess of the V_eb breakdown voltage, typically around 5-10 volts for general purpose silicon transistors. In the monostable configuration, only one of the transistors requires protection.

Monostable multivibrator circuit

Figure 2: Basic BJT monostable multivibrator.

Figure 3: Basic BJT bistable multivibrator (suggested values: R1, R2 = 1 kΩ R3, R4 = 10 kΩ).

In the monostable multivibrator, the one resistive-capacitive network (C₂-R₃ in figure 1) is replaced by a resistive network (just a resistor). The circuit can be thought as a 1/2 astable multivibrator. Q2 collector voltage is the output of the circuit (in contrast to the astable circuit, it has a perfect square waveform since the output is not loaded by the capacitor).

When triggered by an input pulse, a monostable multivibrator will switch to its unstable position for a period of time, and then return to its stable state. The time period monostable multivibrator remains in unstable state is given by t = ln(2)R₂C₁. If repeated application of the input pulse maintains the circuit in the unstable state, it is called a retriggerable monostable. If further trigger pulses do not affect the period, the circuit is a non-retriggerable multivibrator.

For the circuit in Figure 2, in the stable state Q1 is turned off and Q2 is turned on. It is triggered by zero or negative input signal applied to Q2 base (with the same success it can be triggered by applying a positive input signal through a resistor to Q1 base). As a result, the circuit goes in State 1 described above. After elapsing the time, it returns to its stable initial state.

Bistable multivibrator circuit

Main article: Flip-flop (electronics)

In the bistable multivibrator, both the resistive-capacitive network are replaced by resistive networks (just resistors or direct coupling).

This latch circuit is similar to an astable multivibrator, except that there is no charge or discharge time, due to the absence of capacitors. Hence, when the circuit is switched on, if Q1 is on, its collector is at 0 V. As a result, Q2 gets switched off. This results in more than half +V volts being applied to R4 causing current into the base of Q1, thus keeping it on. Thus, the circuit remains stable in a single state continuously. Similarly, Q2 remains on continuously, if it happens to get switched on first.

Switching of state can be done via Set and Reset terminals connected to the bases. For example, if Q2 is on and Set is grounded momentarily, this switches Q2 off, and makes Q1 on. Thus, Set is used to "set" Q1 on, and Reset is used to "reset" it to off state.

References

1. ^ Multivibrator in IEEE Std. 100 Dictionary of Standards Terms 7th ed.,IEEE Press, 2000 ISBN 0-7381-2601-2 page 718
2. ^ William Henry Eccles and Frank Wilfred Jordan, "Improvements in ionic relays" British patent number: GB 148582 (filed: 21 June 1918; published: 5 August 1920).
3. ^ ^{a b} Donald Fink (ed), Electronics Engineers' Handbook, McGraw Hill, 1975 ISBN 070209804, page 16-40

See also

• Blocking oscillator
• RC circuit
• Schmitt trigger

External links

• Java applets simulating the multivibrator circuits.
• Monostable Circuits based on NAND gates see the "NOT gate astable" based on RC circuit