Fig 1 gives the circuit of an astable multivibrator using BJTs while Fig 2 gives the waveforms of collector voltages and base voltages of the two transistors.

Transistor T_{1} along with collector circuit resistor R_{c1} and coupling capacitor C_{b1} forms one stage of R-C coupled amplifier. Its output is coupled through capacitor C_{b1} to the other R-C coupled amplifier stage formed by transistor T_{2}, collector circuit resistor R_{c2} and coupling capacitor C_{b2}. The output of this second state is coupled through capacitor C_{b2} to the input of the first amplifier state. Resistors R_{B1} and R_{B2} provide the ON stage base bias currents to the transistors T_{1} and T_{2}. In a symmetrical astable multivibrator, R_{B1} = R_{B2} = R_{B}, C_{b1} = C_{b2 }= C_{b}, R_{c1} = R_{c2} = R_{c} and the two transistors T_{1} and T_{2} are identical.

## Operation of the Circuit

### Starting of Waveform

(i) Let the collector power supply Vcc be suddenly put ON at time t = t_{1}. Then due to slight mismatch, let the collector current I_{c1} of transistor T_{1} be slightly greater than the collector current I_{c2} of transistor T_{2}. Then the rate of fall of V_{cl} is more than that of V_{c2}.

(ii) For such sudden application of voltage, capacitors act as short circuits and voltages across them cannot change instantaneously. Hence the changes in collector voltages of T_{1} from the initial value of Vcc to V_{c1} (V_{c1} < Vcc) will make the base of transistor T_{2} negative.

(iii) This negative voltage at the base of T_{2} reduces the conduction current of T_{2} and increases the collector voltage V_{c2} i.e., makes it move towards Vcc.

(iv) This increase in V_{c2} gets transferred through capacitor C_{b2} to the base of transistor T_{1} making its base voltage more positive. This increase the collector current of transistor T_{1}.

(v) Increased collector current of T_{2} will further reduce collector voltage V_{cl}, make base of T_{2} more negative and reduce collector current of T_{2}.

(vi) This forms a cumulative action and with loop gain > 1, the whole above sequence of operation occurs instantaneously with the result that transistor T_{1} goes into saturation while transistor T_{2} goes into OFF region.

Thus, we find that as soon as this astable multivibrator is switched on, T_{1} goes ON and T_{2} goes OFF. Let, this time instant be t = 0.

### Voltages and Currents of Transistor T_{1} at time t = 0.

At time t = 0, for large Vcc and large V_{BB},

……(1)

……(2)

……(3)

……(4)

### Voltages and Currents of Transistor T_{2} at time t = 0

Collector current of T_{2} is zero. Hence at t = 0, …..(5)

Voltage at the base of T_{2} at time t = 0 can be obtained from the fact that the voltage on capacitor C_{b1} is V_{CC} at the instant of switching ON the power supply before the beginning of the regenerative feedback sequence. This implies that the collector terminal of capacitor C_{b1} is V_{CC} and the base side voltage is V_{B2,ON}. At the end of the regenerative cycle, the collector side voltage of capacitor C_{b1} has fallen from V_{CC} to V_{CE,sat} (almost zero). But the voltage across capacitor C_{b1} cannot change instantaneously. Hence the voltage at the base of transistor T_{2} is given by,

…..(6)

### Circuit Behavior in Quasi-Stable State (0 < t < t_{1})

Voltage across capacity C_{b1} rises from V_{B2,OFF} (t = 0) towards V_{BB}. Charging path is provided by C_{b1} and R_{B2} assuming that . At any time, instant t, voltage V_{B2} is given by,

…….(7)

Thus the voltage V_{B2} (t) rises exponentially with time constant R_{B2}.C_{b1}. However, as soon as V_{B2} equal V_{B2,ON} at time t_{1}, T_{2} starts conducting and V_{B2} (t) remains constant at V_{B2,ON} as shown in Fig 2.

At time t = t_{1}

…….(8)

Solving Equation (6) and (8) simultaneously we get,

……(9)

Assuming that VBB >> VB2ON, Equation (9) becomes,

…….(10)

If V_{BB} = V_{CC}, Equation (10) reduced to,

…….(11)

**Circuit Behavior at time t = t _{1}:** At time t=t

_{1}, transistor T

_{2}starts conducting since V

_{B2,ON}is reached. Collector voltage V

_{c2}of T

_{2}begins to fall. This fall in V

_{c2}is coupled through C

_{b2}to the base of T

_{1}resulting in equal reduction in V

_{B1}. This in turn causes reduction in collector current of T

_{1}and increase in collector voltage V

_{c1}of T

_{1}. This increase in V

_{c1}is coupled to the base of T

_{1}through C

_{b1}causing increased conduction of T

_{2}. This regenerative process continues with the end result that T

_{2}goes into saturation while T

_{1}gets cutoff. This entire process takes place instantaneously at t = t

_{1}.

**Circuit Behavior during Quasi-Stable State:** During this time period, capacitor C_{b2} charges from V_{B2,OFF }(t=0) towards V_{BB}, exponentially with time constant R_{B1}.C_{b2}. At time t = t_{2}, the instantaneous base voltage reaches V_{B1,ON} and transistor T_{1} goes into conduction.

Time interval (t_{2} – t_{1}) may be expressed as,

……(12)

However, V_{B1,ON }is very small compared with V_{BB.} Hence Equation (12) may be put as,

…..(13)

If …..(14)

Periodic Time: Total time period T is the sum of t_{1} and (t_{2}-t_{1}).

Thus, ……(15)

For a symmetrical multivibrator, we have R_{B1} = R_{B2} = R_{B} and C_{b1} = C_{b2} = C_{b}. Then equation (15) reduces to,

…..(16)

From Eq. (15) we find that subject to the approximations, periodic time of multivibrator is independent of supply voltage V_{CC}, temperature and junction voltage.

Frequency of astable multivibrator …..(17)