Astable Multivibrator - Engineering Projects

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 T₁ 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 T₂, 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 T₁ and T₂. 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 T₁ and T₂ are identical.

Operation of the Astable Multivibrator Circuit

Starting of Waveform

(i) Let the collector power supply Vcc be suddenly put ON at time t = t₁. Then due to slight mismatch, let the collector current I_c1 of transistor T₁ be slightly greater than the collector current I_c2 of transistor T₂. 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 T₁ from the initial value of Vcc to V_c1 (V_c1 < Vcc) will make the base of transistor T₂ negative.

(iii) This negative voltage at the base of T₂ reduces the conduction current of T₂ 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 T₁ making its base voltage more positive. This increase the collector current of transistor T₁.

(v) Increased collector current of T₂ will further reduce collector voltage V_cl, make base of T₂ more negative and reduce collector current of T₂.

(vi) This forms a cumulative action and with loop gain > 1, the whole above sequence of operation occurs instantaneously with the result that transistor T₁ goes into saturation while transistor T₂ goes into OFF region.

Thus, we find that as soon as this astable multivibrator is switched on, T₁ goes ON and T₂ goes OFF. Let, this time instant be t = 0.

Voltages and Currents of Transistor T₁ at time t = 0.

At time t = 0, for large Vcc and large V_BB,

$V_{c1} = V{CE,sat} \approx 0$ ……(1)

$I_{c1,sat} = \dfrac{V_{CC}-V_{CE,sat}}{R_{c1}} \approx \dfrac{V_{CC}}{R_{c1}}$ ……(2)

$V_{B1,ON} \approx 0$ ……(3)

$I_{B,ON} = \dfrac{V_{BB}-V_{BE,sat}}{R_{B1}} \approx \dfrac{V_{BB}}{R_{B1}}$ ……(4)

Voltages and Currents of Transistor T₂ at time t = 0

Collector current of T₂ is zero. Hence at t = 0, $V_{c2,OFF} \approx V_{CC}$ …..(5)

Voltage at the base of T₂ 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 T₂ is given by,

$V_{B2,OFF}(t=0) \approx V_{B2,ON}-V_{CC}$ …..(6)

Circuit Behavior in Quasi-Stable State (0 < t < t₁)

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 $V_{c1} \approx 0$ . At any time, instant t, voltage V_B2 is given by,

$V_{B2}^{(t)} = V_{BB} + [V_{B2,OFF}(t=0)-V_{BB}] \in \dfrac{-t}{R_{B2}C_{b1}}$ …….(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 t₁, T₂ starts conducting and V_B2 (t) remains constant at V_B2,ON as shown in Fig 2.

At time t = t₁

$V_{B2,ON} = V_{BB} + - VBB [V_{B2,OFF}(t=0)-V_{BB}] \in \dfrac{-t}{R_{B2}C_{b1}}$ …….(8)

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

$t_1 = R_{B2} \times C_{b1} ln [\dfrac{V_{BB} + (V_{CC}-V_{B2,ON})}{V_{BB}-V_{B2,ON}}]$ ……(9)

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

$t_1 = R_{B2} \times C_{b1} (1 + \dfrac{V_{CC}}{V_{BB}})$ …….(10)

If V_BB = V_CC, Equation (10) reduced to,

$t_1 \approx ln R_{B2} \times C_{b1}$

$\approx 0.69 ln R_{B2} \times C_{b1}$ …….(11)

Circuit Behavior at time t = t₁: At time t=t₁, transistor T₂ starts conducting since V_B2,ON is reached. Collector voltage V_c2 of T₂ begins to fall. This fall in V_c2 is coupled through C_b2 to the base of T₁ resulting in equal reduction in V_B1. This in turn causes reduction in collector current of T₁ and increase in collector voltage V_c1 of T₁. This increase in V_c1 is coupled to the base of T₁ through C_b1 causing increased conduction of T₂. This regenerative process continues with the end result that T₂ goes into saturation while T₁ gets cutoff. This entire process takes place instantaneously at t = t₁.

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 = t₂, the instantaneous base voltage reaches V_B1,ON and transistor T₁ goes into conduction.

Time interval (t₂ – t₁) may be expressed as,

$(t_2-t_1) = R_{B1} \times C_{b2} ln [\dfrac{V_{BB} + (V_{CC}-V_{B1,ON})}{V_{BB}-V_{B1,ON}}]$ ……(12)

However, V_B1,ONis very small compared with V_BB. Hence Equation (12) may be put as,

$(t_2-t_1) = R_{B1} \times C_{b2} ln (1 + \dfrac{V_{CC}}{V_{BB}})$ …..(13)

If $V_{BB} = V_{CC}, then (t_2-t_1) \approx 0.69 R_{B1} \times C_{b2}$ …..(14)

Periodic Time: Total time period T is the sum of t₁ and (t₂-t₁).

Thus, $T \approx 0.69 (R_{B1} \times C_{b2} + R_{B2} \times C_{b1})$ ……(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,

$T = 1.38 R_BC_B$ …..(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 $= \dfrac{1}{T} = \dfrac{1}{1.38 R_B C_b}$ …..(17)

Operation of the Astable Multivibrator Circuit

Starting of Waveform

Voltages and Currents of Transistor T1 at time t = 0.

Voltages and Currents of Transistor T2 at time t = 0

Circuit Behavior in Quasi-Stable State (0 < t < t1)

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Voltages and Currents of Transistor T₁ at time t = 0.

Voltages and Currents of Transistor T₂ at time t = 0

Circuit Behavior in Quasi-Stable State (0 < t < t₁)