** Aim **

To design and simulate an Astable Multivibrator circuit.

**
Components **

Name |
EDWin Components Used |
Description |
Number of components required |

BC107 | BC107A | Transistor | 2 |

RES | RC05 | Resistor | 4 |

CAP | CASE-A600 | Capacitor | 2 |

VDC | VDC | Dc voltage source | 1 |

GND | SPL0 | Ground | 1 |

** Theory
**

**Astable Multivibrator** is a two stage switching circuit in which
the output of the first stage is fed to the input of the
second stage and vice versa. The outputs of both the stages are complementary. This free
running multivibrator generates square wave without any
externaltriggering pulse. The circuit has two stable states
and switches back and forth from one state to another, remaining in each
state for a time depending upon thedischarging of the capacitive circuit.

The multivibrator is one form of relaxation oscillator, the frequency of which may be controlled by external synchronizing pulses.

In our experiment we are using transistor, as the amplifying device and also it is a collector coupled multivibrator.

Figure shows the basic symmetrical astable multivibrator in which components in one half of a cycle of the circuit are identical to their counterpart in the other half. Square wave output can be obtained from the collector point of Q1 or Q2.

**
Operation**

When supply voltage, V_{CC} is applied, one transistor will conduct more
than the other due to some circuit imbalance. Initially let
us assume that Q1
is conducting and Q2 is cut-off. Then V_{C1,} the output of Q1 is equal to *V _{CESAT}*
which is approximately zero and V

When Q1 is OFF and Q2 is ON the voltage V_{B1} increases
exponentially with a time constant R_{2}C_{2} towards V_{CC}
. Therefore Q1 is driven to saturation and Q2 to cut-off. Now the voltage
levels are:

* V _{B1}=V_{BESAT}, V_{C1}=V_{CESAT}*,
V

From the above it is clear that when Q2 is ON the falling voltage V_{C2} permits the discharging of capacitor C2 which inturn
drives Q1 into cut-off. The rising
voltage of V_{C1} is fed back to the base of Q2 tending to turn
it ON. This process is regenerative.

*Derivation of time period*

The charging equation for a capacitor is given by

Capacitor voltage,

Hence

where V_{C} - the capacitor voltage,

*V _{INIT}* – the initial
capacitor voltage,

*V _{FIN}* – the final
capacitor voltage

t – the time period of charging.

R and C – the resistor and capacitor through which charging occurs.

The capacitor discharges from –V_{CC} to V_{CC}.

Therefore *V _{IN}=(-V_{CC})*,

Substituting this in equation (2)

Taking natural logarithm,

For a symmetrical astable multivibrator,

Charging and discharging time periods are given by,

From equation(5)

where T is the total time period.

Since the multivibrator is symmetrical

**Design**

Design Specifications

Manufacturer’s specifications

Applying KVL for the collector side of Q2.

, (since it is a symmetrical astable multivibrator)

Applying KVL for the base loop of the circuit

, (since it is a symmetrical astable multivibrator.)

** Design of C **

The total time period T is given by

,(since it is a symmetrical astable multivibrator.)

From equations (1) and (2)

The free running frequency is given by

Assume the frequency as 100Hz.

**Procedure**

* EDWinXP-> Schematic Editor:*The circuit diagram is drawn by
loading components from the library. Wiring and proper net assignment has been made. The values are
assigned for relevant components.

* EDWinXP-> Mixed Mode Simulator:* The circuit is preprocessed. The desired test points and
waveform markers are placed. The Transient Analysis parameters have been set. The Transient Analysis is
executed and output observed in Waveform Viewer.

**Result**

The output waveform may be observed in the waveform viewer.