## Projects

**Astable Multivibrator
**

** 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 | SMB_VDC | Dc voltage source | 1 |

GND | SMB_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

_{C2}is equal to V

_{CC}. At this instant

C1 charges exponentially with the time constant R_{1}C_{1} towards the
supply voltage through R1 and correspondingly V_{B2} also increases

exponentially
towards V_{CC}. When V_{B2} crosses the coupling voltage Q2 starts
conducting and V_{C2} falls to V_{CESAT}. Also V_{B1} falls due to capacitive

coupling between collector of Q2 and base of Q1, thereby driving Q1 into OFF
state. The rise in voltage V_{C1} is coupled through C1 to the base

of Q2 causing
a small overshoot in voltage V_{B2}. Thus Q1 is OFF and Q2 is ON. At this instant
the voltage levels are:

V_{B1} is negative, *V _{C1}=V_{CC}, V_{B2}=V_{BESAT}*
and

*V*.

_{C2}=V_{CESAT} 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

_{B2}is negative and

*V*.

_{C2}=V_{CC} 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})*,

*V*, V

_{FIN}=V_{CC}_{C@ }0V.

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
**

* EDWin 2000
-> 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.

* EDWin 2000 -> 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.