The two states of circuit are only stable for a limited time and the circuit switches between them with the output alternating between positive and negative saturation values.

**Multivibrators**

The
two states of circuit are only stable for a limited time and the circuit
switches between them with the output alternating between positive and negative
saturation values.

Analysis
of this circuit starts with the assumption that at time *t=*0 the output has just switched to state 1, and the transition
would have occurred.

An
op-amp Astable multivibrator is also called as free running oscillator. The
basic principle of generation of square wave is to force an op-amp to operate
in the saturation region (±Vsat).

A
fraction β =R2/(R1+R2) of the output is feedback to the positive input terminal
of op-amp. The charge in the capacitor increases & decreases upto a
threshold value called ±βVsat. The charge in the capacitor triggers the op-amp
to stay either at +Vsat or –Vsat.

Asymmetrical
square wave can also be generated with the help of Zener diodes. Astable multi
vibrator do not require a external trigger pulse for its operation & output
toggles from one state to another and does not contain a stable state.

Astable
multi vibrator is mainly used in timing applications & waveforms
generators.

1. The expression of fo is obtained
from the charging period t1 & t2 of capacitor as T=2RCln (R1+2R2)/R1

2.
To
simplify the above expression, the value of R1 & R2 should be taken as R2 =
1.16R Such that fo simplifies to fo =1/2RC.

3.
Assume
the value of R1 and find R2.

4. Assume the value of C & Determine R from
fo =1/2R C

5. Calculate the threshold point from βVSATl =
R1lVTl/ R1-R2 l/βVSATl w h e r e β is the feedback ratio.

A
multivibrator which has only one stable and the other is quasi stable state is
called as Monostable multivibrator or one-short multivibrator. This circuit is
useful for generating signal output pulse of adjustable time duration in
response to a triggering signal. The width of the output pulse depends only on
the external components connected to the op-amp. Usually a negative trigger
pulse is given to make the output switch to other state. But, it then return to
its stable state after a time interval determining by circuit components. The
pulse width T can be given as T = 0.69RC. For Monostable operation the
triggering pulse width Tp should be less then T, the pulse width of Monostable
multivibrator. This circuit is also called as time delay circuit or gating
circuit.

1.
Calculating β from expression

2.
The value of R and C from the pulse width time expression.

3.
Triggering pulse width T_{p} must be much smaller than T. Tp < T.

This
signal generator gives two waveforms: a triangle-wave and a square- wave. The
central component of this circuit is the integrator capacitor CI. Basically we
are interested in performing two functions on CI: *charge it, discharge it - repeat indefinitely.* The output waveforms
are shown here and it is apparent that a square wave generator followed by an
integrator acts as a triangular wave generator.

The
triangle peaks and period may not accurately meet +/-10V swing at 100 us. The
main reason is that current source and thresholds are derived from Zener diodes
- not exactly the most accurate reference.

A
triangle wave implies that the circuit generates a linear voltage ramp. One way
to achieve this goal is by charging discharging CI with a constant current. The
Op Amp Integrator provides for this.

**Ramp Up**

Connect
R_{I} to V_{N} and With V- held at the virtual ground (0V), a
constant current flows from V- to V_{N}.

I_{in}
= V_{N} / R_{I}.

CI
integrates Iin creating a positive linear ramp at Vo. The ramp is linear
because Vo changes proportionally to the time elapsed ΔT.

ΔVo
= - V_{N} / (C_{I} ∙ R_{I}) ∙ ΔT

**Ramp Down
**Connect R_{I} to V_{P}** **and constant
current flows from V_{P} to V-,

I_{in}
= - V_{P} / R_{I}.

Now
Vo ramps down linearly ΔVo = - V_{P} / (C_{I} ∙ R_{I})
∙ ΔT

Ramp
Up:ΔV_{o}/ΔT= -V_{N}/(C_{I}R_{I})

Ramp
Down:ΔVo /ΔT = - V_{P} / ( C_{I}∙R_{I} )

These
equations show the parameters available to control the ramp up / down speeds.
Asymmetrical voltage swings are got by including a reference voltage VREF to
the comparator's negative input.

V_{th}+
=V_{REF}∙(R_{1}+R_{2})/R_{2}-V_{N}∙R_{1}/R_{2}

V_{th}-
= V_{REF} ∙ (R_{1}+R_{2})/R_{2} -V_{P}
∙ R_{1} / R_{2}

When
do we switch from charging to discharging CI? Basically, there is a need to
pick two levels - *an upper and a lower
threshold *- to define the bounds of the triangle wave. The circuit ramps up
or* *down, reversing at the upper and
lower thresholds.

·
With
one leg of RI at VN, the output **ramps up**
until the **Upper Threshold (Vth+ )** is
reached. Then RI is switched from VN to VP.

·
With
one leg of RI at VP, the output **ramps
down** until the **Lower Threshold (Vth-
)** is reached. Then RI is switched from VP to VN.

An
Op Amp Comparator with two thresholds. Produce circuit changes in output state
from VN to VP (or vice-versa) depending on the upper Vth+ and lower Vth-
thresholds.

Vth+=-V_{N}∙R_{1}/R_{2}

Vth-
= -V_{P} ∙ R_{1} / R_{2}

Comparator Working:

o
When
Vin > Vth+, the output switches to VP, the POSITIVE output state.

o
When
Vin < Vth-, the output switches to VN, the NEGATIVE output state.

Zener
diodes D1 and D2 set the positive and negative output levels:

*V _{P}=V_{fD1}+V_{ZD2}
V_{N} = V_{fD2} + V_{ZD1}*.

These
output levels do double duty - they set the comparator thresholds, and set the
voltage levels for the next stage - the integrator.

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