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Wave sh

aping

1

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015 2

The RC Integrator

An RC integrator is a circuit that approximates

the mathematical process of integration.

Integration is a summing process, and a basic

integrator can produce an output that is a

running sum of the input under certain

conditions.

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015Oscillators By S.M.Mehzabeen 3

The RC Integrator• A basic RC integrator

circuit is simply a

capacitor in series with a

resistor and the source.

The output is taken across

the capacitor.

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The RC Integrator• When a pulse generator is connected to the input

of an RC integrator, the capacitor will charge and

discharge in response to the pulses.

• When the input pulse goes

HIGH, the pulse generator

acts like a battery in

series with a switch and

the capacitor charges.

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The RC Integrator• When the pulse generator goes low, the small

internal impedance of the generator makes it

look like a closed switch has replaced the

battery. • The pulse generator now acts

like a closed switch and the

capacitor discharges.

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Examples

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Solution1. Time constant

2. Compute the Vout for one

time constant

3. Time to finish discharging

sFKRC 100)001.0)(100(

VVVout 3.610)63.0(

s 5005

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The RC Integrator

• Waveforms for the RC integrator depend on the time

constant () of the circuit. If the time constant is short

compared to the period of the input pulses, the capacitor

will fully charge and discharge. For an RC circuit, = RC.

The output will reach 63% of the final value in 1.

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The RC Integrator – e.g.

• What is if R = 10 k and C = 0.022 F?220 s

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0

The RC Integrator

• If t is increased, the waveforms approach

the average dc level as in the last

waveform. The output will appear

triangular but with a smaller amplitude.

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1

The RC Integrator• Alternatively, the

input frequency can be

increased (T shorter).

The waveforms will

again approach the

average dc level of

the input.

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2

Example

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3

Solution1. Time constant

2. Calculate the first pulse

3. Calculate the second pulse

4. Calculate the second pulse

sFKRC 47)01.0)(7.4(

mveeVVt

FC 958)1(5)1( 4710

mveeVVt

iC 696)(958)( 4715

VeVmVeVVVVt

FiFC 52.1)5696(5)( 4710

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4

Solution

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5

The RC Differentiator

• An RC differentiator is a circuit that

approximates the mathematical process of

differentiation. Differentiation is a process

that finds the rate of change, and a basic

differentiator can produce an output that is

the rate of change of the input under certain

conditions.

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6

The RC Differentiator

• A basic RC differentiator

circuit is simply a

resistor in series with a

capacitor and the source.

The output is taken across

the resistor.

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7

The RC Differentiator• When a pulse generator is connected to the input

of an RC differentiator, the capacitor appears as

an instantaneous short to the rising edge and

passes it to the resistor. • The capacitor looks like

a short to the rising

edge because voltage

across C cannot change

instantaneously.

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8

The RC Differentiator• After the initial edge has passed, the capacitor

charges and the output voltage decreases

exponentially.

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9

Example

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0

Solution1. Time constant sFKRC 8.1)120)(15(

2. tw is bigger than 5 time constant 90 us

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1

The RC Differentiator• The falling edge is a rapid change, so it is passed

to the output because the capacitor voltage cannot

change instantaneously. The type of response shown

happens when t is much less than the pulse width

(t<< tw).

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2

The RC Differentiator• The output shape is

dependent on the

ratio of t to tw.

• When 5t = tw, the

pulse has just

returned to the

baseline when it

repeats.

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3

The RC Differentiator• If t is long compared to the pulse width, the

output does have time to return to the original

baseline before the pulse ends. The resulting

output looks like a pulse with “droop”.

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4

The RL Integrator• Like the RC integrator, an RL integrator is a

circuit that approximates the mathematical process

of integration. Under equivalent conditions, the

waveforms look like the RC integrator. For an RL

circuit, t = L/R.• A basic RL integrator circuit is a resistor in

series with an inductor and the source. The

output is taken across the resistor.

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5

The RL Integrator – e.g.

• What is the time constant

if R = 22 kW and L = 22 mH?

1.0 ms

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6

Example

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7

Solution1. Time constant ns

kH

RL 2

1020

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8

The RL Integrator• When the pulse generator output goes high, a voltage

immediately appears across the inductor in

accordance with Lenz ’ s law. The instantaneous

current is zero, so the resistor voltage is

initially zero.

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9

The RL Integrator• At the top of the input pulse, the inductor voltage

decreases exponentially and current increases. As a

result, the voltage across the resistor increases

exponentially. As in the case of the RC integrator, the

output will be 63% of the final value in 1t.

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0

The RL Integrator• When the pulse goes low, a reverse voltage is induced across

L opposing the change. The inductor voltage initially is a

negative voltage that is equal and opposite to the generator;

then it exponentially increases.

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1

The RL Differentiator• An RL differentiator is also a circuit that

approximates the mathematical process of

differentiation. It can produce an output that is

the rate of change of the input under certain

conditions. • A basic RL differentiator

circuit is an inductor in series

with a resistor and the source.

The output is taken across the

inductor.

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2

The RL Differentiator• When a pulse generator is connected to the input of

an RL differentiator, the inductor has a voltage

induced across it that opposes the source; initially,

no current is in the circuit.

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3

The RL Differentiator• After the initial edge has passed, current

increases in the circuit. Eventually, the

current reaches a steady state value given by

Ohm’s law.

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4

The RL Differentiator• Next, the falling edge of the pulse causes a

(negative) voltage to be induced across the inductor

that opposes the change. The current decreases as

the magnetic field collapses.

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5

The RL Differentiator• As in the case of the RC differentiator, the

output shape is dependent on the ratio of t to

tw. • When 5t = tw, the pulse has

just returned to the

baseline when it repeats.• If t is long compared to

the pulse width, the output

looks like a pulse with

“droop”.

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6

Application• An application of an integrator is to generate a time

delay. The voltage at B rises as the capacitor charges

until the threshold circuit detects that the capacitor

has reached a predetermined level.

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7

Selected Key TermsIntegrator: A circuit producing an output that

approaches the mathematical integral of the

input.Time constant: A fixed time interval, set by R and C, or R and

L values, that determines the time response of a circuit.

Transient time: An interval equal to approximately five time

constants.

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8

Selected Key Terms

Steady state: The equilibrium condition of a circuit that occurs

after an initial transient time.

Differentiator: A circuit producing an output that approaches

the mathematical derivative of the input.

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015Oscillators By S.M.Mehzabeen

MULTIVIBRATORS

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MULTIVIBRATOR MULTIVIBRATOR

ASTABLEASTABLE BISTABLEBISTABLE MONOSTABLEMONOSTABLE

CLASSIFICATION

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A MULTIVIBRATOR is an electronic circuit that switches rapidly by means of positive feedback between two or more states.

Its basically a two amplifier circuit.

A multivibrator generates square, pulse, triangular waveforms.

Also called as nonlinear oscillators or function generators.

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Collector - Coupled Astable Multivibrator

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It consists of two common emitter amplifying stages.

Each stage provides a feedback through a capacitor at the input of the other .

Since the amplifying stage introduces a 180 degrees phase shift and another 180 degrees phase shift is introduced by a capacitor

The feedback signal and the circuit works as an oscillator.

In other words because of capacitive coupling none of the transistor can remain permanently out-off or saturated.

Instead circuit has two quasi-stable states (ON and OFF) and it makes periodic transition between these two states.

The output of an astable multivibrator is available at the collector terminal of the either transistors.

The two outputs are 180degrees out of phase with each other. Therefore one of the output is said to be the complement of the other.

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Emitter - Coupled Astable Multivibrator

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In a collector coupled symmetrical astable multivibrator if it is desired to vary the frequency., then it is necessary

to vary both the timing capacitor simultaneously,

to vary both the timing resistor subject to the conduction that the values are enough to keep the transistors in saturation,

to vary VBB which also cannot be varied over a long range.

Thus it is difficult to achieve frequency control in collector coupled astable multivibrator,

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In order to explain the operation of the circuit, it is necessary that the following conditions must be satisfied.

i.In D.C. conduction i.e. with timing capacitor C removed bias should be so adjusted that both the transistors are in active region.

ii.Under D.C. condition, the D.C. loop gain should be less than unity to void bistable operation.

iii.In the active region, the loop gain must be greater than unity at some non-zero frequency.

iv.Bias conditions ar3e so adjusted that with the capacitor C concerned, during normal operation, transistor C1 operates between cut-off and saturation while transistor C2 operates at the same time between its active region and the off region. This transistor Q1 operates in saturated mode and transistor Q1 operates in saturated mode and transistor Q2 operates in unsaturated mode.

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MONOSTABLE MULTIVIBRATOR

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Monostable Multivibrators can produce a very short

pulse or a much longer rectangular shaped waveform.

Leading edge rises in time with the externally

applied trigger pulse.

Trailing edge is dependent upon the RC time constant

of the feedback components used.

This RC time constant may be varied with time to

produce a series of pulses which have a controlled

fixed time delay in relation to the original

trigger pulse as shown below.

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Monostable Multivibrator Waveforms

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The time constant of Monostable Multivibrators can be changed by varying the values of the capacitor CT, the resistor, RT or both.

Monostable multivibrators are generally used

to increase the width of a pulse orto produce a time delay within a circuit

Since the frequency of the output signal is always the same as that for the trigger pulse input, the only difference is the pulse width.

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The Bistable Multivibrator is another type of two state device similar to the Monostable Multivibrator

The difference is that BOTH states are stable.

Bistable Multivibrators have TWO stable states. (hence the name: “Bi” meaning two)

Maintains in given output state indefinitely unless an external trigger is applied forcing it to change state.

As bistable multivibrators have two stable states they are more commonly known as Latches and Flip-flops for use in sequential type circuits.

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The bistable multivibrator can be switched over from one stable state to the other by the application of an external trigger pulse.

Thus, it requires two external trigger pulses before it returns back to its original state.

In each of the two states, one of the transistors is cut-off while the other transistor is in saturation.

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The bistable multivibrators output is dependent upon the application of two individual trigger pulses, switch position “A” or position “B”.

So Bistable Multivibrators can produce a very short output pulse or a much longer rectangular shaped output.

Leading edge rises in time with the externally applied trigger pulse.

Trailing edge is dependent upon a second trigger pulse.

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Bistable Multivibrator Waveform

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Schmitt triggerSchmitt trigger belongs to a class of bistable multivibrator circuits.

In a bistable, there exist two D.C. couplings from each output to input of the other.

But in Schmitt trigger circuit, there exists only one coupling.

If in the emitter coupled bistable the feedback network from the collector of transistor Q2 to the base of transistor Q1 is removed , it becomes a Schmitt trigger circuit.

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The Schmitt trigger is used for wave shaping circuits.

It can be used for generation of a square wave from a sine wave input.

Basically, the circuit has two opposite operating states like in all other multivibrator circuits.

The trigger signal is not, typically, a pulse waveform but a slowly varying A.C. Voltage.

The Schmitt trigger is level sensitive and switches the output state at two distinct trigger levels.

One of the triggering levels is called a lower trigger level and the other as upper trigger level

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CIRCUIT DIAGRAM

The circuit contains of 2 identical transistors Q1 and Q2 coupled through an emitter RE.

The resistor R1 and R2 form a voltage divider across the VCC supply and ground.

These resistors provide a small forward bias on the base of transistor Q2.

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Let us suppose that initially there is no signal at the input.

Then as soon as the power supply VCC is switched on, the transistor Q2 starts conducting.

The flow of its current through resistor RE produces a voltage drop across it.

This voltage drop acts as a reverse bias across the emitter junction of transistor Q1 due to which it cuts-off.

As a result of this, the voltage at its collector rises to VCC.

This rising voltage is coupled to the base of transistor Q2 through the resistor R1.

It increases the forward bias at the base of transistor Q2 and therefore drives it into saturation and holds it there.

At this instant, the collector voltage, level are VC1 = VCC and VC2 = VCE(sat)

Working

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Suppose an A.C. signal is applied at the input of the Schmitt trigger (i.e. at the base of the transistor Q1).

As the input voltage increases above zero, nothing will happen till it crosses the upper trigger level (U.L.T).

As the input voltage increases, above the upper trigger level, the transistor Q1 conducts.

The point, at which it starts conducting, is known as upper trigger point (U.T.P).

As the transistor Q1 conducts, its collector voltage falls below VCC.

This fall is coupled through resistor R1 to the base of transistor Q2 which reduces its forward bias.

This in turn reduces the current of transistor Q2 and hence the voltage drop across the resistor RE.

As a result of this, the reverse bias of transistor Q1 is reduced and it conducts more.

As the transistor Q1 conducts more heavily, its collector further reduces due to which the transistor Q1 conducts near cut-off.

This process continues till the transistor Q1 is driven into saturation and Q2 into cut-off.

At this instant, the collector voltage levels are VC1 = VCE(sat) and VC2 = VCC

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The transistor Q1 will continue to conduct till the input voltage falls below the lower trigger level (L.T.L).

When the input voltage becomes equal to the lower trigger level, the emitter base junction of transistor Q1 becomes reverse biased.

As a result of this, its collector voltage starts rising toward VCC.

This rising voltage increases the forward bias across transistor Q2 due to which it conducts.

The point, at which transistor Q2 starts conducting, is

called lower trigger point (L.T.P).

Soon the transistor Q2 is driven into saturation and Q1 to cur-off.

This completes one cycle.

The collector voltage levels at this instant are VC1 = VCC and VC2 = VCE(sat).

No change in state will occur during the negative half cycle of the input voltage.

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The output of a Schmitt trigger is a positive going pulse width depends upon the time during which transistor Q1 is conducting.

The conduction time is set by the upper and lower trigger levels.

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Bistable Multivibrator Triggering

To change the stable state of the binary it is necessary to apply an appropriate pulse in the circuit, which will try to bring both the transistors to active region and the resulting regenerative feedback will result on the change of state.

Triggering may be of two following types:

Asymmetrical triggering

Symmetrical triggering

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Asymmetrical triggering

In asymmetrical triggering, there are two trigger inputs for the transistors Q1 and Q2. Each trigger input is derived from a separate triggering source. To induce transition among the stable states, initially the trigger is applied to the bistable. For the next transition, now the identical trigger must appear at the transistor Q2. Thus it can be said that in asymmetrical triggering, trigger pulses derived from two separate source and connected to the two transistors Q1 and Q2 individually, sequentially change the state of the bistable.

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Asymmetrical triggering of Bistable Multivibrator

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Symmetrical Triggering

There are various symmetrical triggering methods called

symmetrical collector triggering,

symmetrical base triggering and

symmetrical hybrid triggering.

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Symmetrical base triggering (positive pulse)

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Diodes D1 and D2 are steering diodes.

Here the positive pulses, try to turn ON and OFF transistor.

Thus when transistor Q1 is OFF and transistor Q2 is ON, the respective base voltages and V B1N, OFF and VB2N, ON. It will be seen that VB1N, OFF > VB1N, ON.

Thus diode D2 is more reverse-biased compared to diode D1.When the positive differentiated pulse amplitude is greater than (VB1N, OFF + Vɣ),

the diode D1 gets forward biased,

transistor Q1 enters the active region,

with subsequent regenerative feedback Q1 gets ON,

transistor Q2 becomes OFF. On the arrival of the next trigger pulse now the diode D2 will be forward biased and ultimately with regenerative feedback it will be in the ON state.

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