Wave Shaping Circuits

8/11/2019 Wave Shaping Circuits

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Wave shaping circuitsa`


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High Pass Circuit


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High Pass Circuit

Signal is attenuated or damped at low frequencies with the output

increasing at +20dB/Decade (6dB/Octave) until the frequency reaches

the cut-off point ( c) where again R = Xc.

At cut-off frequency, where the output voltage amplitude

is 1/2 = 70.7% of the input signal value or -3dB (20 log (Vout/Vin)) ofthe input value.

Phase angle ( ) of the output signal LEADSthat of the input and isequal to +45oat frequency c.


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Step Response

Voltage on capacitor cannot change instantaneously. So Vout = Vin initially.

Response of RC High Pass Circuit to Standard waveforms


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RC

Fall Time

Vout

time

1.0

0.9

0.1 10%

90%

100%

1/e~37%

e

t

RC

Fall Time & Time Constant ( )


Step Response


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Pulse Response


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Square Wave Response Response


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Square Wave Response Response


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Ramp Response

Let a, be the slop of input ramp signal therefore it can be representedas : Vi(t) = at Now Apply KVL to RC circuit.

Vi = Vc + VR

Vi = (q/c) + VR ---- 1

at = (q/c) + Vo ---- 2Differentiate eq. 2 on both sides wrt t we get

--3

Since dq/dt = i Vo = i . R i = Vo/R = dq/dt = Vo/R

Therefore , -- 4

Hence solution to this differential equation is given by,


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Ramp Response

]1[ RCt

eaRCVo

Nature of output depends on Value of RC time constant.


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High-pass RC circuit as Differentiator:

A circuit in which the output voltage is directly proportional to the

derivative of the input voltage is called a differentiating circuit.

Mathematically, the output voltage is given by:

Output (Vo) d/dt input (Vi)

If a d.c. or constant input is applied to such a circuit, the output will bezero. It is because the derivative of the constant is zero.


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High-pass RC circuit as Differentiator:

Let Vi , be the input alternating voltage and let i be The resultingalternating current. The charge q on the capacitor at any instant is:

q = C.Vc and i = dq/dt

i = d/dt (CVc)

i = C d/dt (Vc)

Since the capacitive reactance is very larger than R, the input voltage

can be consider equal to the capacitor voltage without any error,, i.e

Vc= Vi ,

i = C . d/dt (Vi)

output voltage is given by:Vo= iR Or Vo=(C . d/dt (Vi)).R

Vo=RC d/dt ( Vi)

where RC is a constant, and Hence Output d/dt (input)

RC High pass circuit can work as differentiator for smaller values ofRC time constant.


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Applications:Some important applications of a differentiating circuit are given as

under:

To generate a square wave from a triangular wave input.

To generate a step from a ramp input.

To generate a series of narrow pulses called spikes from the

rectangular or square waveform. The pips are used as trigger pulses or

synchronization pulses in circuits used in television and cathode ray

oscilloscopes.


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Low Pass Circuit


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Low Pass Circuit

This Cut-off, Corner or Breakpoint frequency is defined as

being the frequency point where the capacitive reactance and resistanceare equal, R = Xc . When this occurs the output signal is attenuated

to 70.7% of the input signal value or -3dB (20 log (Vout/Vin)) of the

input.

The Phase Angle ( ) of the output signal LAGSbehind that of theinput and at the -3dB cut-off frequency ( c) and is - 45oout of phase.

This is due to the time taken to charge the plates of the capacitor as the

input voltage changes, resulting in the output voltage (the voltage acrossthe capacitor) laggingbehind that of the input signal.

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Wave Shaping Circuits