Draw the differentiator circuit, Electrical Engineering

Assignment Help:

Q. Draw the differentiator circuit. Explain its principle of operation with necessary waveforms ?

A circuit in which the output voltage is directly proportional to the derivative of the input signal is called differentiator circuit i.e. v0=d/dt(input). A differentiating circuit can be arranged by a simple RC series circuit. Here the values of R and C are selected in such a way that the time constant (RC) of the circuit should be very small than the time period of the input wave and reactance of the capacitor is very large as compared to the value of the resistor. Thus the current flowing in the differentiator circuit is to a large extent decided by the capacitive reactance; the current will be leading the input voltage by 90 degrees approximately. Due to this current, the voltage developed across the resistor also leads the input voltage by 90 degrees.

If the input is a sinusoidal signal and given by

            vi = V sin(ωt)

Then the output will be leading this voltage by 90 degrees.

           vo = Vsin (ωt+90)= V cos(ωt).

Thus we find that the output is a differentiated form of the input signal. This can be proved mathematically.

       The output voltage VO = i*R

But since XC>>R, the current (i)is dependent upon capacitor alone. Therefore, the rate of change of charge across the capacitor gives the current

             i = dQ/dt

but the charge Q across the capacitor C is given as

             Q = C*VC

Where VC is the voltage across the capacitor

           i = dQ/dt = d/dt(C*VC) =C* d(vt)/dt

            vo = i* R = CR*d/dt(vt)

When a dc voltage is applied to the differentiating circuit, its output will be zero since the derivative of a constant is zero. For a square wave input, the differentiator output will be sharp narrow pulses. When the input to the differentiator circuit is a triangular wave, the output will be a square or rectangular wave. For a sine wave input, the output of the differentiator will be a cosine wave.


Related Discussions:- Draw the differentiator circuit

Write explanatory notes on hard disk drive controller, Write explanatory no...

Write explanatory notes on Hard disk drive controller. Hard disk drive controller: It converts instructions from software running upon the computer to the electrical signals

Basic electromagnetic principles, It has been known for a thousand years or...

It has been known for a thousand years or more (originating in China) that certain (magnetic) materials would always orientate    themselves in a  particular direction if suspended

Case 2 a>b - program description, Case 2 ( A>B) Suppose XX = 05H ( stor...

Case 2 ( A>B) Suppose XX = 05H ( stored  in A ) And  YY = 02H ( stored  in B). Then carry  flag will  reset by CMP instruction, since  A> B in this  case JNC  will transfer the

Bjt, what is compensation of bjt

what is compensation of bjt

Explain in detail the operation of 8255 in mode 1, Explain in detail the op...

Explain in detail the operation of 8255 in mode1 taking suitable example. In mode1, Ports A and B are programmed as input or output ports and Port C is used for handshaking.

Balanced budget laws, Balanced Budget Laws: Laws (usually passed by right-w...

Balanced Budget Laws: Laws (usually passed by right-wing governments) that require governments to run balanced budgets regardless of state of the overall economy. These lawshave th

Methods for speed and torque control of induction motors, Q. Methods for sp...

Q. Methods for speed and torque control of induction motors? The following are methods available for speed and torque control of induction motors. • Pole-changing method

Modern physics, jsidjsiod dkndkdisd dknssbs bsjbabd asj u dhihf ujojdsajfs...

jsidjsiod dkndkdisd dknssbs bsjbabd asj u dhihf ujojdsajfs sjssaidhsidw idgsdusadidjwap ewkeowr krwnrh bwvr [ wrj wrj 1 nnwoi khiwrjw ko e woewerijr rjwr jr rjhpr

Direct current charging and discharging circuit, 1. The circuit shown belo...

1. The circuit shown below is a DC charging and discharging circuit. a. At t = 0 sec, switch S1 is thrown to position 1 ("pos1"). Write the mathematical expressions for V

Slack running fit, Illustrate the conventional representations of the follo...

Illustrate the conventional representations of the following guide to the selection of Fits: (i) Slack Running Fit (ii) Loose Running Fit (iii) Easy Running Fit (iv) No

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd