differentiator&integrator

08.408 Analog Integrated circuits Lab Manual

Differentiator and Integrator using Opamp

Aim: To test differentiator and integrator circuits using ua741op-amp

Components required : CRO (20Mhz ,dual channel) Resistors Signal generator Oscilloscope probes ua741 opamp, capacitors,multimeters

Differentiation and IntegrationOp-amp circuits are often designed and implemented for signal differentiation and integration. Until recently (before computer-based control), control algorithms (such as PID) containing differentials and integrals were implemented in discrete circuit components. Differentiation is also useful for obtaining velocity measurements from a signal representing a position or determining a signal's frequency (recall the amplitude of the time derivative of a sinusoid is scaled by its frequency). Figure 1 below shows an ideal op-amp integrator and differentiators with input-output relationships that are theoretically correct, but have practical implementation issues discussed below. In this lab, practically realizable differentiators and integrators will be built using op-amps, resistors and capacitors

A differentiator is a circuit whose output magnitude is determined by the rate at which the voltage applied to its input changesThe external components connected to the differentiator op-amp are

I) A capacitor connected to the inverting inputII) A feedback resistor between inverting input and output

The resistor and capacitor combination form part of the RC network

Dept of ECE,VKCET


The differentiator is configured in the same way as the inverting amplifier(closed loop)

The Differentiator The ideal differentiator is inherently unstable in practice due to the presence of some high

frequency noise in every electronic system. An ideal differentiator would amplify this small noise. For instance, if vnoise = Asin(wt) is differentiated, the output would be vout = Awcos(wt). Even if A = 1mV, when w = 2p(10MHz) vout would have an amplitude of 63V! To circumvent this problem, it is traditional to include a series resistor at the input and a parallel capacitor across the feedback resistor as shown in figure , converting the differentiator to an integrator at high frequencies for filtering.

Adding the input resistor Rin limits the differentiators increase in gain at a ratio of Rf/Rin. The circuit now acts like a differentiator amplifier at low frequencies and an amplifier with resistive feedback at high frequencies giving much better noise rejection. Additional attenuation of higher frequencies is accomplished by connecting a capacitor C1 in parallel with the differentiator feedback resistor, Rf. This then forms the basis of a Active High Pass Filter

Dept of ECE,VKCET


Figure 1: A Practical DifferentiatorPrelab

1)Derive the expression for gain of the differentiator2) Draw the expected output to a 1Vp-p square wave,sine, ramp input3) Mathematically ,perform the process of differentiation using all the above mentioned functions4) Simulate the circuit in any circuit simulation software

Design and Procedure1. Select fa equal to the highest frequency of the input signal to be differentiated. Then assuming a

value of C1 less that 1uF Calculate the value of Rf.2. Choose fb=20fa and calculate the values of R1 and Cf such that R1C1=RfCf. Select fa<fb<fc3. The input will be differentiated properly if the time period T of the input signal is larger than or

equal to RfC1 T≥RfC1

4. Repeat the experiment for all three conditions ;RC<T,RC>T and RC=T

5. Sketch the wave forms forVi = ± 1Vsquare wave at 100Hz

. Vi = ± 1V square wave at 500Hz

Vi = ± 1V square wave at 1kHz

Vi = ± 1V triangle wave at 100Hz


Vi = ± 1V triangle wave at 1kHz

Vi = 0.5V sin 2π 100t

Vi = 0.5V sin 2π 500t

Vi = 0.5V sin 2π 1000t

6.Draw the magnitude frequency plot from the square wave response and find fa,fb,fc practical and compare with theoretical values

7.Tabulate the readings taken in the experiment and observation and write the result.

8.Short the input capacitor with a switch and find the effect of that on the differentiator output

Dept of ECE,VKCET


Trouble shooting and fault correction in the circuit:

Observation ,Tabular column and sample calculation

Result: The differentiating amplifier using ua741op-amp was designed for fa=_____ fb=_______

The practical values obtained from graph are fa=____, fb=_____ and fc=______

Post lab 1) What type of active filter is the differentiating amplifier?2) Differentiate the impulses from the output of the differentiating amplifier and plot the output3) Explain the application of differentiation in waveform generators4) What are the types of numerical differentiation methods5)

Dept of ECE,VKCET


Dept of ECE,VKCET


Practical integrator Op-amps allow you to make nearly perfect integrators such as the practical integrator shown in

figure The circuit incorporates a large resistor in parallel with the feedback capacitor. This is necessary because real op-amps have a small current flowing at their input terminals called the "bias current". This current is typically a few nanoamps, and is neglected in many circuits where the currents of interest are in the microamp to milliamp range. However, if you apply a nanoamp current to a 0.1mF capacitor, it won't take long until it charges and becomes effectively an open circuit not allowing any current to flow! The feedback resistor gives a path for the bias current to flow. The effect of the resistor on the response is negligible at all but the lowest frequencies.

A integrator is a circuit whose output magnitude is determined by the integral of the voltage applied to its input with respect to timeThe external components connected to the integrator op-amp are a)A capacitor connected to the feedback between inverting input and outputb)A input resistor between inverting input and input sourcec)A feedback resistor between inverting input and outputThe resistor and capacitor combination form part of the RC network

Prelab 1)Derive the expression for gain of the integrator

Dept of ECE,VKCET


2)Draw the expected output to a 1Vp-p square wave,sine, ramp input3)Mathematically ,perform the process of integration using all the above mentioned functions4)Simulate the circuit in any circuit simulation software

Design and Procedure: Design a practical integrator to operate accurately at f = 1kHz (and above) and with the magnitudeof the gain = 1 for a 1kHz sinewave input. Use standard values for resistors and capacitors. Yourdesign must not clip for any of the input waveforms

1. Select fa equal to the highest frequency of the input signal to be integrated. Then assuming a value of C1 less that 1uF Calculate the value of R12. Choose fb=10fa and calculate the values of R1 and Cf such that R1CF and RfCf. Select fa<fb3. The input will be integrated properly if the time period T of the input signal is greater than or equal to RfC1 T<RfCf 4. Repeat the experiment for all three conditions ;RC<T,RC>T and RC=T

5. Sketch the wave forms forVi = ± 1Vsquare wave at 100Hz

. Vi = ± 1V square wave at 500Hz

Vi = ± 1V square wave at 1kHz



Vi = ± 1V triangle wave at 1kHz

Vi = 0.5V sin 2π 100t

Vi = 0.5V sin 2π 500t

Vi = 0.5V sin 2π 1000t

6.Draw the magnitude frequency plot from the square wave response and find fa,fb practical and compare with theoretical values

7) Apply dc offset from signal generator and repeat steps 3 to 6

Dept of ECE,VKCET


8)Tabulate the readings taken in the experiment , observation and write the result.

Trouble shooting and fault correction in the circuit:

Observation ,Tabular column and sample calculation

Result: The integrating amplifier using ua741op-amp in inverting configuration was designed for fa=_____ fb=_______

The practical values obtained from graph are fa=____and fb=_____

Post lab 1)What type of active filter is the integrating amplifier?2)Integrate the impulses from the output of the differentiating amplifier and plot the output3)Explain the application of integration in waveform generators4) What is the impulse response of an integrator.5) Differentiate a waveform and get the original signal before differentiation6) What are the numerical methods of integration 7) What is relationship between liquid level and flow

Dept of ECE,VKCET

differentiator&integrator

Documents

Transcript of differentiator&integrator