Wednesday, May 25, 2011

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Electric Analog Computation

               Electronic analog computation is one of the basic concepts in the field of modern electronic computing. In electronic analog computation any equation  can be solved by using some analog circuits which is designed by using op-amps .In my assignment I try to present the concept of electronic analog computation by solving a differential equation with a correspondent circuit .

        Electronic analog computation is such kind of electronic computation in which basic analog computing elements such as adders ,integrators ,multipliers, comparators etc are used to solve any desired equation such as differential equations etc .It is the basic concepts of analog computer.
            In this a differential equation is solved by electronic analog computation.


                   Let a differential equation be :
                                          
 D2v+k1Dv+k2v-v1=0……………….(1)   Where, k1 and k2 are constant terms.

           In the starting I assumed that D2v is available in the form of a voltage .Then by means of an integrator I will get  the voltage proportional to Dv. A second integrator gives the voltage proportional to v .Then an adder gives –( k1Dv+k2v-v1)  From the equation it is equal to D2v
and hence the output of this summing amplifier is fed to the input terminal ,where I had assumed that D2v was available in the first place.

       The integrator 1 has a time constant RC=1s, and hence its output at terminal 1 is –Dv .This voltage is fed to a similar integrator 2 and the voltage at terminal 2 is +v. The voltage at terminal 1 is fed to summing amplifier 1 which gain is 1 and in the output terminal 3 I get + k1Dv- v1.
         where k1=(R/R1).At the end the output of terminal 2 and 3 are fed to summing amplifier 2,from where I will get  D2v= - (k1Dv+k2v-v1) at terminal 4.


 
Fig1.1: Electronic analog computing circuit for calculating a differential equation .

              By electronic analog computation we can solve any kind of equation by some basics circuits using op-amp .But we have to careful to set the gain of the circuits because in some steps the constant term of the equation is  represent by the gain of the correspondent circuit .So, we have to design the circuits according to gain which represents the constant term


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