I need to "design" a circuit of op-amps so I'll get:
v''+a*v'+b*v=c*vin
where the Vs are outputs and their derivatives, vin is the input voltage, and a, b, c would consist of some combinations of capacitors + resistors.
So here is what I did:
I split vin (a function of t) into 3 functions. V1(t), V2(t), V3(t). vin(t)=v1(t)+v2(t)+v3(t)
And then I went ahead and put my integrating circuits + inverting op amp circuits in so that
v(1)=1/(R1C1*R2C2)(integrate(integrate(v1(t),{t,0,t1}),{t,0,t1})
v''=1/(R1R2C1C2)v1(t)
v(2)=1/(R3C3)(integrate(v2(t),{t,0,t1}}
v'=1/(R3C3)v2(t)
v=-(Ri/Rf)*v3(t)
It seems all fine to me except how would I divide vin(t) so that v1(t),v2(t) and v3(t) are all equal? 2 of them are time dependent and one isn't...
v''+a*v'+b*v=c*vin
where the Vs are outputs and their derivatives, vin is the input voltage, and a, b, c would consist of some combinations of capacitors + resistors.
So here is what I did:
I split vin (a function of t) into 3 functions. V1(t), V2(t), V3(t). vin(t)=v1(t)+v2(t)+v3(t)
And then I went ahead and put my integrating circuits + inverting op amp circuits in so that
v(1)=1/(R1C1*R2C2)(integrate(integrate(v1(t),{t,0,t1}),{t,0,t1})
v''=1/(R1R2C1C2)v1(t)
v(2)=1/(R3C3)(integrate(v2(t),{t,0,t1}}
v'=1/(R3C3)v2(t)
v=-(Ri/Rf)*v3(t)
It seems all fine to me except how would I divide vin(t) so that v1(t),v2(t) and v3(t) are all equal? 2 of them are time dependent and one isn't...
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