Mathematica Asked on May 1, 2021
So I’m doing some operations in Mathematica and I arrive to this expression:
Clear[ZC1, s, CC1, ZCR1, R1, KVL1, V1, I1, V2, I2, KVL2, R2, param, a, b, c, d, cond, aux, Tran1RC, Tran2RC,
R3, R4, CC3, Circuito, gain, Tfilter];
ZC1 = 1/(s*CC1)
ZCR1 = Simplify[(R1*ZC1)/(R1 + ZC1)]
KVL1 = V1 == ZCR1*I1 + V2;
KVL2 = V2 == R2*(I1 + I2);
param = a == V1/V2;
cond = I2 == 0;
aux = Solve[KVL1 && KVL2 && param && cond, {a, V1, V2, I2}]
a = a /. aux[[1]][[1]]
param = b == -(V1/I2);
cond = V2 == 0;
aux = Solve[KVL1 && KVL2 && param && cond, {b, V1, V2, I2}]
b = b /. aux[[1]][[1]]
param = c == I1/V2;
cond = I2 == 0;
aux = Solve[KVL1 && KVL2 && param && cond, {c, I1, V2, I2}]
c = c /. aux[[1]][[1]]
param = d == -(I1/I2);
cond = V2 == 0;
aux = Solve[KVL1 && KVL2 && param && cond, {d, I1, I2, V2}]
d = d /. aux[[1]][[1]]
Tran1RC = {{a, b}, {c, d}};
Tran1RC // MatrixForm
a = a /. {R1 -> R3, R2 -> R4, CC1 -> CC3}
b = b /. {R1 -> R3, R2 -> R4, CC1 -> CC3}
c = c /. {R1 -> R3, R2 -> R4, CC1 -> CC3}
d = d /. {R1 -> R3, R2 -> R4, CC1 -> CC3}
Tran2RC = {{a, b}, {c, d}};
Tran2RC // MatrixForm
Circuito = Simplify[Tran1RC.Tran2RC];
Circuito // MatrixForm
gain = Circuito[[1]][[1]] /. {CC3 -> 10 CC1, R2 -> R3 + R4}
Tfilter = Simplify[1/gain]
Now the final expression I want to simplify according to variable s meaning that I want to arrive with expression in powers of s (s^1 and s^2) both in the numerator and the denominator. Exactly how shall I do this?
EDIT: Put the full workable code
Rfilter = Together[Tfilter];
Collect[Numerator[Rfilter], s]/Collect[Denominator[Rfilter], s]
yielding
(R3 R4 + R4^2 +
(CC1 R1 R3 R4 + 10 CC1 R3^2 R4 + CC1 R1 R4^2 + 10 CC1 R3 R4^2) s +
(10 CC1^2 R1 R3^2 R4 + 10 CC1^2 R1 R3 R4^2) s^2)
/
(2 R1 R3 + R3^2 + 2 R1 R4 + 2 R3 R4 +
R4^2 +
(11 CC1 R1 R3^2 + 22 CC1 R1 R3 R4 + 10 CC1 R3^2 R4 + CC1 R1 R4^2 + 10 CC1 R3 R4^2) s +
(10 CC1^2 R1 R3^2 R4 + 10 CC1^2 R1 R3 R4^2) s^2)
Correct answer by John Doty on May 1, 2021
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