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jrive

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following your example...

jrive 210
November 11 2020
0 0

@acer following your previous example, I tried the following: 
 

(C1+C2)^(1/2)/(C1^(1/2)*C2^(1/2)*L1^(1/2))

 (16)
> 

``
> 

S1 := sqrt(Ceq) = sqrt(C1)*sqrt(C2)/sqrt(C1+C2)

Ceq^(1/2) = C1^(1/2)*C2^(1/2)/(C1+C2)^(1/2)

 (17)
> 

S2 := (1/rhs = 1/lhs)(S1)

(C1+C2)^(1/2)/(C1^(1/2)*C2^(1/2)) = 1/Ceq^(1/2)

 (18)
> 

tmp := subs(S2, `ωres`)

(C1+C2)^(1/2)/(C1^(1/2)*C2^(1/2)*L1^(1/2))

 (19)
> 

rationalize(tmp)

(C1+C2)^(1/2)/(C1^(1/2)*C2^(1/2)*L1^(1/2))

 (20)
>  
 

  I was expecting to be able to get the answer down to  1/(sqrt(Ceq) sqrt(L1)) per the substitutions above.  It would be better still if I could get the final answer to display 1/(sqrt(Ceq L1)).

 

Thanks again!
 

Download new_filter_solution.mw

 

Ok - great- Thank you. additional commen...

jrive 210
November 11 2020
0 0

@acer  -- perfect, thank you!!!

Ok - great- Thank you. additional commen...

jrive 210
November 06 2020
0 0

@acer thank you.

There's something I don't get...I have three unknowns (assuming C1=C2), so not sure why I can't use the inequality.  I occurs to me I could instead use C1=C2 in the system of equations (restricting the gain to 1)  - maybe that'll work. 

I still need to look at this further, though.   The solution for  R1 results in an imaginary value which shouldn't be the case....

 

Thank you for your help!

not really...

jrive 210
November 05 2020
0 0

@acer what you're seeing are typos when I entered the data on here, since I could not cut and paste it directly from my Maple doc.

Currently, I get this error and have not been able to resolve it, no matter what I try:

sys := {`&omega;res` = 0.1635*10^8*2*Pi, simplify(z3res) = 9 + 0.000150*I, 1 <= abs(vores/vin)}

sol2 := solve(sys, {C1, C2, L1, R1})

Warning, solve may be ignoring assumptions on the input variables.
Error, (in unknown) invalid input: SolveTools:-Inequality expects its 1st argument, eqns, to be of type ({list, set})({`<`, `<=`, `=`}), but received [C2 < 0, And(-(-1+signum(0, C1+C2, 1))*Pi <= Pi, -Pi < -(-1+signum(0, C1+C2, 1))*Pi)]

(I can't figure out how to copy Maple input onto here --the formatting gets all messed up.)  Please see attached file.

Thanks for any pointers!  filter.mw

> 

restart
> 

assume(vin, real)
> 

assume(C1, real)
> 

assume(C2, real)
> 

assume(L1, real)
> 

assume(R1, real)
> 

assume(omega, real)
> 

assume(vin, real)
> 

z1 := R1/((I*omega*C1)*(R1+1/(I*omega*C1)))

-I*R1/(omega*C1*(R1-I/(omega*C1)))

 (1)
> 

simplify(-I*R1/(omega*C1*(R1-I/(omega*C1))), 'size')

I*R1/(-R1*omega*C1+I)

 (2)
> 

 

> 

 

> 

z2 := z1+I*omega*L1

-I*R1/(omega*C1*(R1-I/(omega*C1)))+I*omega*L1

 (3)
> 

z3 := z2/((I*omega*C2)*(z2+1/(I*omega*C2)))

-I*(-I*R1/(omega*C1*(R1-I/(omega*C1)))+I*omega*L1)/(omega*C2*(-I*R1/(omega*C1*(R1-I/(omega*C1)))+I*omega*L1-I/(omega*C2)))

 (4)
> 

simplify(-I*(-I*R1/(omega*C1*(R1-I/(omega*C1)))+I*omega*L1)/(omega*C2*(-I*R1/(omega*C1*(R1-I/(omega*C1)))+I*omega*L1-I/(omega*C2))))

(I*C1*L1*R1*omega^2+omega*L1-I*R1)/(-I-C1*C2*L1*R1*omega^3+I*C2*L1*omega^2+R1*(C1+C2)*omega)

 (5)
> 

 

> 

voc := vin/((I*omega*C1)*(R1+1/(I*omega*C1)))

-I*vin/(omega*C1*(R1-I/(omega*C1)))

 (6)
> 

simplify(-I*vin/(omega*C1*(R1-I/(omega*C1))))

I*vin/(-R1*omega*C1+I)

 (7)
> 

zthev := simplify(z1)

I*R1/(-R1*omega*C1+I)

 (8)
> 

vounloaded := voc/((I*omega*C2)*(zthev+I*omega*L1+1/(I*omega*C2)))

-vin/(omega^2*C1*(R1-I/(omega*C1))*C2*(I*R1/(-R1*omega*C1+I)+I*omega*L1-I/(omega*C2)))

 (9)
> 

simplify(-vin/(omega^2*C1*(R1-I/(omega*C1))*C2*(I*R1/(-R1*omega*C1+I)+I*omega*L1-I/(omega*C2))))

-I*vin/(-I-C1*C2*L1*R1*omega^3+I*C2*L1*omega^2+R1*(C1+C2)*omega)

 (10)
> 

simplify(-vin/(omega^2*C1*(R1-I/(omega*C1))*C2*(I*R1/(-R1*omega*C1+I)+I*omega*L1-I/(omega*C2))))

-I*vin/(-I-C1*C2*L1*R1*omega^3+I*C2*L1*omega^2+R1*(C1+C2)*omega)

 (11)
> 

 

> 

 

> 

sol1 := solve(Im(vounloaded) = 0, omega)

Warning, solve may be ignoring assumptions on the input variables.

  

0, (C1*C2*L1*(C1+C2))^(1/2)/(C1*C2*L1), -(C1*C2*L1*(C1+C2))^(1/2)/(C1*C2*L1)

 (12)
> 

> 

`&omega;res` := sol1[2]

(C1*C2*L1*(C1+C2))^(1/2)/(C1*C2*L1)

 (13)
> 

vounloaded

-vin/(omega^2*C1*(R1-I/(omega*C1))*C2*(I*R1/(-R1*omega*C1+I)+I*omega*L1-I/(omega*C2)))

 (14)
> 

vores := simplify(subs(omega = `&omega;res`, vounloaded))

-C1*vin/C2

 (15)
> 

``
> 

NULL
> 

z3res := simplify(subs(omega = `&omega;res`, z3))

(C1^2*R1-I*(C1*C2*L1*(C1+C2))^(1/2))/C2^2

 (16)
> 

simplify((C1^2*R1-I*(C1*C2*L1*(C1+C2))^(1/2))/C2^2)

(C1^2*R1-I*(C1*C2*L1*(C1+C2))^(1/2))/C2^2

 (17)
> 

 

> 

sys := {abs(vores/vin) >= 1, `&omega;res` = (0.1356e8*2)*Pi, simplify(z3res) = 9+I*0.150e-3}

{(C1^2*R1-I*(C1*C2*L1*(C1+C2))^(1/2))/C2^2 = 9.+0.150e-3*I, (C1*C2*L1*(C1+C2))^(1/2)/(C1*C2*L1) = 85199992.78, 1 <= abs(C1/C2)}

 (18)
> 

``
> 

sol2 := solve(sys, {C1, C2, L1, R1})

Warning, solve may be ignoring assumptions on the input variables.

  

Error, (in unknown) invalid input: SolveTools:-Inequality expects its 1st argument, eqns, to be of type ({list, set})({`<`, `<=`, `=`}), but received [C2 < 0, And(-(-1+signum(0, C1+C2, 1))*Pi <= Pi, -Pi < -(-1+signum(0, C1+C2, 1))*Pi)]

  
> 

sol := sol2[3]

sol2[3]

 (19)
> 

R1sol := sol2[4]

sol2[4]

 (20)
> 

C1sol := sol2[1]

sol2[1]

 (21)
> 

``

Solution

> 

subs(C2 = 0.10e-10, L1sol)

sol2[3]

 (22)
> 

subs(C2 = 0.10e-10, R1sol)

sol2[4]

 (23)
> 

``

 

how did it solve for you?...

jrive 210
November 05 2020
0 0

@Kitonum thank you.  What did you change to get it to solve for you?  I never was able to get the solution you got; is it because you entered the formulas into sys, as opposed to the variables to which they were assigned?  (eg. you entered 1<=abs(C1/C2, instead of abs(vores/vin)>=1? 

Thanks again

 

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