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Simplify symbolic Mathematica

Posted 11 years ago
Hi,

Is it possible to combine or simplify the following transfer functions with Mathematica?
Subscript[Z, 1]=Subscript[R, L]/(1+Subscript[sR, L] Subscript[C, k])
Subscript[Z, 2]=Subscript[Z, 1]+1/Subscript[sC, pt]
Subscript[Z, 3]=(Subscript[Z, 2]*Subscript[sL, h])/(Subscript[Z, 2]+Subscript[sL, h])
Subscript[Z, 4]=Subscript[Z, 3]+Subscript[R, pri]+s Subscript[L, st]
Subscript[Z, 5]=(1/Subscript[Z, 4]+s Subscript[C, p]+s Subscript[C, v])^-1
Subscript[Z, in]=Subscript[Z, 5]+Subscript[R, Ls]+s Subscript[L, s]+1/(s Subscript[C, s])
TraditionalForm[FullSimplify[(Subscript[Z, 1]*Subscript[Z, 3]*Subscript[Z, 5])/(Subscript[Z, 2]*Subscript[Z, 4]*Subscript[Z, in])]]
 Subscript[Z, 1] = Subscript[R, L]/(
  1 + Subscript[sR, L] Subscript[C, k])
 TransferFunctionModel[Subscript[Z, 1], s]
 
 Subscript[Z, 2] = Subscript[Z, 1] + 1/Subscript[sC, pt]
 FullSimplify[TransferFunctionModel[Subscript[Z, 2], s]]
 Zn = Together[ExpandAll[%]]
 pcs1 = Denominator[Zn]
 

Subscript[Z, 3] = (Subscript[Z, 2]*Subscript[sL, h])/(Subscript[Z,
    2] + Subscript[sL, h])
FullSimplify[TransferFunctionModel[Subscript[Z, 3], s]]


Subscript[Z, 4] =
Subscript[Z, 3] + Subscript[R, pri] + s Subscript[L, st]
TraditionalForm[
FullSimplify[TransferFunctionModel[Subscript[Z, 4], s]]]


Subscript[Z, 5] = (1/Subscript[Z, 4] + s Subscript[C, p] +
   s Subscript[C, v])^-1
FullSimplify[TransferFunctionModel[Subscript[Z, 5], s]]

Subscript[Z, in] =
Subscript[Z, 5] + Subscript[R, Ls] + s Subscript[L, s] + 1/(
  s Subscript[C, s])
TransferFunctionModel[Subscript[Z, in], s]

TraditionalForm[
FullSimplify[(Subscript[Z, 1]*Subscript[Z, 3]*Subscript[Z, 5])/(
  Subscript[Z, 2]*Subscript[Z, 4]*Subscript[Z, in])]]

FullSimplify[TransferFunctionModel[%, s]]
for example you get the following for Z, 2
(1 + Subscript[R, L] Subscript[sC, pt] +
Subscript[C, k] Subscript[sR, L])/(Subscript[sC, pt] +
Subscript[C, k] Subscript[sC, pt] Subscript[sR, L])

 For the remaining Z,3 & Z,4 & Z,5, Z,in etc. equations, it is even more complicated.

how can I simplify the  functions given above?
This is about the transfer function of a circuit.


Thanks for your helps
POSTED BY: C_wullf
2 Replies
Posted 11 years ago
a figure to see:


POSTED BY: C_wullf
Posted 11 years ago
(sL_h R_L)/((C_k sR_L+1)(R_L/(C_k sR_L+1)+sL_h+1/sC_pt )((sL_h (C_k sR_L+R_L sC_pt+1))/((C_k sR_L+1)(sL_h sC_pt+1)+R_L sC_pt )+sL_st+R_pri)(1/((sL_h (C_k sR_L+R_L sC_pt+1))/((C_k sR_L+1)(sL_h sC_pt+1)+R_L sC_pt )+sL_st+R_pri )+s(C_p+C_v))(1/(1/((sL_h (C_k sR_L+R_L sC_pt+1))/((C_k sR_L+1)(sL_h sC_pt+1)+R_L sC_pt )+sL_st+R_pri )+s(C_p+C_v))+1/(sC_s )+sL_s+R_Ls))
for Z1*Z3*Z5/(Z2*Z4*Zin) is obtained the following.
POSTED BY: C_wullf
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