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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])^-1Subscript[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])^-1FullSimplify[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
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Posted 11 years ago
 a figure to see:
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.