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These are answers submitted by andy.zhou.nuaa

You answer is very useful to me. Although there is a little dismatch on the condition of vds>300, the precision is enough for my appliction. 

tks again for ur help.

id=gfs*(vgs-Vth), other condition keep the same!

tks very much,Robert Israel !

best regards!


   forgive my poor knowledge, Some conclusion you made such as "Provided w1/w2 is not a rational number, Vcs_max = V1 + V2" i don't undertstand very well, i need further help if you would like to help me. could u post a workseet showing how to find the max value of voltage on Cs.

     Note: is there any books or articles focus on high-order resonant circuit , could recommend one for me?

    because the presence of  Cp, i think status which Cs stores all the energy is impossilbe occurs in this circuit. 

  i know it can be solved by substitue constants with values. i want to know does the value has generality, i worry some problems come up:

 Does the following problem will be exsit:

 when Lp=1mH, the function is  the monotone function.

 when Lp=10mH, the function is the monotonous fuction.

that is what i worry!

  with ur help. the problem has been solved!


  assmue A,B, theta is real and there is a function Tran() in maple

 i write these command in maple


 then the result will be  sqrt(A^2+B^2)*sin(t+arctan(B/A));

My problem is how to build this function ?

   let me describe the question again!

 how to translate A*sin(t) + B*cos(t) to C*sin(t+theta) by maple?  where theta = arctan(B/A)
C = sqrt(A^2+B^2)

 For acer:

    my expression is  A*sin(t)+B*cos(t) not A*cos(t)+B*sin(t) , so when A=1,B=1, t=Pi, the equation is also  establish. 

Thanks for jakubi's help, but your answer is not i want. maybe something wrong with description of my problem, so rewrite it:


     v := A*sin(t)+B*cos(t); 

  we both know v can be simplified to following expression:

  v := C*sin(t+theta)   where  C := sqrt(A^2+B^2) , theta := arctan(B/A).

So i want to know how this could be done by maple?  Can the results be simplified in ODE equations directly?


       you mean this equations doesn't have an solution because there
is an identity not involving those variables. Can u write in detail, are there any math theory prove this conclusion.

   Tanks very much !


eqns := {La+Lp/nlpa^2+Lm/(nsp^2*npa^2), Lm = LEF1, Lp+Lm/nsp^2 = LAB1, Lp+Rs^2*Lm/((omega^2*Lm^2+Rs^2)*nsp^2) = LAB2, La+Lp/nlpa^2+Rs^2*Lm/((omega^2*Lm^2+Rs^2)*nsp^2*npa^2) = LCD2, (nsp^2*Rp^2+omega^2*nsp^2*Lp^2+omega^2*Lp*Lm)*nsp^2*Lm/(nsp^4*Rp^2+2*omega^2*Lp*Lm*nsp^2+omega^2*Lm^2+omega^2*nsp^4*Lp^2) = LEF2};


 vars := {Lm, Lp, nsp, La, nlpa, npa};

solve(eqns, vars);  #  "nothing display in maple"


 This is the right Equation:

 eqns := a*(x/sqrt(x^2-1)+2*x/(Pi*(x^2-1))-1-2/(Pi*x)) = 1

 it have the same problem with the first equation!

 i am very sorry for waste someone's time!!

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