jrive

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These are questions asked by jrive

I do not understandwhat this result from Maple means.

I don't know what it means when a result has "Root of", and in this case, there is also a big summation sign for which I can't tell if the variables underneath it are part of the summartion, or what.  I'd appreciate any guidance to make sense of what this means..

restart

with(inttrans)

assump := R1::real, R2::real, L1::real, C1::real, C2::real, L2::real, omega::real, M::real, R1 > 0, R2 > 0, L1 > 0, C1 > 0, L2 > 0, C2 > 0, omega > 0, M > 0

R1::real, R2::real, L1::real, C1::real, C2::real, L2::real, omega::real, M::real, 0 < R1, 0 < R2, 0 < L1, 0 < C1, 0 < L2, 0 < C2, 0 < omega, 0 < M

(1)

expr := Vin/(s*(R1+s*L1-1/(s*C1)+(omega*M)^2/(R2+s*L2-1/(s*C2))))

Vin/(s*(R1+s*L1-1/(s*C1)+omega^2*M^2/(R2+s*L2-1/(s*C2))))

(2)

invlaplace(expr, s, t)

Vin*C1*(sum(exp(_alpha*t)*(-1+C2*_alpha*(L2*_alpha+R2))/(4*C1*C2*L1*L2*_alpha^3+2*C1*C2*M^2*_alpha*omega^2+3*C1*C2*L1*R2*_alpha^2+3*C1*C2*L2*R1*_alpha^2+2*C1*C2*R1*R2*_alpha-2*C1*L1*_alpha-2*C2*L2*_alpha-C1*R1-C2*R2), _alpha = RootOf(1+C1*C2*L1*L2*_Z^4+(C1*C2*L1*R2+C1*C2*L2*R1)*_Z^3+(C1*C2*M^2*omega^2+C1*C2*R1*R2-C1*L1-C2*L2)*_Z^2+(-C1*R1-C2*R2)*_Z)))

(3)

NULL

Download for_help2.mw

given :

Zin := ((Rsp + (omega*L2 - omega02^2*L2/omega)*I)*(Rpp + (omega*L1 - omega01^2*L1/omega)*I) + 0.01*omega^2*L1*L2)/(Rsp + (omega*L2 - omega02^2*L2/omega)*I)

how do I get Maple to cancel out the common term, and simplify this equation into:

Zin := Rpp + (omega*L1 - omega01^2*L1/omega)*I + (0.01*omega^2*L1*L2)/(Rsp + 
(omega*L2 - omega02^2*L2/omega)*I)

Why doesn't Maple do this automatically with something like simplify or some other command?

Thank you!

I am trying to install Syrup in my home computer (I have it installed in my work computer).  I followed the instructions in the Readme file: 

From Standard Maple:
    Open the file Syrup-Installer.mla.
    To do so, use File -> Open, choose file type 
    "Maple Library Archive (.mla)", select the file, and
    click "Open".

Everything seemed to work and the help page opened up:  But, it is not the syrup help page.  furthermore, when I type ?Syrup, it doesn't open it either.

 

When I try to run a worksheet that uses Syrup (that works on my work computer), I get these errors:

I"m going to reboot now and try again.  

Jorge

I don't understand where the the csgn(L) comes from in the solution below:

all the variables are defined as real:

coupled_network_vbat.mw

 

Thanks in advance for any help.

 

Jorge

 

Not sure what  I did, but now  the typsetting rule assistant pops up every time I executre my document (twice!).  Searching the internet, I found that I should be able to turn it off by "expanding the blocks" (?) and then finding the call to this assistant.  Problem is, I can't find this "Expand block"  -- it is not under View it they claim it is in various posts.  Also, if I step through the worksheet, I can't find it ; it only pops up when I execute the entire worksheet.  I attached it here for someone to guide me on how to find where/why this is happening.

 

Thanks!coupled_network.mw
 

restart

with(Syrup)

interface('displayprecision' = 4)

SyrupDefaults:-infolevel := 1; SyrupDefaults:-subscript_params := true

 

 

Circuit Netlist

 

ckt1

Definitions

 

Cp := 1/(`&omega;0p`^2*Lp)

1/(`&omega;0p`^2*Lp)

(1.2.1)

Cs := 1/(`&omega;0s`^2*Ls)

1/(`&omega;0s`^2*Ls)

(1.2.2)

M := k*sqrt(Ls*Lp)

k*(Ls*Lp)^(1/2)

(1.2.3)

assumptions := `and`(`and`(`and`(`and`(`and`(`and`(`&omega;0p` > 0, `&omega;0s` > 0), Lp > 0), Ls > 0), k > 0), Rp > 0), Rs > 0), omega > 0NULL

0 < `&omega;0p` and 0 < `&omega;0s` and 0 < Lp and 0 < Ls and 0 < k and 0 < Rp and 0 < Rs, 0 < omega

(1.2.4)

NULL

 

Simplifications

 

`&omega;0p` := `&omega;0p`

`&omega;0p`

(1.3.1)

`&omega;0s` := `&omega;0s`

`&omega;0s`

(1.3.2)

Rs := Rs

Rs

(1.3.3)

Rp := Rp

Rp

(1.3.4)

Lp := Lp

Lp

(1.3.5)

Ls := Ls

Ls

(1.3.6)

Not On Resonance

 

 

w := omega

omega

(1.3.1.1)

 

Solve System

 

sol, rest := `assuming`([Solve("ec:ckt1", analysis = ac, 'returnall')], [assumptions])

NULL

Solution

 

 

s := I*w

I*omega

(1.5.1)

vin := eval(v[N03], sol)

vin

(1.5.2)

Secondary Current

I2sol := `assuming`([simplify(eval(i[L2], rest))], [assumptions])

omega^3*k*Ls^(1/2)*Lp^(1/2)*vin/(Lp*Ls*(k-1)*(k+1)*omega^4+I*(Lp*Rs+Ls*Rp)*omega^3+(Ls*(`&omega;0p`^2+`&omega;0s`^2)*Lp+Rp*Rs)*omega^2+I*(-Lp*Rs*`&omega;0p`^2-Ls*Rp*`&omega;0s`^2)*omega-Ls*Lp*`&omega;0p`^2*`&omega;0s`^2)

(1.5.3)

NULL

sol1 := solve(I2sol = I2, k)[1]

(1/2)*(Lp^(1/2)*Ls^(1/2)*vin*omega+(4*I2^2*Lp^2*Ls^2*omega^4-4*I2^2*Lp^2*Ls^2*omega^2*`&omega;0p`^2-4*I2^2*Lp^2*Ls^2*omega^2*`&omega;0s`^2+4*I2^2*Lp^2*Ls^2*`&omega;0p`^2*`&omega;0s`^2-(4*I)*I2^2*Lp^2*Ls*Rs*omega^3+(4*I)*I2^2*Lp^2*Ls*Rs*omega*`&omega;0p`^2-(4*I)*I2^2*Lp*Ls^2*Rp*omega^3+(4*I)*I2^2*Lp*Ls^2*Rp*omega*`&omega;0s`^2-4*I2^2*Lp*Ls*Rp*Rs*omega^2+Lp*Ls*vin^2*omega^2)^(1/2))/(I2*Lp*Ls*omega^2)

(1.5.4)

Coupling

kcoup := `assuming`([simplify(sol1)], [assumptions])

(1/2)*(vin*omega+(-4*(omega+`&omega;0p`)*I2^2*(omega-`&omega;0p`)*((-omega^2+`&omega;0s`^2)*Ls+I*Rs*omega)*Lp-4*(I*(omega+`&omega;0s`)*Rp*I2^2*(omega-`&omega;0s`)*Ls+omega*(I2^2*Rp*Rs-(1/4)*vin^2))*omega)^(1/2))/(Ls^(1/2)*Lp^(1/2)*I2*omega^2)

(1.5.5)

 

Zmutual

Zmutual := `assuming`([expand(abs(vin/I2sol))], [assumptions])

(Lp^2*Ls^2*k^4*omega^8-2*Lp^2*Ls^2*k^2*omega^8+2*Lp^2*Ls^2*k^2*omega^6*`&omega;0p`^2+2*Lp^2*Ls^2*k^2*omega^6*`&omega;0s`^2-2*Lp^2*Ls^2*k^2*omega^4*`&omega;0p`^2*`&omega;0s`^2+Lp^2*Ls^2*omega^8-2*Lp^2*Ls^2*omega^6*`&omega;0p`^2-2*Lp^2*Ls^2*omega^6*`&omega;0s`^2+Lp^2*Ls^2*omega^4*`&omega;0p`^4+4*Lp^2*Ls^2*omega^4*`&omega;0p`^2*`&omega;0s`^2+Lp^2*Ls^2*omega^4*`&omega;0s`^4-2*Lp^2*Ls^2*omega^2*`&omega;0p`^4*`&omega;0s`^2-2*Lp^2*Ls^2*omega^2*`&omega;0p`^2*`&omega;0s`^4+Lp^2*Ls^2*`&omega;0p`^4*`&omega;0s`^4+2*Lp*Ls*Rp*Rs*k^2*omega^6+Lp^2*Rs^2*omega^6-2*Lp^2*Rs^2*omega^4*`&omega;0p`^2+Lp^2*Rs^2*omega^2*`&omega;0p`^4+Ls^2*Rp^2*omega^6-2*Ls^2*Rp^2*omega^4*`&omega;0s`^2+Ls^2*Rp^2*omega^2*`&omega;0s`^4+Rp^2*Rs^2*omega^4)^(1/2)/(omega^3*k*Ls^(1/2)*Lp^(1/2))

(1.5.6)

plot([subs(L = 34*exp(1)-6*omega0 and 34*exp(1)-6*omega0 = 2*Pi*0.85e5, R = 0.1e-1, omega = 2*Pi*85000, Zmutual), subs(L = 0.34e-4, omega0 = 2*Pi*0.85e5, R = 0.1e-1, omega = 2*Pi*79000, Zmutual)], k = 0 .. 1, numpoints = 1000)

plot([subs(Lp = 34*exp(1)-6, Ls = 60*exp(1)-6, omega0 = 2*Pi*85000, Rp = 0.1e-1, Rs = 0.1e-1, R = 0.1e-1, omega = 2*Pi*85000, Zmutual), subs(Lp = 34*exp(1)-6, Ls = 60*exp(1)-6, omega0 = 2*Pi*85000, Rp = 0.1e-1, Rs = 0.1e-1, Rp = 0.1e-1, Rs = 0.1e-1, R = 0.1e-1, omega = 2*Pi*79000, Zmutual)], k = 0 .. 1, numpoints = 1000)

plot(subs(L = 0.34e-4, omega0 = 2*Pi*0.85e5, Rp = 0.1e-1, Rs = 0.1e-1, R = 0.1e-1, k = .25, Zmutual), omega = 0.79e5 .. 0.90e5, numpoints = 1000)

NULL

Primary Current

I1sol := `assuming`([simplify(eval(i[L1], rest))], [assumptions])

-I*omega*vin*(-Ls*omega^2+`&omega;0s`^2*Ls+I*Rs*omega)/(Lp*Ls*(k-1)*(k+1)*omega^4+I*(Lp*Rs+Ls*Rp)*omega^3+(Ls*(`&omega;0p`^2+`&omega;0s`^2)*Lp+Rp*Rs)*omega^2+I*(-Lp*Rs*`&omega;0p`^2-Ls*Rp*`&omega;0s`^2)*omega-Ls*Lp*`&omega;0p`^2*`&omega;0s`^2)

(1.5.7)

at resonance

I1sol_res := simplify(eval(I1sol, [omega = omega0, `&omega;0s` = omega0, `&omega;0p` = omega0]))

vin*Rs/(Lp*Ls*k^2*omega0^2+Rp*Rs)

(1.5.8)

NULL

Self Impedance

Zpself := simplify(vin/I1sol)

(I*Lp*(k+1)*Ls*(k-1)*omega^4+(-Lp*Rs-Ls*Rp)*omega^3+I*(Ls*(`&omega;0p`^2+`&omega;0s`^2)*Lp+Rp*Rs)*omega^2+(Lp*Rs*`&omega;0p`^2+Ls*Rp*`&omega;0s`^2)*omega-I*Lp*Ls*`&omega;0p`^2*`&omega;0s`^2)/(omega*(-Ls*omega^2+`&omega;0s`^2*Ls+I*Rs*omega))

(1.5.9)

NULL

at resonance

zpself_res := simplify(eval(Zpself, omega = omega0))

(I*Lp*(k+1)*Ls*(k-1)*omega0^4+(-Lp*Rs-Ls*Rp)*omega0^3+I*(Ls*(`&omega;0p`^2+`&omega;0s`^2)*Lp+Rp*Rs)*omega0^2+(Lp*Rs*`&omega;0p`^2+Ls*Rp*`&omega;0s`^2)*omega0-I*Lp*Ls*`&omega;0p`^2*`&omega;0s`^2)/(omega0*(-Ls*omega0^2+`&omega;0s`^2*Ls+I*Rs*omega0))

(1.5.10)

 

Normalized

ZselfN := collect(simplify(`assuming`([expand(simplify(I2sol/I1sol))], [assumptions])), Ls)

I*omega^2*k*Ls^(1/2)*Lp^(1/2)/((-omega^2+`&omega;0s`^2)*Ls+I*Rs*omega)

(1.5.11)

 

Normalized Magnitude

`assuming`([MagZpselfN = simplify(eval(I2sol/I1sol, [`&omega;0p` = omega0, `&omega;0s` = omega0]))], [assumptions])

MagZpselfN = I*omega^2*k*Ls^(1/2)*Lp^(1/2)/(-Ls*omega^2+Ls*omega0^2+I*Rs*omega)

(1.5.12)

Plots

 

Zself as a function of Coupling Coefficient

plot(subs(L = 0.34e-4, omega0 = 2*Pi*0.85e5, Rp = 0.1e-1, Rs = 0.1e-1, R = 0.1e-1, omega = 2*Pi*85000, Zpself/Zmutual), k = 0 .. 1, numpoints = 1000)

plot(subs(Lp = 34*exp(1)-6, Ls = 60*exp(1)-6, omega0 = 2*Pi*0.85e5, Rp = 0.1e-1, Rs = 0.1e-1, R = 0.1e-1, omega = 2*Pi*85000, abs(Zpself/Zmutual)), k = 0 .. 1, numpoints = 1000)

 

Normalized - Off Resonance

plot(subs(L = 0.34e-4, omega0 = 2*Pi*0.85e5, Rp = 0.1e-1, Rs = 0.1e-1, R = 0.1e-1, omega = 2*Pi*79000, Zpself/Zmutual), k = 0 .. 1, numpoints = 1000)

plot(subs(Lp = 34*exp(1)-6, Ls = 60*exp(1)-6, omega0 = 2*Pi*0.85e5, Rp = 0.1e-1, Rs = 0.1e-1, R = 0.1e-1, omega = 2*Pi*79000, abs(Zpself/Zmutual)), k = 0 .. 1, numpoints = 1000)

 

Normalized, at a given coupling

plot(subs(L = 0.34e-4, omega0 = 2*Pi*0.85e5, Rp = 0.1e-1, Rs = 0.1e-1, R = 0.1e-1, k = .25, Zpself/Zmutual), omega = 0.79e5 .. 0.90e5, numpoints = 1000)

plot(subs(Lp = 34*exp(1)-6, Ls = 60*exp(1)-6, omega0 = 2*Pi*0.85e5, Rp = 0.1e-1, Rs = 0.1e-1, R = 0.1e-1, k = .25, abs(Zpself/Zmutual)), omega = 0.79e5 .. 0.90e5, numpoints = 1000)

 

Not Normalized, at a given coupling

plot(subs(Lp = 0.34e-4, Ls = 0.60e-4, omega0 = 2*Pi*0.85e5, Rp = 0.1e-1, Rs = 0.1e-1, R = 0.1e-1, k = .25, abs(Zpself)), omega = 0.79e5 .. 0.90e5, numpoints = 1000)

NULL

 

 

NULL

Solution2

   


 

Download coupled_network.mw

 

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