jrive

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These are questions asked by jrive

I'm trying derive the equation for a matching resistor pad.  In order for me to get a solution (eg for R2), I had to "manually" solve the one equation and then substitute the resulting value in the other.  Why doesn't solve do the same thing?  

restart

NULLeq1 := (R2+Rhi)*R1/(R1+R2+Rhi) = Rlo

(R2+Rhi)*R1/(R1+R2+Rhi) = Rlo

(1)

NULL

eq2 := R1*Rlo/(R1+Rlo)+R2 = Rhi

R1*Rlo/(R1+Rlo)+R2 = Rhi

(2)

``

R1sol := solve(eq2, R1)

-Rlo*(R2-Rhi)/(R2-Rhi+Rlo)

(3)

R2sol := solve(subs(R1 = R1sol, eq1), R2)

(Rhi^2-Rhi*Rlo)^(1/2), -(Rhi^2-Rhi*Rlo)^(1/2)

(4)

restart

NULLeq1 := (R2+Rhi)*R1/(R1+R2+Rhi) = RloNULL

(R2+Rhi)*R1/(R1+R2+Rhi) = Rlo

(5)

 

NULLeq2 := R1*Rlo/(R1+Rlo)+R2 = RhiNULL

R1*Rlo/(R1+Rlo)+R2 = Rhi

(6)

s := `assuming`([solve({eq1, eq2}, {R1, R2})], [`and`(Rhi > 0, Rlo > 0)])

{R1 = RootOf((Rhi-Rlo)*_Z^2-Rhi)*Rlo, R2 = -(RootOf((Rhi-Rlo)*_Z^2-Rhi)*Rhi-RootOf((Rhi-Rlo)*_Z^2-Rhi)*Rlo-Rhi)/(RootOf((Rhi-Rlo)*_Z^2-Rhi)-1)}

(7)
 

``

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Given this simplified solution, 

sol1 := (-vin + sqrt(-4*I2^2*R^2 + vin^2))/(2*I2*omega0*L)

how do I bring the denominator back under the radical?

I have solution to system of equations that results (I assign it to) in:

I2sol := -I*omega0*k*L*vin*1/(L^2*k^2*omega0^2 + R^2)

I then try to solve it for k by doing

solve(I2sol = I2, k)

but that doesn't work.  What is the "right" Maple way to rearrange I2 such that the expression is the solution(s) for k?

I can't figure out what Maple is complaining about with this error.  In fact, this is an exact copy/paste from another section in my document that runs fine.  This section, however, generates the error, "Error, missing operator `;`.

I appreciate any help!

for_mapleprimes_help.mw

How do I solve sol1 in terms of DC and T (and tau)?
restart

eq1 := x2 = x1+(A-x1)*(1-exp(-ton/tau))

 

 

eq2 := x1 = x2*exp(-toff/tau)

 

eq3 := T = ton+toff

 

NULL

eq4 := DC = ton/T

 

sol1 := simplify(`assuming`([solve({eq1, eq2}, {x1, x2})], [`and`(`and`(`and`(`and`(A > 0, tau > 0), ton > 0), toff > 0), T > 0)]))

{x1 = A*(exp(-ton/tau)-1)*exp(-toff/tau)/(exp((-toff-ton)/tau)-1), x2 = (exp(-ton/tau)-1)*A/(exp((-toff-ton)/tau)-1)}

(5)

Thank youNULL

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