Simplify the V/I equation

I want to determine V/I (voltage/current) symbolically from the equation using solve function, but the answer that I got from it is just V not V/I.

This is my code:

clear Vx Vy Vcm Cin Ca Cfb Ccm s x y gm Zin solx soly
syms Vx Vy Vo Cin Ca Cfb Ccm s x y gm Zin Vcm
eqns = [2*((Cin*(Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)) + (y*((2*Ca)/Cfb + 1))/(2*Ca*s))*((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1))/(Ca*(((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1) + 1)) - (y*((2*Ca)/Cfb + 1))/(2*Ca*s) - Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)))*s*Ccm+2*x*s*Cin==(-((Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)) + (y*((2*Ca)/Cfb + 1))/(2*Ca*s))*(Cfb/(2*Ccm) + 1))/(((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1) + 1))*(2/Zin+2*s*Cin+2*s*Ccm)];
S = solve(eqns);
sol = [S]

sol = 

x is V (voltage) and y is I (current). You can see that it still have variable y in the answer. I want y to be at left hand side. Is there any way to do it?

[Sam Chak]

Perhaps using the isolate() function, so that the variable y appears on the left side.

syms Vx Vy Vo Cin Ca Cfb Ccm s x y gm Zin Vcm
eqn  = [2*((Cin*(Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)) + (y*((2*Ca)/Cfb + 1))/(2*Ca*s))*((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1))/(Ca*(((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1) + 1)) - (y*((2*Ca)/Cfb + 1))/(2*Ca*s) - Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)))*s*Ccm+2*x*s*Cin==(-((Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)) + (y*((2*Ca)/Cfb + 1))/(2*Ca*s))*(Cfb/(2*Ccm) + 1))/(((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1) + 1))*(2/Zin+2*s*Cin+2*s*Ccm)];
ySol = isolate(eqn, y)

ySol = 

[Napath]

Thank you for the response! I want the left side to be x/y (V/I) is there any way? or can I just use sol/ysol?

[Sam Chak]

@Napath Is this a type of transfer function?

[Napath]

Kind of, the s is represent factor in frequency domain. I want to get the Zin (Vin/Iin) from my circuit.

[Sam Chak]

Hi @Napath

If the equation eqn is correctly described, we should observe the following form:

.

This implies that the two terms can be separated into:

.

However, I do not see this form in your equation. Moreover, the transfer function should be properly derived from the governing differential equations. However, this important step has been overlooked, and you immediately introduce the algebraic equation, eqn.

syms Vx Vy Vo Cin Ca Cfb Ccm s x y gm Zin Vcm
eqn  = [2*((Cin*(Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)) + (y*((2*Ca)/Cfb + 1))/(2*Ca*s))*((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1))/(Ca*(((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1) + 1)) - (y*((2*Ca)/Cfb + 1))/(2*Ca*s) - Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)))*s*Ccm+2*x*s*Cin==(-((Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)) + (y*((2*Ca)/Cfb + 1))/(2*Ca*s))*(Cfb/(2*Ccm) + 1))/(((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1) + 1))*(2/Zin+2*s*Cin+2*s*Ccm)]

eqn = 

●

% ySol = isolate(eqn, y)

[Walter Roberson]

syms Vx Vy Vo Cin Ca Cfb Ccm s x y gm Zin Vcm
eqns = [2*((Cin*(Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)) + (y*((2*Ca)/Cfb + 1))/(2*Ca*s))*((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1))/(Ca*(((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1) + 1)) - (y*((2*Ca)/Cfb + 1))/(2*Ca*s) - Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)))*s*Ccm+2*x*s*Cin==(-((Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)) + (y*((2*Ca)/Cfb + 1))/(2*Ca*s))*(Cfb/(2*Ccm) + 1))/(((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1) + 1))*(2/Zin+2*s*Cin+2*s*Ccm)];
size(eqns)

ans = 1×2

1 1

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You have a scalar equation. When you solve() a system of equations and do not specify which variable to solve for, it uses symvar() to choose one of the variables out of the set. Most likely it will solve for x in this situation, which might not be what you want.

Answer 1

[Walter Roberson]

Use the usual trick of substition of variables. If x/y = z then it follows that x = y*z so substitute in y*z for x and solve for z

syms Vx Vy Vo Cin Ca Cfb Ccm s x y gm Zin Vcm
syms Z
eqns = [2*((Cin*(Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)) + (y*((2*Ca)/Cfb + 1))/(2*Ca*s))*((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1))/(Ca*(((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1) + 1)) - (y*((2*Ca)/Cfb + 1))/(2*Ca*s) - Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)))*s*Ccm+2*x*s*Cin==(-((Vcm*((2*Ca)/Cfb - ((2*Ca)/Cfb + 1)*(Cin/Ca + 1)) + (y*((2*Ca)/Cfb + 1))/(2*Ca*s))*(Cfb/(2*Ccm) + 1))/(((2*Ca)/Cfb + 1)*(Cfb/(2*Ccm) + 1) + 1))*(2/Zin+2*s*Cin+2*s*Ccm)];
eqns1 = subs(eqns, x, y*Z);
S = solve(eqns1, Z)

S = 

eqn2 = x/y == simplify(S)

eqn2 = 

[Torsten]

The right-hand side of eqn2 still depends on y.

[Walter Roberson]

If the right hand side is not intended to depend on y, then the equations are incorrect.