Collect the coefficients of a symbolic expression for an Op Amp circuit function

Hello,

I have writen function for Op Amp Sallen-Key Circuit. All values including the 's' are used as symbolic expresion.

I would need to rearange the variables in order to have on the left side the V2/V1. I have been trying to use solve(V2,V1) but are not rearanged.

On the right side I would need the denominator to be on the form of . I have been trying with factor(G) but it gives denominator on the form of .

Is there any way to achieve the above.

Giannis

Answer 1

[Dyuman Joshi]

syms A Ga Gb G1 G2 C2 V1 V2 s

%Defining expression
expr = V2 == A*((G1*G2*V1 + C2*G2*V2*s)/(C2^2*s^2+G1*G2 + C2*G1*s + 2*C2*G2*s) - Gb*V2/(Ga+Gb))

expr = 

%Isolating V2 to LHS
expr = isolate(expr,V2)

expr = 

%Assuming that V2/V1 can isolated from the expression
%Dividing both sides of the expression by V1 to obtain V2/V1 on the left side
expr = expr/V1

expr = 

If you want to simplify the RHS, this approach works good enough -

%Get numerator and denominator of RHS in a rational form
[n,d] = numden(rhs(expr))

n = 

d = 

%Redefine the expression
expr = lhs(expr) == n/d

expr = 

If you want the coefficient of s^2 in the denominator to be 1, get its coefficient by using coeffs and divide d by the coefficient.

[NGiannis]

Thank you Dyuman Joshi for your reply

Still I am not able to bring the denominatior to the form . I can get the funciton V2/V1 as per your guidance but I can not brink a funciton to the form I need when I devide with the coeficient of the s^2.

dcoef=coeffs(d,s)

%Devide numerator and denominator with the s^2 coeficient

n=n/(C2^2*Ga + C2^2*Gb + A*C2^2*Gb)

d=d/(C2^2*Ga + C2^2*Gb + A*C2^2*Gb)

I have been trying to use partfrac(d) and simplify(d) but seems are not giving whant I need.

Giannis

[Star Strider]

Use the collect function first, then coeffs —

syms A Ga Gb G1 G2 C2 V1 V2 s

%Defining expression
expr = V2 == A*((G1*G2*V1 + C2*G2*V2*s)/(C2^2*s^2+G1*G2 + C2*G1*s + 2*C2*G2*s) - Gb*V2/(Ga+Gb))

expr = 

%Isolating V2 to LHS
expr = isolate(expr,V2)

expr = 

%Assuming that V2/V1 can isolated from the expression
%Dividing both sides of the expression by V1 to obtain V2/V1 on the left side
expr = expr/V1

expr = 

%Get numerator and denominator of RHS in a rational form
[n,d] = numden(rhs(expr))

n = 

d = 

n = collect(n, s)

n = 

d = collect(d, s)

d = 

[dc,dterms] = coeffs(d, s);
Denominator_Coefficients = dc.'

Denominator_Coefficients = 

Denominator_s_terms = dterms.'

Denominator_s_terms = 

%Redefine the expression
expr = lhs(expr) == n/d

expr = 

.

[NGiannis]

Thank you Star Strider for your reply.

[Star Strider]

My pleasure!