Find the relation between 2 variables

[Debdut]

Homework Statement

Find the relation between Vin and Vout

Relevant Equations

V1 = (-gm1 * Vin + s* C1 * Vout) / (gmc + s * C1)
gmc * V1 + s * C2 * Vout = Vx * (s * rb * C2 + 1) / rb
s * C1 * (V1 - Vout) + s * C2 * (Vx - Vout) = gm2 * Vx + Vout / ro2

Here is the equation I obtain after simplification, I don't know if it is correct:
gmc * V1 + s * C2 * Vout = [{s * (C1 + C2) * ro2 + 1} * Vout - s * C1 * ro2 * V1] * (s * rb * C2 + 1) / {ro2 * rb * (s * C2 - gm2)}

I need to eliminate V1 to find the relation between Vin and Vout.

 

[BvU]

Can you post the complete problem statement ?
And please understand that telepathy isn't everyone's forte, so tell us what this is about.

##\ ##

 

[WWGD]

Can you post the complete problem statement ?
And please understand that telepathy isn't everyone's forte, so tell us what this is about.

##\ ##

I don't know if they rewrote, but he explained in the line at the bottom. Though , OP , please use Latex to write your question.

 

[e_jane]

V1 = (-gm1 * Vin + s* C1 * Vout) / (gmc + s * C1)
gmc * V1 + s * C2 * Vout = Vx * (s * rb * C2 + 1) / rb
s * C1 * (V1 - Vout) + s * C2 * (Vx - Vout) = gm2 * Vx + Vout / ro2

For clarity's sake, is the following an accurate statement of the three equations?

##\qquad \textrm{Eqn 1: } V_1 = \dfrac{-g_{m_1} V_{in} + sC_1V_{out}}{g_{m_c} + sC_1}##

##\qquad \textrm{Eqn 2: } g_{m_c} V_1 + s C_2 V_{out} = V_x \dfrac{s r_b C_2 + 1}{r_b}##

##\qquad \textrm{Eqn 3: } s C_1 \left(V_1 - V_{out}\right) + s C_2 \left(V_x - V_{out}\right) = g_{m_2} V_x + \dfrac{V_{out}}{r_{o_2}}##

Thank you!

 

[Debdut]

For clarity's sake, is the following an accurate statement of the three equations?

##\qquad \textrm{Eqn 1: } V_1 = \dfrac{-g_{m_1} V_{in} + sC_1V_{out}}{g_{m_c} + sC_1}##

##\qquad \textrm{Eqn 2: } g_{m_c} V_1 + s C_2 V_{out} = V_x \dfrac{s r_b C_2 + 1}{r_b}##

##\qquad \textrm{Eqn 3: } s C_1 \left(V_1 - V_{out}\right) + s C_2 \left(V_x - V_{out}\right) = g_{m_2} V_x + \dfrac{V_{out}}{r_{o_2}}##

Thank you!

Yes, these are the equations. Thank you very much.

 

[Debdut]

I am sorry for not elaborating. The equations are obtained by KCL of the above image.
Here ##V_1##, ##V_x##, ##V_{in}## and ##V_{out}## are variables and all else are constants. I need to find the relation between ##V_{in}## and ##V_{out}##.

 

[Debdut]

Hi, I found the solution using the method of determinants. It was not difficult. Thanks.

 

[WWGD]

Hi, I found the solution using the method of determinants. It was not difficult. Thanks.

If not overly long, why not write it here so others can benefit from it?